This document summarizes a mathematical model of generalized porothermoelasticity for a porous asphalt material. The model considers a poroelastic half-space saturated with fluid and constructs governing equations for the stresses, strains, displacements, and temperatures of the solid and fluid phases. The equations are derived using the theory of generalized porothermoelasticity with one relaxation time. Numerical solutions to the equations are obtained by applying the model to an asphalt material subjected to thermal shock on its surface. Graphs of the temperature, stresses, strains, and displacements within the material are presented.
Measuring the Thermal Conductivities of Low Heat Conducting Disk Samples by M...IJERA Editor
This article aims to establish an experimental procedure to measure heat transmission coefficients in low heat conductive materials. The newly developed model takes as starting point the application of Fourier’s law to a disk sample when a temperature gradient is established between its faces. The power of a heating element is determined as the heat transfer coefficient of the problem disk. Initially, a glass vessel containing water is placed in direct contact with the heating element; then, a problem plastic disk is placed between this element and the glass vessel, treating the set as a composite wall. Prior to the above the water equivalent of a calorimetric set (vessel + water + accessories) and the thermal conductivity of the vessel must be determined. The thermal conductivity of the problem plastic disk sample is obtained for temperatures ranging from 30 to 70° C. The results reveal the existence of some type of structural transition for the problem material.
Chemical reaction and radiation effect on mhd flow past an exponentially acce...Alexander Decker
This document describes a mathematical analysis of MHD fluid flow past an exponentially accelerated vertical plate embedded in a porous medium. The analysis considers the effects of variable temperature, mass diffusion, radiation, and a heat source on the flow characteristics. The governing equations for this problem are derived and non-dimensionalized. The non-dimensional equations are then solved using the Laplace transform technique. The effects of various physical parameters like the magnetic field, radiation, heat generation, and chemical reaction on the velocity, temperature, and concentration profiles are determined.
Analysis of mhd non darcian boundary layer flow and heat transfer over an exp...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
ANALYSIS OF POSSIBILITY OF GROWTH OF SEVERAL EPITAXIAL LAYERS SIMULTANEOUSLY ...ijoejournal
We analyzed nonlinear model with varying in space and time coefficients of growth of epitaxial layers
from gas phase in a vertical reactor with account native convection. We formulate several conditions to
increase homogeneity of epitaxial layers with varying of technological process parameters.
Natural convection in a two sided lid-driven inclined porous enclosure with s...IAEME Publication
This document summarizes a study of natural convection in a two-sided lid-driven inclined porous enclosure with a sinusoidal thermal boundary condition on one wall. The governing equations for the fluid flow and heat transfer were solved numerically using a finite difference method. Results are presented for streamlines, isotherms, local Nusselt number, and average Nusselt number for various values of thermal radiation and heat generation parameters at different inclination angles of the enclosure. The key findings are that the flow pattern and temperature field depend significantly on the thermal parameters and inclination angle. Grid independence studies were performed to validate the numerical results.
In the present paper we carried out several experiments in oxygen or dry air, at low
temperature of some metallic samples. In order to be able to extend or estimate the corrosion
phenomenon we made use of the modelling of oxygen diffusion through rust layers (oxides) and of
solving the parabolic equations of diffusion, respectively. The diffusion equation is important for
modelling the oxygen diffusion within biological systems and for modelling the neutron flux from
nuclear reactors.
Measuring the Thermal Conductivities of Low Heat Conducting Disk Samples by M...IJERA Editor
This article aims to establish an experimental procedure to measure heat transmission coefficients in low heat conductive materials. The newly developed model takes as starting point the application of Fourier’s law to a disk sample when a temperature gradient is established between its faces. The power of a heating element is determined as the heat transfer coefficient of the problem disk. Initially, a glass vessel containing water is placed in direct contact with the heating element; then, a problem plastic disk is placed between this element and the glass vessel, treating the set as a composite wall. Prior to the above the water equivalent of a calorimetric set (vessel + water + accessories) and the thermal conductivity of the vessel must be determined. The thermal conductivity of the problem plastic disk sample is obtained for temperatures ranging from 30 to 70° C. The results reveal the existence of some type of structural transition for the problem material.
Chemical reaction and radiation effect on mhd flow past an exponentially acce...Alexander Decker
This document describes a mathematical analysis of MHD fluid flow past an exponentially accelerated vertical plate embedded in a porous medium. The analysis considers the effects of variable temperature, mass diffusion, radiation, and a heat source on the flow characteristics. The governing equations for this problem are derived and non-dimensionalized. The non-dimensional equations are then solved using the Laplace transform technique. The effects of various physical parameters like the magnetic field, radiation, heat generation, and chemical reaction on the velocity, temperature, and concentration profiles are determined.
Analysis of mhd non darcian boundary layer flow and heat transfer over an exp...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
ANALYSIS OF POSSIBILITY OF GROWTH OF SEVERAL EPITAXIAL LAYERS SIMULTANEOUSLY ...ijoejournal
We analyzed nonlinear model with varying in space and time coefficients of growth of epitaxial layers
from gas phase in a vertical reactor with account native convection. We formulate several conditions to
increase homogeneity of epitaxial layers with varying of technological process parameters.
Natural convection in a two sided lid-driven inclined porous enclosure with s...IAEME Publication
This document summarizes a study of natural convection in a two-sided lid-driven inclined porous enclosure with a sinusoidal thermal boundary condition on one wall. The governing equations for the fluid flow and heat transfer were solved numerically using a finite difference method. Results are presented for streamlines, isotherms, local Nusselt number, and average Nusselt number for various values of thermal radiation and heat generation parameters at different inclination angles of the enclosure. The key findings are that the flow pattern and temperature field depend significantly on the thermal parameters and inclination angle. Grid independence studies were performed to validate the numerical results.
In the present paper we carried out several experiments in oxygen or dry air, at low
temperature of some metallic samples. In order to be able to extend or estimate the corrosion
phenomenon we made use of the modelling of oxygen diffusion through rust layers (oxides) and of
solving the parabolic equations of diffusion, respectively. The diffusion equation is important for
modelling the oxygen diffusion within biological systems and for modelling the neutron flux from
nuclear reactors.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
The document discusses residual stresses that arise during welding due to localized heating and rapid cooling. It analyzes how welding conditions like travel speed, specimen size, constraints, and preheating can affect residual stress distributions. A finite element model is used to simulate butt welding and predict residual stresses in the weld and base metal. The results show that transverse and longitudinal residual stresses are highest near the weld and decrease with increasing distance. Faster travel speeds, larger specimen sizes, and preheating can reduce residual stresses, while external constraints decrease transverse shrinkage and associated stresses.
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction have a greater influence on fluid velocity and temperature profiles. Nan
This document summarizes research on the structure and phase behavior of Cu-Ni nanoalloys. It uses thermodynamic modeling to predict how the phase diagrams and mixing/demixing behavior depend on nanoparticle size, shape, and temperature. The modeling indicates Cu-Ni nanoalloys can form either mixed particles or Janus particles, depending on the synthesis temperature, with nickel preferentially segregating to surfaces. Phase maps are provided to guide experimentalists on controlling particle structure.
Convective Heat And Mass Transfer Flow Of A Micropolar Fluid In A Rectangular...IJERA Editor
In this chapter we make an investigation of the convective heat transfer through a porous medium in a Rectangular enclosure with Darcy model. The transport equations of liner momentum, angular momentum and energy are solved by employing Galerkine finite element analysis with linear triangular elements. The computation is carried out for different values of Rayleigh number – Ra micropolar parameter – R, spin gradient parameter, Eckert number Ec and heat source parameter. The rate of heat transfer and couple stress on the side wall is evaluated for different variation of the governing parameters.
Mathematical modelling and analysis of three dimensional darcyIAEME Publication
This document presents a mathematical model and numerical analysis of three-dimensional natural convection in an inclined porous box using the Darcy-Brinkman flow model. Governing equations for mass, momentum and energy are derived in dimensionless form using parameters like Rayleigh number, Darcy number, and aspect ratios. Numerical solutions are obtained for varying parameters like Rayleigh number, Darcy number, and angle of inclination. Results show that average Nusselt number first increases and then decreases with inclination angle, due to a transition from multicellular to unicellular flow patterns. Three-dimensional effects are more pronounced at lower aspect ratios.
Effect of rotation on the onset of Rayleigh-Bénard convection in a layer of F...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
This document summarizes a study that examines heat and mass transfer over a vertical plate in a porous medium with Soret and Dufour effects, a convective surface boundary condition, chemical reaction, and magnetic field. The governing equations for the fluid flow, heat transfer, and mass transfer are presented. Similarity solutions are used to transform the governing partial differential equations into ordinary differential equations, which are then solved numerically. The results are presented graphically to show the influence of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number.
B. Dragovich: On Modified Gravity and CosmologySEENET-MTP
This document discusses modified gravity and cosmological solutions. It introduces Einstein's theory of gravity and some of its problems, including lack of renormalizability and prediction of dark energy and dark matter. It then presents a nonlocal modified gravity model to address these issues. The model yields nonsingular bouncing cosmological solutions for the scale factor in the form a(t) = a0(σeλt + τe−λt), which exist for different values of spatial curvature. These solutions depend on the cosmological constant and satisfy the equations of motion for certain conditions on the parameters of the nonlocal gravity action.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Effect of lowering condensing surface temperature on the performance of solar...IAEME Publication
This study examines the effect of lowering the condensing surface temperature on the performance of a solar still. Experiments were conducted where the condensing glass surface temperature was reduced by placing ice on it, increasing the temperature difference between the evaporating and condensing surfaces. The results showed a maximum 205% increase in distillate output was obtained with a 54% reduction in condensing surface temperature, for a constant evaporating water temperature of 50°C. Lowering the condensing surface temperature significantly improved the solar still's performance by increasing the temperature difference that drives evaporation and condensation.
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
This document presents a mathematical analysis of unsteady free convection flow along a porous vertical plate with constant heat and mass flux in a rotating system. The analysis considers the effects of heat source and thermal diffusion. Perturbation technique is used to obtain expressions for velocity, temperature, concentration profiles, skin friction, and Nusselt number. Key findings include that increasing Schmidt number decreases skin friction, increasing Grashoff number increases skin friction, and increasing Prandtl number decreases Nusselt number. Graphs and tables are used to discuss the effects of various parameters on flow variables.
Radial Heat Transport in Packed Beds-III: Correlations of Effective Transport...inventionjournals
The reliability and accuracy of experimental with predictions data of two models ("MC model" Marshall and Coberly model, [1] and modified model by Ibrahim et al. [2] are investigated for the effective radial thermal conductivity (Ker), and the wall heat transfer coefficient (hw) in packed beds in the absence of chemical reactions. The results were evaluated by the modified mathematical model as to the boundary bed inlet temperature; (To) number of terms of the solution series and number of experimental points used in the estimate. Very satisfactory was attained between the predicted and measured temperature profiles for a range of experiments. These cover a range of tube to (equivalent) particle diameter ratios from dt /dp = 4 to 10; Reynolds numbers ranged between 3.8-218 for particle, and elevated pressure from 11 to 20 bar for particle catalyst pellets. In all cases the fluid flowing throughout the bed has been air. The results indicate to the choice of the inlet boundary condition can have a large impact on the values of obtained parameters. And model parameters have been shown to be dependent on the pressure inside the reactor. The following correlations for both (hw) and (Ker) respectively under a given conditions obtained by using multiple regressions of our results that based on the modified mathematical model: Nuw = 67.9Re0.883(dt /dp) -0.635(P/Po) -1.354 Ker = 0.2396 + 0.0041Re The results accuracy of these correlations obtained from the modified mathematical model are more than the results accuracy of correlations obtained from MC model with respect to experimental data; these accuracy of both correlations reach up to 91% and 65% for (hw) and (Ker) respectively; which these results indicate to the reliability
TWO FLUID ELECTROMAGNETO CONVECTIVE FLOW AND HEAT TRANSFER BETWEEN VERTICAL W...IAEME Publication
The mixture of viscous and magneto convective flow and heat transfer between a long vertical wavy wall and a parallel flat wall in the presence of applied electric field parallel to gravity , magnetic field normal to gravity in the presence of source or sink is investigated. The non-linear equations governing the flow are solved using the linearization technique. The effect of Grash of number and width ratio is to promote the flow for both open and short circuits. The effect of Hartmann number is to suppress the flow, the effect of source is to promote and the effect of sink is to suppress the velocity for open and short circuit s. Conducting ratio decreases the temperature where as width ratio increases the temperature.
11.effect of radiation and chemical reaction on transient mhd free convective...Alexander Decker
This document analyzes the effects of radiation, chemical reaction, and transient magnetohydrodynamic (MHD) free convective flow over a vertical plate through porous media. The governing equations for this unsteady, viscous flow are presented and non-dimensionalized. The equations are then linearized using a perturbation method about a small parameter. Solutions are obtained by reducing the coupled, nonlinear partial differential equations to a set of ordinary differential equations that can be solved analytically. Parameters such as the chemical reaction parameter, thermal Grashof number, and radiation parameter are discussed in relation to their effects on the convective heat transfer along the plate.
Effect of radiation and chemical reaction on transient mhd free convective fl...Alexander Decker
This document analyzes the effects of radiation, chemical reaction, and transient magnetohydrodynamic (MHD) free convective flow over a vertical plate through porous media. The governing equations for mass, momentum, energy and concentration are presented and solved using a perturbation method. Parameters like chemical reaction rate, thermal and mass Grashof numbers, rarefaction, magnetic field, radiation, and suction are studied. Graphical results are discussed for practical parameter ranges regarding heat and mass transfer characteristics of the transient flow.
Effect of radiation and chemical reaction on transient mhd free convective fl...Alexander Decker
This document analyzes the effects of radiation, chemical reaction, and transient magnetohydrodynamic (MHD) free convective flow over a vertical porous plate. The governing equations for mass, momentum, energy and concentration are presented and solved using perturbation methods. Parameters like chemical reaction rate, thermal and mass Grashof numbers, rarefaction, magnetic field, radiation, and suction are studied. Graphical results are discussed for practical parameter ranges regarding heat and mass transfer over the plate embedded in a porous medium under the influence of thermal radiation and chemical reaction.
BFO – AIS: A FRAME WORK FOR MEDICAL IMAGE CLASSIFICATION USING SOFT COMPUTING...ijsc
Medical images provide diagnostic evidence/information about anatomical pathology. The growth in
database is enormous as medical digital image equipment’s like Magnetic Resonance Images (MRI),
Computed Tomography (CT), and Positron Emission Tomography CT (PET-CT) are part of clinical work.
CT images distinguish various tissues according to gray levels to help medical diagnosis. Ct is more
reliable for early tumours and haemorrhages detection as it provides anatomical information to plan radio
therapy. Medical information systems goals are to deliver information to right persons at the right time and
place to improve care process quality and efficiency. This paper proposes an Artificial Immune System
(AIS) classifier and proposed feature selection based on hybrid Bacterial Foraging Optimization (BFO)
with Local Search (LS) for medical image classification.
REAL-TIME INTRUSION DETECTION SYSTEM FOR BIG DATAijp2p
The objective of the proposed system is to integrate the high volume of data along with the important
considerations like monitoring a wide array of heterogeneous security. When a real time cyber attack
occurred, the Intrusion Detection System automatically store the log in distributed environment and
monitor the log with existing intrusion dictionary. At the same time the system will check and categorize the
severity of the log to high, medium, and low respectively. After the categorization, the system will
automatically take necessary action against the user-unit with respect to the severity of the log. The
advantage of the system is that it utilize anomaly detection, evaluates data and issue alert message or
reports based on abnormal behaviour.
A PROPOSED MULTI-DOMAIN APPROACH FOR AUTOMATIC CLASSIFICATION OF TEXT DOCUMENTSijsc
Classification is an important technique used in information retrieval. Supervised classification suffers
from certain limitations concerning the collection and labeling of the training dataset. When facing Multi-
Domain classification, multiple training datasets and classifiers are needed which is relatively difficult. In
this paper an unsupervised classification system is proposed that can manage the Multi-Domain
classification problem as well. It is a multi-domain system where each domain represented by an ontology.
A document is mapped on each ontology based on the weights of the mutual tokens between them with the
help of fuzzy sets, resulting in a mapping degree of the document with each domain. An experiment carried
out showing satisfying classification results with an improvement in the evaluation results of the proposed
system compared to Apache Lucene.
BUILDING A SYLLABLE DATABASE TO SOLVE THE PROBLEM OF KHMER WORD SEGMENTATIONijnlc
Word segmentation is a basic problem in natural language processing. With the languages having the
complex writing system like the Khmer language in Southern of Vietnam, this problem really very
intractable, posing the significant challenges. Although there are some experts in Vietnam as well as
international having deeply researched this problem, there are still no reasonable results meeting the
demand, in particular, no treated thoroughly the ambiguous phenomenon, in the process of Khmer
language processing so far. This paper present a solution based on the syllable division into component
clusters using two syllable models proposed, thereby building a Khmer syllable database, is still not
actually available. This method using a lexical database updated from the online Khmer dictionaries and
some supported dictionaries serving role of training data and complementary linguistic characteristics.
Each component cluster is labelled and located by the first and last letter to identify entirety a syllable. This
approach is workable and the test results achieve high accuracy, eliminate the ambiguity, contribute to
solving the problem of word segmentation and applying efficiency in Khmer language processing.
A PREDICTION METHOD OF GESTURE TRAJECTORY BASED ON LEAST SQUARES FITTING MODELVLSICS Design
Implicit interaction based on context information is widely used and studied in the virtual scene. In context
based human computer interaction, the meaning of action A is well defined. For instance, the right wave is
defined turning paper or PPT in context B, And it mean volume up in context C. However, we cannot use
the context information when we select the object to be manipulated. In view of this situation, this paper
proposes using the least squares fitting curve beam to predict the user's trajectory, so as to determine what
object the user’s wants to operate. At the same time, the fitting effects of the three curves were compared,
and the curve which is more accord with the hand movement trajectory is obtained. In addition, using the
bounding box size control the Z variable to move in an appropriate location. Experimental results show
that the proposed in this paper based on bounding box size to control the Z variables get a good effect; by
fitting the trajectory of a human hand, to predict the object that the subjects would like to operate. The
correct rate is 91%.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
The document discusses residual stresses that arise during welding due to localized heating and rapid cooling. It analyzes how welding conditions like travel speed, specimen size, constraints, and preheating can affect residual stress distributions. A finite element model is used to simulate butt welding and predict residual stresses in the weld and base metal. The results show that transverse and longitudinal residual stresses are highest near the weld and decrease with increasing distance. Faster travel speeds, larger specimen sizes, and preheating can reduce residual stresses, while external constraints decrease transverse shrinkage and associated stresses.
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction have a greater influence on fluid velocity and temperature profiles. Nan
This document summarizes research on the structure and phase behavior of Cu-Ni nanoalloys. It uses thermodynamic modeling to predict how the phase diagrams and mixing/demixing behavior depend on nanoparticle size, shape, and temperature. The modeling indicates Cu-Ni nanoalloys can form either mixed particles or Janus particles, depending on the synthesis temperature, with nickel preferentially segregating to surfaces. Phase maps are provided to guide experimentalists on controlling particle structure.
Convective Heat And Mass Transfer Flow Of A Micropolar Fluid In A Rectangular...IJERA Editor
In this chapter we make an investigation of the convective heat transfer through a porous medium in a Rectangular enclosure with Darcy model. The transport equations of liner momentum, angular momentum and energy are solved by employing Galerkine finite element analysis with linear triangular elements. The computation is carried out for different values of Rayleigh number – Ra micropolar parameter – R, spin gradient parameter, Eckert number Ec and heat source parameter. The rate of heat transfer and couple stress on the side wall is evaluated for different variation of the governing parameters.
Mathematical modelling and analysis of three dimensional darcyIAEME Publication
This document presents a mathematical model and numerical analysis of three-dimensional natural convection in an inclined porous box using the Darcy-Brinkman flow model. Governing equations for mass, momentum and energy are derived in dimensionless form using parameters like Rayleigh number, Darcy number, and aspect ratios. Numerical solutions are obtained for varying parameters like Rayleigh number, Darcy number, and angle of inclination. Results show that average Nusselt number first increases and then decreases with inclination angle, due to a transition from multicellular to unicellular flow patterns. Three-dimensional effects are more pronounced at lower aspect ratios.
Effect of rotation on the onset of Rayleigh-Bénard convection in a layer of F...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
This document summarizes a study that examines heat and mass transfer over a vertical plate in a porous medium with Soret and Dufour effects, a convective surface boundary condition, chemical reaction, and magnetic field. The governing equations for the fluid flow, heat transfer, and mass transfer are presented. Similarity solutions are used to transform the governing partial differential equations into ordinary differential equations, which are then solved numerically. The results are presented graphically to show the influence of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number.
B. Dragovich: On Modified Gravity and CosmologySEENET-MTP
This document discusses modified gravity and cosmological solutions. It introduces Einstein's theory of gravity and some of its problems, including lack of renormalizability and prediction of dark energy and dark matter. It then presents a nonlocal modified gravity model to address these issues. The model yields nonsingular bouncing cosmological solutions for the scale factor in the form a(t) = a0(σeλt + τe−λt), which exist for different values of spatial curvature. These solutions depend on the cosmological constant and satisfy the equations of motion for certain conditions on the parameters of the nonlocal gravity action.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Effect of lowering condensing surface temperature on the performance of solar...IAEME Publication
This study examines the effect of lowering the condensing surface temperature on the performance of a solar still. Experiments were conducted where the condensing glass surface temperature was reduced by placing ice on it, increasing the temperature difference between the evaporating and condensing surfaces. The results showed a maximum 205% increase in distillate output was obtained with a 54% reduction in condensing surface temperature, for a constant evaporating water temperature of 50°C. Lowering the condensing surface temperature significantly improved the solar still's performance by increasing the temperature difference that drives evaporation and condensation.
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
This document presents a mathematical analysis of unsteady free convection flow along a porous vertical plate with constant heat and mass flux in a rotating system. The analysis considers the effects of heat source and thermal diffusion. Perturbation technique is used to obtain expressions for velocity, temperature, concentration profiles, skin friction, and Nusselt number. Key findings include that increasing Schmidt number decreases skin friction, increasing Grashoff number increases skin friction, and increasing Prandtl number decreases Nusselt number. Graphs and tables are used to discuss the effects of various parameters on flow variables.
Radial Heat Transport in Packed Beds-III: Correlations of Effective Transport...inventionjournals
The reliability and accuracy of experimental with predictions data of two models ("MC model" Marshall and Coberly model, [1] and modified model by Ibrahim et al. [2] are investigated for the effective radial thermal conductivity (Ker), and the wall heat transfer coefficient (hw) in packed beds in the absence of chemical reactions. The results were evaluated by the modified mathematical model as to the boundary bed inlet temperature; (To) number of terms of the solution series and number of experimental points used in the estimate. Very satisfactory was attained between the predicted and measured temperature profiles for a range of experiments. These cover a range of tube to (equivalent) particle diameter ratios from dt /dp = 4 to 10; Reynolds numbers ranged between 3.8-218 for particle, and elevated pressure from 11 to 20 bar for particle catalyst pellets. In all cases the fluid flowing throughout the bed has been air. The results indicate to the choice of the inlet boundary condition can have a large impact on the values of obtained parameters. And model parameters have been shown to be dependent on the pressure inside the reactor. The following correlations for both (hw) and (Ker) respectively under a given conditions obtained by using multiple regressions of our results that based on the modified mathematical model: Nuw = 67.9Re0.883(dt /dp) -0.635(P/Po) -1.354 Ker = 0.2396 + 0.0041Re The results accuracy of these correlations obtained from the modified mathematical model are more than the results accuracy of correlations obtained from MC model with respect to experimental data; these accuracy of both correlations reach up to 91% and 65% for (hw) and (Ker) respectively; which these results indicate to the reliability
TWO FLUID ELECTROMAGNETO CONVECTIVE FLOW AND HEAT TRANSFER BETWEEN VERTICAL W...IAEME Publication
The mixture of viscous and magneto convective flow and heat transfer between a long vertical wavy wall and a parallel flat wall in the presence of applied electric field parallel to gravity , magnetic field normal to gravity in the presence of source or sink is investigated. The non-linear equations governing the flow are solved using the linearization technique. The effect of Grash of number and width ratio is to promote the flow for both open and short circuits. The effect of Hartmann number is to suppress the flow, the effect of source is to promote and the effect of sink is to suppress the velocity for open and short circuit s. Conducting ratio decreases the temperature where as width ratio increases the temperature.
11.effect of radiation and chemical reaction on transient mhd free convective...Alexander Decker
This document analyzes the effects of radiation, chemical reaction, and transient magnetohydrodynamic (MHD) free convective flow over a vertical plate through porous media. The governing equations for this unsteady, viscous flow are presented and non-dimensionalized. The equations are then linearized using a perturbation method about a small parameter. Solutions are obtained by reducing the coupled, nonlinear partial differential equations to a set of ordinary differential equations that can be solved analytically. Parameters such as the chemical reaction parameter, thermal Grashof number, and radiation parameter are discussed in relation to their effects on the convective heat transfer along the plate.
Effect of radiation and chemical reaction on transient mhd free convective fl...Alexander Decker
This document analyzes the effects of radiation, chemical reaction, and transient magnetohydrodynamic (MHD) free convective flow over a vertical plate through porous media. The governing equations for mass, momentum, energy and concentration are presented and solved using a perturbation method. Parameters like chemical reaction rate, thermal and mass Grashof numbers, rarefaction, magnetic field, radiation, and suction are studied. Graphical results are discussed for practical parameter ranges regarding heat and mass transfer characteristics of the transient flow.
Effect of radiation and chemical reaction on transient mhd free convective fl...Alexander Decker
This document analyzes the effects of radiation, chemical reaction, and transient magnetohydrodynamic (MHD) free convective flow over a vertical porous plate. The governing equations for mass, momentum, energy and concentration are presented and solved using perturbation methods. Parameters like chemical reaction rate, thermal and mass Grashof numbers, rarefaction, magnetic field, radiation, and suction are studied. Graphical results are discussed for practical parameter ranges regarding heat and mass transfer over the plate embedded in a porous medium under the influence of thermal radiation and chemical reaction.
BFO – AIS: A FRAME WORK FOR MEDICAL IMAGE CLASSIFICATION USING SOFT COMPUTING...ijsc
Medical images provide diagnostic evidence/information about anatomical pathology. The growth in
database is enormous as medical digital image equipment’s like Magnetic Resonance Images (MRI),
Computed Tomography (CT), and Positron Emission Tomography CT (PET-CT) are part of clinical work.
CT images distinguish various tissues according to gray levels to help medical diagnosis. Ct is more
reliable for early tumours and haemorrhages detection as it provides anatomical information to plan radio
therapy. Medical information systems goals are to deliver information to right persons at the right time and
place to improve care process quality and efficiency. This paper proposes an Artificial Immune System
(AIS) classifier and proposed feature selection based on hybrid Bacterial Foraging Optimization (BFO)
with Local Search (LS) for medical image classification.
REAL-TIME INTRUSION DETECTION SYSTEM FOR BIG DATAijp2p
The objective of the proposed system is to integrate the high volume of data along with the important
considerations like monitoring a wide array of heterogeneous security. When a real time cyber attack
occurred, the Intrusion Detection System automatically store the log in distributed environment and
monitor the log with existing intrusion dictionary. At the same time the system will check and categorize the
severity of the log to high, medium, and low respectively. After the categorization, the system will
automatically take necessary action against the user-unit with respect to the severity of the log. The
advantage of the system is that it utilize anomaly detection, evaluates data and issue alert message or
reports based on abnormal behaviour.
A PROPOSED MULTI-DOMAIN APPROACH FOR AUTOMATIC CLASSIFICATION OF TEXT DOCUMENTSijsc
Classification is an important technique used in information retrieval. Supervised classification suffers
from certain limitations concerning the collection and labeling of the training dataset. When facing Multi-
Domain classification, multiple training datasets and classifiers are needed which is relatively difficult. In
this paper an unsupervised classification system is proposed that can manage the Multi-Domain
classification problem as well. It is a multi-domain system where each domain represented by an ontology.
A document is mapped on each ontology based on the weights of the mutual tokens between them with the
help of fuzzy sets, resulting in a mapping degree of the document with each domain. An experiment carried
out showing satisfying classification results with an improvement in the evaluation results of the proposed
system compared to Apache Lucene.
BUILDING A SYLLABLE DATABASE TO SOLVE THE PROBLEM OF KHMER WORD SEGMENTATIONijnlc
Word segmentation is a basic problem in natural language processing. With the languages having the
complex writing system like the Khmer language in Southern of Vietnam, this problem really very
intractable, posing the significant challenges. Although there are some experts in Vietnam as well as
international having deeply researched this problem, there are still no reasonable results meeting the
demand, in particular, no treated thoroughly the ambiguous phenomenon, in the process of Khmer
language processing so far. This paper present a solution based on the syllable division into component
clusters using two syllable models proposed, thereby building a Khmer syllable database, is still not
actually available. This method using a lexical database updated from the online Khmer dictionaries and
some supported dictionaries serving role of training data and complementary linguistic characteristics.
Each component cluster is labelled and located by the first and last letter to identify entirety a syllable. This
approach is workable and the test results achieve high accuracy, eliminate the ambiguity, contribute to
solving the problem of word segmentation and applying efficiency in Khmer language processing.
A PREDICTION METHOD OF GESTURE TRAJECTORY BASED ON LEAST SQUARES FITTING MODELVLSICS Design
Implicit interaction based on context information is widely used and studied in the virtual scene. In context
based human computer interaction, the meaning of action A is well defined. For instance, the right wave is
defined turning paper or PPT in context B, And it mean volume up in context C. However, we cannot use
the context information when we select the object to be manipulated. In view of this situation, this paper
proposes using the least squares fitting curve beam to predict the user's trajectory, so as to determine what
object the user’s wants to operate. At the same time, the fitting effects of the three curves were compared,
and the curve which is more accord with the hand movement trajectory is obtained. In addition, using the
bounding box size control the Z variable to move in an appropriate location. Experimental results show
that the proposed in this paper based on bounding box size to control the Z variables get a good effect; by
fitting the trajectory of a human hand, to predict the object that the subjects would like to operate. The
correct rate is 91%.
ANALYSIS OF MMSE SPEECH ESTIMATION IMPACT IN WEST SUMATRA'S NOISESsipij
This study aimed to estimate the original voice signal which is interrupted by noise with MMSE method
based on Wiener filter. The Wiener filter is classified as the MMSE estimator studied by previous
researchers. The study assessed the voice signal input count down by European woman that are distorted
by two types of noises, the one is noise based on the outdoor location, sound of siren firefighter, and the
other is the indoor location noise, which represented by noise in lecturer room in campus. The two process
signal is estimated by MMSE estimator which approximated by Wiener filter that must have founded and
counted the covariance of each signal processes are related to the system. Thus the researchers tried to
estimate both types of sounds noisy European woman are due to interference noise source of fire fighter
and faculty room and assess its impact in the form of graphs vote against a function of time, the pattern
shape of the signal and SNR.
INNOVATIVE AND SOCIAL TECHNOLOGIES ARE REVOLUTIONIZING SAUDI CONSUMER ATTITUD...ijsptm
The Internet today connects about 40% of the world population. Half of these are living outside the
advanced economies, often in some countries that are quickly climbing the developmental ladder, with
diverse populations and inarguable economic potentialities including Saudi Arabia. There are 20 million
Internet users in Saudi Arabia by the end of 2016. This research examines the impact of the Internet,
innovation, disruption and the dynamics that affect adoption of electronic commerce (e-commerce) in
Saudi Arabia. The study further analyzes the influence of Internet security and its impact on the users’
decision-making process. The data have gathered through questionnaires that disseminated to 2,823 Saudi
Internet male and female users through email. The response rate was 23%. The important findings have
discussed in this study that shows that there are significant factors that are influencing the adoption of ecommerce,
including legal procedures to ease of doing business, ease of doing businesses and security
features and controls introduced by the online vendors.
MULTIMODAL BIOMETRICS RECOGNITION FROM FACIAL VIDEO VIA DEEP LEARNINGsipij
Biometrics identification using multiple modalities has attracted the attention of many researchers as it
produces more robust and trustworthy results than single modality biometrics. In this paper, we present a
novel multimodal recognition system that trains a Deep Learning Network to automatically learn features
after extracting multiple biometric modalities from a single data source, i.e., facial video clips. Utilizing
different modalities, i.e., left ear, left profile face, frontal face, right profile face, and right ear, present in
the facial video clips, we train supervised denoising auto-encoders to automatically extract robust and nonredundant
features. The automatically learned features are then used to train modality specific sparse
classifiers to perform the multimodal recognition. Experiments conducted on the constrained facial video
dataset (WVU) and the unconstrained facial video dataset (HONDA/UCSD), resulted in a 99.17% and
97.14% rank-1 recognition rates, respectively. The multimodal recognition accuracy demonstrates the
superiority and robustness of the proposed approach irrespective of the illumination, non-planar
movement, and pose variations present in the video clips.
Natural Language Toolkit (NLTK) is a generic platform to process the data of various natural (human)
languages and it provides various resources for Indian languages also like Hindi, Bangla, Marathi and so
on. In the proposed work, the repositories provided by NLTK are used to carry out the processing of Hindi
text and then further for analysis of Multi word Expressions (MWEs). MWEs are lexical items that can be
decomposed into multiple lexemes and display lexical, syntactic, semantic, pragmatic and statistical
idiomaticity. The main focus of this paper is on processing and analysis of MWEs for Hindi text. The
corpus used for Hindi text processing is taken from the famous Hindi novel “KaramaBhumi by Munshi
PremChand”. The result analysis is done using the Hindi corpus provided by Resource Centre for Indian
Language Technology Solutions (CFILT). Results are analysed to justify the accuracy of the proposed
work.
A CASE STUDY ON AUTO SOCIALIZATION IN ONLINE PLATFORMSIJMIT JOURNAL
This document presents a case study on how the theory of auto socialization can be applied to understand socialization in online platforms. The study examined how clinical research associates used a Yammer platform to socialize with their employer organization. The results showed that the associates did not imitate or conform to the values of management as represented on Yammer. As they could not reflect the significant others on the platform, they rejected the socialization attempt. The document discusses how mastery learning used in MOOCs lacks an interaction dimension, hindering socialization and contributing to high dropout rates. It argues online learning needs to incorporate social aspects to be effective.
A thorough review of trust models is carried out in this paper to reveal the key capabilities of existing trust
models and compare how they differ among disciplines. Trust decisions are risky due to uncertainties and
the loss of control. On the other hand, not trusting might mean giving up some potential benefits. Advances
in electronic transactions, mutliagent systems, and decision support systems create a necessity to develop
trust and reputation models. The development of such models will allow for trust reasoning and decisions
to be made in situations with high risk and uncertainty. In recent years, several attempts have been made to
model reputation and trust. However, perceiving trust differently and the lack of having a unified trust
definition are among the main causes of the proliferation of many trust models across different disciplines.
A STUDY ON QUANTITATIVE PARAMETERS OF SPECTRUM HANDOFF IN COGNITIVE RADIO NET...ijwmn
The innovation of wireless technologies requires dynamic allocation of spectrum band in an efficient
manner. This has been achieved by Cognitive Radio (CR) networks which allow unlicensed users to make
use of free licensed spectrum, when the licensed users are kept away from that spectrum. The cognitive
radio makes decision, switching from primary user to secondary user and vice-versa, based on its built-in
interference engine. It allows secondary users to makes use of a channel based on its availability i.e. on the
absence of the primary user and they should vacate the channel once the primary user re-enters and
continue their communication on another available channel and this process in the cognitive radio is
known as spectrum mobility. The main objective of spectrum mobility is that, there is no interruption
caused due to the channel occupied by secondary users and maintains a good quality of service. In order to
achieve better spectrum mobility, it is mandatory to choose an effective spectrum handoff strategy with the
capability of predicting spectrum mobility. The handoff strategy with its parameters and its impact is an
important concept in spectrum mobility but fairly explored. In this paper an empirical study on quantitative
parameters involved in spectrum mobility prediction are discussed in detail. These parameters are studied
extensively because they play a vital role in the spectrum handoff process moreover the impact of these
parameters in various handoff methods can be used to predict the effectiveness of the system.
NETWORK PERFORMANCE ENHANCEMENT WITH OPTIMIZATION SENSOR PLACEMENT IN WIRELES...ijwmn
From one side, sensor manufacturing technology and from other side wireless communication technology
improvement has an effect on the growth and deployment of Wireless Network Sensor (WSN). The
appropriate performance of WSN has abundant necessity which has dependent on the different parameters
such as optimize sensor placement and structure of network sensor. The optimized placement in WSN not
only would optimize number of sensors, but also help to reach to the more precise information. Therefore
different solutions are proposed to reduce cost and increase life time of sensor networks that most of them
are concentrated in the field of routing and information transmission. In this paper, places which they need
new sensors placement or sensor movements are determined and then with applying these changes,
performance of WSN will calculate. To achieve the optimum placement, the network should evaluate
precisely and effective criteria on the performance should extract. Therefore the criteria should be ranked
and after weighting with using AHP algorithms, with use of Geographical Information System (GIS), these
weighted criteria will combined and in the locations which WSN doesn’t have enough performance, new
sensor placement will create. New proposed method, improve 21.11% performance of WSN with sensor
placement in the low performance locations. Also the number of added sensor is 26.09% which is lowest
number of added sensors in comparison with other methods.
A NOVEL METHOD FOR PERSON TRACKING BASED K-NN : COMPARISON WITH SIFT AND MEAN...sipij
Object tracking can be defined as the process of detecting an object of interest from a video scene and
keeping track of its motion, orientation, occlusion etc. in order to extract useful information. It is indeed a
challenging problem and it’s an important task. Many researchers are getting attracted in the field of
computer vision, specifically the field of object tracking in video surveillance. The main purpose of this
paper is to give to the reader information of the present state of the art object tracking, together with
presenting steps involved in Background Subtraction and their techniques. In related literature we found
three main methods of object tracking: the first method is the optical flow; the second is related to the
background subtraction, which is divided into two types presented in this paper, then the temporal
differencing and the SIFT method and the last one is the mean shift method. We present a novel approach
to background subtraction that compare a current frame with the background model that we have set
before, so we can classified each pixel of the image as a foreground or a background element, then comes
the tracking step to present our object of interest, which is a person, by his centroid. The tracking step is
divided into two different methods, the surface method and the K-NN method, both are explained in the
paper. Our proposed method is implemented and evaluated using CAVIAR database.
ROBUST FEATURE EXTRACTION USING AUTOCORRELATION DOMAIN FOR NOISY SPEECH RECOG...sipij
Previous research has found autocorrelation domain as an appropriate domain for signal and noise
separation. This paper discusses a simple and effective method for decreasing the effect of noise on the
autocorrelation of the clean signal. This could later be used in extracting mel cepstral parameters for
speech recognition. Two different methods are proposed to deal with the effect of error introduced by
considering speech and noise completely uncorrelated. The basic approach deals with reducing the effect
of noise via estimation and subtraction of its effect from the noisy speech signal autocorrelation. In order
to improve this method, we consider inserting a speech/noise cross correlation term into the equations used
for the estimation of clean speech autocorrelation, using an estimate of it, found through Kernel method.
Alternatively, we used an estimate of the cross correlation term using an averaging approach. A further
improvement was obtained through introduction of an overestimation parameter in the basic method. We
tested our proposed methods on the Aurora 2 task. The Basic method has shown considerable improvement
over the standard features and some other robust autocorrelation-based features. The proposed techniques
have further increased the robustness of the basic autocorrelation-based method.
A NOVEL IMAGE STEGANOGRAPHY APPROACH USING MULTI-LAYERS DCT FEATURES BASED ON...ijma
Steganography is the science of hidden data in the cover image without any updating of the cover image.
The recent research of the steganography is significantly used to hide large amount of information within
an image and/or audio files. This paper proposed a new novel approach for hiding the data of secret image
using Discrete Cosine Transform (DCT) features based on linear Support Vector Machine (SVM)
classifier. The DCT features are used to decrease the image redundant information. Moreover, DCT is
used to embed the secrete message based on the least significant bits of the RGB. Each bit in the cover
image is changed only to the extent that is not seen by the eyes of human. The SVM used as a classifier to
speed up the hiding process via the DCT features. The proposed method is implemented and the results
show significant improvements. In addition, the performance analysis is calculated based on the
parameters MSE, PSNR, NC, processing time, capacity, and robustness.
DEVELOPMENT OF AN ANDROID APPLICATION FOR OBJECT DETECTION BASED ON COLOR, SH...ijma
Object detection and recognition is an important task in many computer vision applications. In this paper
an Android application was developed using Eclipse IDE and OpenCV3 Library. This application is able to
detect objects in an image that is loaded from the mobile gallery, based on its color, shape, or local
features. The image is processed in the HSV color domain for better color detection. Circular shapes are
detected using Circular Hough Transform and other shapes are detected using Douglas-Peucker
algorithm. BRISK (binary robust invariant scalable keypoints) local features were applied in the developed
Android application for matching an object image in another scene image. The steps of the proposed
detection algorithms are described, and the interfaces of the application are illustrated. The application is
ported and tested on Galaxy S3, S6, and Note1 Smartphones. Based on the experimental results, the
application is capable of detecting eleven different colors, detecting two dimensional geometrical shapes
including circles, rectangles, triangles, and squares, and correctly match local features of object and scene
images for different conditions. The application could be used as a standalone application, or as a part of
another application such as Robot systems, traffic systems, e-learning applications, information retrieval
and many others.
A COLLAGE IMAGE CREATION & “KANISEI” ANALYSIS SYSTEM BY COMBINING MULTIPLE IM...ijma
The collage is an artistic method to create a new image by combining multiple images under some rules or
conditions for collage creators. To realize a mechanism to interpret “Kansei” of the collage creator by the
combination process of multiple image-materials and a formed collage image, we propose a new system to
analyze the collage work by using a database stored to each collage creation information. The collage
works which a creator made by using this system was evaluated. And also, we clarified how to combine
image-materials to make the good collage image having specific impression.
Motorola Soluciones se enfoca en conectar a clientes comerciales y de seguridad pública a través de innovaciones. Trabaja con socios para cubrir una amplia base de clientes desde pequeñas empresas hasta compañías Fortune 500. Nokia busca ofrecer experiencias personales irresistibles fusionando teléfonos móviles, internet y PC. Kyocera ofrece una amplia gama de productos e integra procesos de desarrollo, producción, ventas y logística. Samsung se compromete a ofrecer productos y servicios de alta calidad que
Launch 3 Telecom is a telecom equipment supplier that sells 3Com products like the 1697-060-000-2.00 I/O item. They offer competitive pricing, expert product knowledge, and quality customer service. Customers can purchase items by phone, email, or online form and select shipping options. Orders are processed for same day shipping with tracking provided. Launch 3 Telecom also offers repair, maintenance, installation, and asset recovery services for telecom equipment.
Asphaltic Material in the Context of Generalized Porothermoelasticity ijsc
In this work, a mathematical model of generalized porothermoelasticity with one relaxation time for poroelastic half-space saturated with fluid will be constructed in the context of Youssef model (2007). We will obtain the general solution in the Laplace transform domain and apply it in a certain asphalt material which is thermally shocked on its bounding plane. The inversion of the Laplace transform will be obtained numerically and the numerical values of the temperature, stresses, strains and displacements will be illustrated graphically for the solid and the liquid.
This document presents a numerical solution for unsteady heat and mass transfer flow past an infinite vertical plate with variable thermal conductivity, taking into account Dufour number and heat source effects. The governing equations are non-linear and coupled, and were solved numerically using an implicit finite difference scheme. Various parameters, including Dufour number and heat source, were found to influence the velocity, temperature, and concentration profiles. Skin friction, Nusselt number, and Sherwood number were also calculated.
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...IAEME Publication
In this paper we analyze the effect of momentum slip, thermal slip and solutal slip on stagnation point flow of MHD nanofluid towards stretching sheet .The governing partial differential equation of flow, heat and mass transfer on considered flow are converted into the ordinary differential equations by means of similarity trans formations .The resulting equations are solved by the Runge-Kutta fourth order method with efficient shooting technique. Effects of various governing parameters on flow, heat and mass transfer are studied through the plots. The various numerical tables which are calculated and tabulated. A comparison of our present results with a previous study has been done and we found that an excellent agreement is there with the earlier results and of ours.
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...theijes
This document summarizes a study that numerically investigates the effects of variable viscosity and thermal conductivity on magnetohydrodynamic (MHD) free convection and mass transfer flow over an inclined vertical surface in a porous medium with heat generation. The governing equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. The results show that increasing the viscosity variation parameter, thermal conductivity parameter, magnetic parameter, permeability parameter, or Schmidt number decreases the fluid velocity, while increasing the heat generation parameter, local Grashof number, or mass Grashof number increases the fluid velocity. Skin friction, Nusselt number, and Sherwood number are also computed and presented in tabular form.
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction more strongly influence velocity and temperature profiles. Nanoparticle shape
MATHEMATICAL MODEL FOR HYDROTHERMAL CONVECTION AROUND A RADIOACTIVE WASTE DEP...Jean Belline
A mathematical model of thermally induced water movement in the vicinity of a hard rock
depository for radioactive waste is presented and discussed. For the low permeability rocks envisaged for
geological disposal the equations describing heat and mass transfer become uncoupled and linear.
Analytic solutions to these linearized equations are derived for an idealized spherical model of a
depository in a uniformly permeable rock mass. As the hydrogeological conditions to be expected at a
disposal site are uncertain, examples of flow paths are presented for a range of different permeabilities,
porosities, boundary conditions and regional cross-flows.
Two-temperature elasto-thermo diffusive response inside a spherical shell wit...IJERA Editor
The present work deals with the investigation of elasto-thermo diffusion interaction of a homogeneous isotropic
spherical shell in the context of two-temperature generalized theory of thermo-elasticity with diffusion. The
inner and outer boundaries of the spherical shell are free from stress and subjected to a time dependent thermal
stoke. The chemical potential is also assumed to be a function of time on the boundary of the shell. The
governing equations are solved in the Laplace transformation by using aoperator theory. The inverse of the
transformed solution is carried out by applying a method of Bellman et al.. The stress, conductive temperature,
displacement, mass concentration and chemical potential are computed numerically and presented graphically in
a number of figures for copper material. A comparison of the results for three different models two-temperature
Lord Shulman model (2TLS), two-temperature Green Naghdi model (2TGN-III) and two-temperature threephase-
lag model (2T3P) arealso presented for the different types of temperature field (one-temperature and twotemperature).
Basic Study on Solid-Liquid Phase Change Problem of Ice around Heat Transfer ...IJERDJOURNAL
Abstract:- Phase change heat transfer around heat transfer tubes is one of the basic problem of an ice heat storage exchanger. It can lead to decrease of thermal storage efficiency and damage of heat transfer tubes if continued freezing further after the ice has bridged because of the generated ice thermal resistance and volume expansion. In this study, we focused on freezing phenomena of phase change material (PCM) between two heat transfer tubes, which can simulate an inside structure of ice heat storage exchangers. Bridging time between two heat transfer tubes was studied numerically. We used water as the PCM, which is filled in the water container. Two horizontal elliptical tubes were used as heat transfer tubes in order to observe the influence of natural convection. Single-domain calculation model was used to calculate arbitrary shape of the two tubes during the ice freezing process. We changed arranged angle and relative position of the tubes to investigate impact of the tube arrangement on freezing phenomenon. In order to confirm the accuracy of our analysis, analytical results were compared with experimental results at the same conditions. Results show that the bridging time was not simply in proportional to the initial temperature of water when considered the natural convection influenced by such as density inversion of water. Moreover, we found that when we set the temperature of tube wall and initial temperature of water as the parameters, bridging time has a similar trend with distance between the axes. Therefore, it is possible to predict the bridging time for elliptical heat transfer tube.
Heat transfer in viscous free convective fluctuating mhd flow through porous ...Alexander Decker
1) The document analyzes heat transfer in a viscous, free convective MHD flow through a porous medium past a vertical porous plate with variable temperature.
2) Governing equations are derived for the flow considering various parameters like porosity, magnetic field, temperature variation in space and time.
3) Solutions are obtained using perturbation methods by decomposing the velocity and temperature into power series of the Eckert number. Expressions for velocity, temperature and skin friction are derived.
Effects of conduction on magneto hydrodynamics mixed convection flow in trian...Alexander Decker
This document summarizes research on magnetohydrodynamic (MHD) mixed convection flow in triangular enclosures. Key points:
1) The study investigates the effects of conduction on MHD mixed convection flow in triangular enclosures using a finite element method.
2) Parameters like the Hartmann number, Prandtl number, Reynolds number, and Rayleigh number are found to strongly influence the flow and thermal fields.
3) Validation of the numerical code is done by comparing average Nusselt numbers to previous research on natural convection in triangular enclosures.
LINEAR STABILITY ANALYSIS ON THE ONSET OF DDC IN A DPM SATURATED WITH CSF WIT...IRJET Journal
This document presents a linear stability analysis of double diffusive convection in a rotating couple stress fluid saturated porous layer with an internal heat source. The analysis is based on a classical normal mode technique using a modified Darcy model that includes a time derivative term and Coriolis term. Expressions are obtained for the stationary and oscillatory Rayleigh numbers as functions of governing parameters like the internal Rayleigh number, couple stress parameter, Taylor number, normalized porosity, and Lewis number. The effects of these parameters on the stability of the system are shown graphically.
EFFECT OF PARTICLE SIZE AND CHEMICAL REACTION ON CONVECTIVE HEAT AND MASS TRA...IAEME Publication
The present work deals with the effect of size of the nano-particle and the liquid like layer formed duo to the natural chemical reaction of the liquid with the metical particle. The particle size and the layer around the particle certainly alter the heat and mass transfer.
Double Diffusive Convection and the Improvement of Flow in Square Porous AnnulusIJERA Editor
There has been increased interest shown in recent years to investigate the behavior of heat and mass transfer in a square annulus with a porous medium fixed between the inner and outer walls. This paper aims to evaluate the Soret effect arising in the case of heat and mass transfer in a porous medium bounded by a square annulus and subjected to isothermal heating of the inner surfaces as well as the outer horizontal surfaces. The phenomenon is governed by 3 partial differential equations, the momentum, energy and concentration equations, that are coupled together and result in a situation where change in one variable affects the other equations and vice versa. The partial differential equations are converted into finite element equations with the help of the Galerkin method and then solved to predict solution variables such as temperature, stream function and concentration in the porous medium. It is found that the heat transfer rate at the hot wall decreases with increasing viscous dissipation effect in the porous medium.
Non-Newtonian Visco-elastic Heat Transfer Flow Past a Stretching Sheet with C...IJERA Editor
In this paper two dimensional flow of a viscoelastic fluid due to stretching surface is considered. Flow analysis is carried out by using closed form solution of fourth order differential equation of motion of viscoelastic fluid. Further (Walters’ liquid B’ model) heat transfer analysis is carried out using convective surface condition. The governing equations of flow and heat transfer are non-linear partial differential equations which are unable to solve analytically hence are solved using Runge-Kutta Numerical Method with efficient shooting technique. The flow and heat transfer characteristics are studied through plots drawn. Numerical values of Wall temperature are calculated and presented in the table and compared with earlier published results which are in good agreement
Natural Convection and Entropy Generation in Γ-Shaped Enclosure Using Lattice...A Behzadmehr
This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation. A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr = 0.71) and Rayleigh numbers ranging from 103 to 106 at the macroscopic scale (Kn = 10-4). In every case, an appropriate value of the characteristic velocity is chosen using a simple model based on the kinetic theory. By considering the obtained dimensionless velocity and temperature values, the distributions of entropy generation due to heat transfer and fluid friction are determined. It is found that for an enclosure with high value of Rayleigh number (i.e., Ra=105), the total entropy generation due to fluid friction and total Nu number increases with decreasing the aspect ratio.
This document summarizes a study on magnetohydrodynamic (MHD) boundary layer flow of a Maxwell fluid past a porous stretching sheet with viscous dissipation. The study investigates the effects of various parameters on heat transfer for two cases: (1) a surface with prescribed wall temperature (PST), and (2) a surface with prescribed wall heat flux (PHF). Governing partial differential equations for momentum and heat transfer are converted to ordinary differential equations using similarity transformations. Numerical solutions are obtained using a shooting technique with a fourth-order Runge-Kutta scheme. Results for different dimensionless parameters are presented graphically for both PST and PHF cases and discussed.
Numerical Study of Heat Transfer in Ternary Nanofluid Over a Stretching Sheet...Atif75347
The new method of enhancing heat transfer through tri- hybrid nanofluid is discussed in the current study and represented in differential equation system.
NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFERFROM SQUARE CYLIND...ijmech
The document numerically investigates natural convection heat transfer from a square cylinder placed horizontally in a square enclosure filled with nanofluids. It presents the following key points:
1) Governing equations for the laminar, steady state, two-dimensional flow of an incompressible nanofluid are developed using the vorticity-stream function formulation.
2) Variables such as thermal conductivity and viscosity are modified to account for the inclusion of nanoparticles based on existing models.
3) The equations are non-dimensionalized and discretized before being solved using the ADI method.
4) Preliminary results show an increase in average Nusselt number with increasing nanoparticle volume fraction over the range
Second Law Analysis of Fluid Flow and Heat Transfer through Porous Channel wi...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document summarizes an article from the International Journal of Mechanical Engineering and Technology (IJMET) that examines the effect of particle size and chemical reaction on convective heat and mass transfer of magnetohydrodynamic (MHD) nanofluid flowing in a cylindrical annulus filled with porous material. The article presents governing equations to model the coupled heat and mass transfer, which are solved numerically. Parameters like the Darcy number, Grashof number, Hartmann number, and Nusselt number are defined. The study aims to provide insights into how particle size and chemical reactions impact convective transport for applications like nuclear technology and space systems.
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Communications Mining Series - Zero to Hero - Session 1DianaGray10
This session provides introduction to UiPath Communication Mining, importance and platform overview. You will acquire a good understand of the phases in Communication Mining as we go over the platform with you. Topics covered:
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ASPHALTIC MATERIAL IN THE CONTEXT OF GENERALIZED POROTHERMOELASTICITY
1. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
DOI:10.5121/ijsc.2017.8103 27
ASPHALTIC MATERIAL IN THE CONTEXT
OF GENERALIZED
POROTHERMOELASTICITY
Mohammad H. Alawi
College of engineering and Islamic architecture, p.o.box:7398 Makkah, Saudi Arabia
ABSTRACT
In this work, a mathematical model of generalized porothermoelasticity with one relaxation time for
poroelastic half-space saturated with fluid will be constructed in the context of Youssef model (2007). We
will obtain the general solution in the Laplace transform domain and apply it in a certain asphalt material
which is thermally shocked on its bounding plane. The inversion of the Laplace transform will be obtained
numerically and the numerical values of the temperature, stresses, strains and displacements will be
illustrated graphically for the solid and the liquid.
KEY-WORDS:
Porothermoelasticity; asphaltic Material; Thermal shock.
NOMENCLATURE
i iu , U The displacements of the skeleton and fluid phases
, ,R, Qλ µ The poroelastic coefficients
11 12 21 22R , R , R , R The mixed and thermal coefficients
s s
0T Tθ = − The temperature increment of the solid where s
T is the solid
f f
0T Tθ = − The temperature increment of the fluid where f
T is the fluid
0T The reference temperature
β The porosity of the material
s* f *
,ρ ρ The density of the solid and the liquid phases respectively
( )s s*
1ρ = −β ρ The density of the solid phase per unit volume of bulk
f f *
ρ = βρ The density of the solid phase per unit volume of bulk
s
11 12ρ = ρ −ρ The mass coefficient of solid phase
f
22 12ρ = ρ − ρ The mass coefficient of fluid phase
12ρ The dynamics coupling coefficient
s* f *
k , k The thermal conductivity of the solid and the fluid phases
( )s s*
k 1 k= −β The thermal conductivity of the solid phase
f f *
k k= β The thermal conductivity of the fluid phase
k The interface thermal conductivity
2. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
28
s f
o o,τ τ The relaxation time of the solid and the fluid phases
ijσ The stress components apply to the solid surface
σ The normal stress apply to the fluid surface
ije The strain component of the solid phase
ε The strain component of the fluid phase
s f
,α α The coefficients of the thermal expansion of the phases
sf fs
,α α The thermoelastic couplings between the phases
s f
E EC ,C The specific heat of the solid and the fluid phases
sf
EC The specific heat couplings between the phases
s s
s E
s
C
k
ρ
η = The thermal viscosity of the solid
f f
f E
f
C
k
ρ
η = The thermal viscosity of the fluid
sf
12 EC
k
ρ
η = The thermal viscosity couplings between the phases
P 3 2= λ + µ
11R s fs
p Q= α + α
22R f sf
R 3 Q= α + α
12R f sf
Q P= α + α
11F s s
EC= ρ
22F f f
EC= ρ
12F ( )s fs
12 22 o3 R R T= − α + α
21F ( )sf f
11 21 o3 R R T= − α + α
1. INTRODUCTION
Due to many applications in the fields of geophysics, plasma physics and related topics, an
increasing attention is being devoted to the interaction between fluid such as water and thermo
elastic solid, which is the domain of the theory of porothermoelasticity. The field of
porothermoelasticity has a wide range of applications especially in studying the effect of using
the waste materials on disintegration of asphalt concrete mixture.
Porous materials make their appearance in a wide variety of settings, natural and artificial and in
diverse technological applications. As a consequence, a variety of problems arise while dealing
with static and strength, fluid flow, heat conduction and the dynamics of such materials. In
connection with the later, we note that problems of this kind are encountered in the prediction of
behavior of sound-absorbing materials and in the area of exploration geophysics, the steadily
growing literature bearing witness to the importance of the subject [1]. The problem of a fluid-
saturated porous material has been studied for many years. A short list of papers pertinent to the
present study includes Biot [2-3], Gassmann [4], Biot and Willis [5], Biot [6], Deresiewicz and
Skalak [7], Mandl [8], Nur and Byerlee [9], Brown and Korringa [10], Rice and Cleary [11],
Burridge and Keller [12], Zimmerman et al. [13-14], Berryman and Milton [15], Thompson and
Willis [16], Pride et al. [17], Berryman and Wang [18], Tuncay and Corapcioglu [19], Alexander
3. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
29
and Cheng [20], Charlez, P. A., and Heugas, O. [21], Abousleiman et al. [22], Ghassemi, A.[23]
and Diek, A S. Tod [24].
The thermo-mechanical coupling in the poroelastic medium turns out to be of much greater
complexity than that in the classical case of impermeable elastic solid. In addition to thermal and
mechanical interaction within each phase, thermal and mechanical coupling occurs between the
phases, thus, a mechanical or thermal change in one phase results in mechanical and thermal
changes throughout the aggregate of asphaltic concrete mixtures. Following Biot, it takes one
physical model to consist a homogeneous, isotropic, elastic matrix whose interstices are filled
with a compressible ideal liquid both solid and liquid form continuous (and interacting) regions.
While viscous stresses in the liquid are neglected, the liquid is assumed capable of exerting a
velocity-dependent friction force on the skeleton. The mathematical model consists of two
superposed continuous phases each separately filling the entire space occupied by the aggregate.
Thus, there are two distinct elements at every point of space, each one characterized by its own
displacement, stress, and temperature. During a thermo-mechanical process they may interact
with a consequent exchange of momentum and energy.
Our development Proceeds by obtaining, the stress-strain-temperature relationships using the
theory of the generalized thermo elasticity with one relaxation time “Lord-Shulman” [25].
Moreover, to the usual isobaric coefficients of thermal expansion of the single-phase materials,
two coefficients appear which represent measures of each phase caused by temperature changes
in the other phase.
As a result of the presence of these "coupling" coefficients, it follows that coefficient of thermal
expansion of the dry material which differs than that of the saturated ones and the expansion of
the liquid in the bulk is not the same as of the liquid phase. Putting into consideration the
applications of geophysical interest, it takes the coefficient of proportionality in the dissipation
term to be independent of frequency, that is, we confine ourselves to low-frequency motions. The
last constituent of the theory is the equations of energy flux. Because the two phases in general,
will be at different temperatures in each point of the material, there is a rise of a heat-source term
in the energy equations representing the heat flux between the phases. It has been taken this
"interphase heat transfer" to be proportional to the temperature difference between the phases.
Finally, by using the uniqueness theorem the proof has been done.
Recently, Youssef has constructed a new version of theory of porothermoelasticity, using the
modified Fourier law of heat conduction. The most important advantage for this theory, is
predicting the finite speed of the wave propagation of the stress and the displacement as well as
the heat [26].
In this paper, a mathematical model of generalized porothermoelasticity with one relaxation time
for poroelastic half-space saturated with fluid will be constructed in the context of Youssef
model. We will obtain the general solution in the Laplace transform domain and apply it in a
certain asphalt material which is thermally shocked on its bounding plane. The inversion of the
Laplace transform will be obtained numerically and the numerical values of the temperature,
displacement and stress will be illustrated graphically.
BASIC FORMULATIONS
Starting by Youssef model of generalized porothermoelasticity [26], the linear governing
equations of isotropic, generalized porothermoelasticity in absence of body forces and heat
sources, are
4. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
30
(i)- Equations of motion
( ) s f
i,jj j,ij i,ii 11 ,i 12 ,i 11 i 12 iu u QU R R u Uµ + λ +µ + − θ − θ = ρ +ρ &&&& , (1)
s f
i,ii j,ij 21 ,i 22 ,i 12 i 22 iRU Qu R R u U+ − θ − θ = ρ +ρ &&&& . (2)
(ii)- Heat equations
( )
2
s s s s f
,ii o 11 12 o 11 ii o 212
k F F T R e T R
t t
∂ ∂
θ = + τ θ + θ + + ε
∂ ∂
(3)
( )
2
f f f s f
,ii o 21 22 o 12 ii o 222
k F F T R e T R
t t
∂ ∂
θ = + τ θ + θ + + ε
∂ ∂
(4)
(iii)- Constitutive equations
( )s f
ij ij kk ij 11 12 ij2 e e Q R Rσ = µ + λ δ + ε − θ − θ δ , (5)
f s
kk 22 21R Qe R Rσ = ε + − θ − θ . (6)
( ) i,iiii,jj,iij uee,uu
2
1
e ==+= (7)
i,iUε = . (8)
FORMULATION THE PROBLEM
We will consider one dimensional half-space 0 x≤ < ∞ is filled with porous, isotropic and
elastic material which is considered to be at rest initially. The displacement will be considered to
be in one dimensional as follows:
( ) ( ) ( )1 2 3u u x,t , u x,t u x,t 0= = = , (9)
( ) ( ) ( )1 2 3U U x,t , U x,t U x,t 0= = = . (10)
Then the governing equations (1)-(8) will take the forms:
(a) Equations of motion
( ) ( ) ( ) ( ) ( )
s f2 2
11 12 11 12
2 2
R Ru Q U
u U
x 2 x 2 x 2 x 2 2
∂θ ∂ θ ρ ρ∂ ∂
+ − − = +
∂ λ + µ ∂ λ + µ ∂ λ + µ ∂ λ + µ λ + µ
&&&& , (11)
s f2 2
21 22 21 22
2 2
R RU Q u
u U
x R x R x R x R R
∂ θ ∂θ ρ ρ∂ ∂
+ − − = +
∂ ∂ ∂ ∂
&&&& . (12)
(b) Equation of heat
2 s 2
s s f o 11 o 2111 12
o2 2 s s s s
T R T RF F u U
x t t k k k x k x
∂ θ ∂ ∂ ∂ ∂
= + τ θ + θ + +
∂ ∂ ∂ ∂ ∂
, (13)
5. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
31
2 f 2
f s f o 12 o 2221 22
o2 2 f f f f
T R T RF F u U
x t t k k k x k x
∂ θ ∂ ∂ ∂ ∂
= + τ θ + θ + +
∂ ∂ ∂ ∂ ∂
. (14)
(c) The constitutive relations
( ) ( ) ( ) ( )
s fxx 11 12R Ru Q U
2 x 2 x 2 2
σ ∂ ∂
= + − θ − θ
λ + µ ∂ λ + µ ∂ λ + µ λ + µ
, (15)
f s22 21R RU Q u
R x R x R R
σ ∂ ∂
= + − θ − θ
∂ ∂
. (16)
u
e
x
∂
=
∂
(17)
U
x
∂
ε =
∂
. (18)
Using the non-dimensional variables as follows:
( ) ( ) ( ) ( ) ( ) ( ) ij2 s f s f
o 0 o 0 0 iju ,U ,x c u,U,x , t , c t, , , T , , ,
2 R
σ σ
′ ′ ′ ′ ′ ′ ′ ′ ′= η τ = η τ θ θ = θ θ σ = σ =
λ + µ
where
sf
2 12 E
o
12
C2
c ,
k
ρλ + µ
= η =
ρ
.
Then, we get
( ) ( ) ( )
2 2 s f
0 11 0 12 11
2 2
12
T R T Ru Q U
u U
x 2 x 2 x 2 x
ρ∂ ∂ ∂ θ ∂ θ
+ − − = +
∂ λ + µ ∂ λ + µ ∂ λ + µ ∂ ρ
&&&& , (19)
( ) ( )2 2 s f
0 21 0 22 22
2 2
12
2 2T R T RU Q u
u U
x R x R x R x R R
λ + µ λ + µρ∂ ∂ ∂ θ ∂ θ
+ − − = +
∂ ∂ ∂ ∂ ρ
&&&& . (20)
2 s 2 s
s s f12 11 21
o2 2 s s s
F R Ru U
x t t k k x k x
∂ θ ∂ ∂ η ∂ ∂
= + τ θ + θ + +
∂ ∂ ∂ η η η ∂ η ∂
, (21)
2 f 2 f
f s f21 12 22
o2 2 f f f
F R Ru U
x t t k k x k x
∂ θ ∂ ∂ η ∂ ∂
= + τ θ + θ + +
∂ ∂ ∂ η η η ∂ η ∂
. (22)
( ) ( ) ( )
s f0 11 0 12
xx
T R T Ru Q U
x 2 x 2 2
∂ ∂
σ = + − θ − θ
∂ λ + µ ∂ λ + µ λ + µ
, (23)
f s0 22 0 21T R T RU Q u
x R x R R
∂ ∂
σ = + − θ − θ
∂ ∂
. (24)
In the above equation, we dropped the prime for convenient.
6. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
32
FORMULATION THE PROBLEM IN LAPLACE TRANSFORM DOMAIN
Applying the Laplace transform for the both sides of the equations (19)-(24) which is defined as
follows:
( ) ( ) st
0
f s f t e dt
∞
−
= ∫ ,
then, we get
2 s f
11 12 13 142
d u d d
L u L U L L
d x dx d x
θ θ
= + + + , (25)
2 s f
21 22 23 242
d U d d
L u L U L L
d x dx d x
θ θ
= + + + , (26)
2 s
s f
31 32 33 342
d d u d U
L L L L
d x d x d x
θ
= θ + θ + + , (27)
2 f
s f
41 42 43 442
d d u d U
L L L L
d x d x d x
θ
= θ + θ + + , (28)
s f
xx 11 12
d u d U
A A A
d x d x
σ = + − θ − θ , (29)
s f
21 22
d U du
B A A
d x dx
σ = + − θ − θ , (30)
d u
e
d x
= (31)
d U
d x
ε = . (32)
where
11 21 12 21 11 21 12 22
11 12 13 14
C AC C AC A AA A AA
L , L , L , L
1 AB 1 AB 1 AB 1 AB
− − − −
= = = =
− − − −
,
21 11 22 12 21 11 22 12
21 22 23 24
C BC C BC A BA A BA
L , L , L , L
1 AB 1 AB 1 AB 1 AB
− − − −
= = = =
− − − −
,
( ) ( ) ( ) ( )s 2 s s 2 s 2 s 2
o o 12 o 11 o 21
31 32 33 34s s s
s s s s F s s R s s R
L , L ,L , L
k k k
+ τ η + τ + τ + τ
= = = =
η η η η
,
( ) ( ) ( ) ( )f 2 f 2 f f 2 f 2
o 21 o o 12 o 22
41 42 43 44f f f
s s F s s s s R s s R
L , L , L , L
k k k
+ τ + τ η + τ + τ
= = = =
η η η η
.
( ) ( ) ( )
2 20 11 0 12 11
11 12 11 12
12
T R T RQ
A ,A , A , C s , C s
2 2 2
ρ
= = = = =
λ + µ λ + µ λ + µ ρ
( ) ( )2 20 21 0 22 22
21 22 21 22
12
2 2T R T RQ
B , A , A , C s , C s ,
R R R R R
λ + µ λ + µρ
= = = = =
ρ
By using equations (25)-(28), we get
7. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
33
8 6 4 2
x x x xD aD bD cD d u 0 − + − + = , (33)
8 6 4 2
x x x xD aD bD cD d U 0 − + − + = , (34)
8 6 4 2 s
x x x xD aD bD cD d 0 − + − + θ = , (35)
8 6 4 2 f
x x x xD aD bD cD d 0 − + − + θ = , (36)
where
11 13 33 14 43 22 23 34 24 44 31 42a = L + L L + L L + L + L L + L L + L + L
( ) ( )
( )
( )( )
( )
11 22 23 34 24 44 31 42 12 21 23 33 24 43
13 21 34 22 33 24 34 43 33 44 32 43 33 42
14 21 44 22 43 23 33 44 34 43 31 43 33 41
22 31 42 23 34 42
b= L L +L L +L L +L +L - L L + L L + L L -
L L L - L L + L (L L - L L ) + L L - L L -
L L L - L L + L L L - L L - L L + L L
+ L L + L + L (L L ( )32 44 24 31 44 34 41 31 42 32 41- L L )+ L L L - L L + L L - L L
11 22 31 42 23 34 42 32 44 24 31 44 34 41 31 42 32 41
12 21 31 42 23 33 42 32 43 24 31 43 33 41
13 21 32 44 34 42 22 33 42 32 43
c= L (L (L + L ) + L (L L - L L ) +L (L L - L L ) +L L - L L )
- L (L (L + L ) + L (L L - L L ) + L (L L - L L ))
+ L (L (L L - L L ) +L (L L - L L ) 14 21 31 44 34 41
22 33 41 31 43 22 31 42 32 41
) - L (L (L L - L L )
+ L (L L - L L )) + L (l L - L L )
11 22 31 42 32 41 12 21 32 41 31 42d =L L (L L - L L ) + L L (L L - L L ) ,
and
n
n
x n
d
D
d x
= .
According to equations (33)-(36) and to bounded state of functions at infinity, we can consider
the following forms
( ) i
4
x
i
i 1
u x,s e−λ
=
= α∑ , (37)
( ) i
4
x
i
i 1
U x,s e−λ
=
= β∑ , (38)
( ) i
4
xs
i
i 1
x,s e−λ
=
θ = γ∑ , (39)
( ) i
4
xf
i
i 1
x,s e−λ
=
θ = ω∑ , (40)
where i , i 1,2,3,4±λ = are the roots of the characteristic equation of the system (33)-(36) which
takes the form
8 6 4 2
a b c d 0λ − λ + λ − λ + = , (41)
To get the relations between the parameters i i i, ,β γ ω and iα , we will use equations (26)-(28) in
the following forms
8. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
34
2 s f
x 22 23 x 24 x 21D L U L D L D L u − − θ − θ = , (42)
2 s f
34 x 31 32 33 xL U D L L L D u − + − θ − θ = , (43)
s 2 f
44 x 41 x 42 43 xL D U L D L L D u − − θ + − θ = , (44)
Inserting the formulas in (37)-(40) into equations (42)-(44), we get
( )2
i 22 i 23 i i 24 i i 21 iL L L L , i 1,2,3,4λ − β + λ γ + λ ω = α = , (45)
( )2
34 i i 31 i 32 i 33 i iL L L L , i 1,2,3,4− β + λ − γ − ω = − λ α = , (46)
( )2
44 i i 41 i i 42 i 43 i iL L L L , i 1,2,3,4λ β − γ + λ − ω = − λ α = , (47)
By solving the system in (45)-(47), we obtain
i
i i
i
H
, i 1,2,3,4
W
β = α = ,
i
i i
i
G
, i 1,2,3,4
W
γ = α = ,
i
i i
i
F
, i 1,2,3,4
W
γ = α = ,
Where
4 2
i i 21 23 33 24 43 i 21 31 42 23 33 42 32 43
24 31 43 33 41 21 31 42 32 41
H ( (L + L L + L L ) - (L (L + L ) + L (L L - L L ) +
L (L L - L L )) + L (L L - L L )) , i 1,2,3,4
= − λ λ
=
5 3 2
i 33 i i 22 33 24 33 44 32 43 33 42 34 i 21 24 43
21 32 44 22 33 42 32 43 21 34 42
G = L - (L L + L L L - L L + L L ) - L (L + L L )
+ (L L L + L (L L - L L )) + L L L , i 1,2,3,4
λ λ λ
λ =
5 3 2
i 43 i i 21 44 22 43 23 33 44 31 43 33 41 23 43 34 i
i 21 31 44 22 33 41 31 43 21 34 41
F = L + (L L - L L + L L L - L L +L L ) + L L L
- (L L L + L (L L - L L )) - L L L , i 1,2,3,4
λ λ λ
λ =
6 4 3 2
i i i 22 24 44 31 42 23 34 i i 22 31 42 23 32 44
24 31 44 31 42 32 41 34 i 23 42 24 41
22 31 42 32 41
W = - + (L + L L + L + L ) - L L - (L (L + L ) - L L L
+L L L + L L - L L ) + L (L L - L L )
+ L (L L - L L ) , i 1,2,3,4
λ λ λ λ
λ
=
Hence, we have
( ) i
4
xi
i
i 1 i
H
U x,s e
W
−λ
=
= α∑ , (48)
( ) i
4
xs i
i
i 1 i
G
x,s e
W
−λ
=
θ = α∑ , (49)
( ) i
4
xf i
i
i 1 i
F
x,s e
W
−λ
=
θ = α∑ , (50)
To get the values of the parameters iα , we have to apply the boundary conditions as follows;
9. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
35
(1) The thermal conditions
We will consider the bounding plane surface of the medium at x = 0 has been thermally loaded by
thermal shock as follows:
( ) ( ) ( )s
00,t 1 H tθ = −β θ , (51)
and
( ) ( )f
00,t H tθ = βθ , (52)
where H(t) is the Heaviside unite step function and 0θ is constant which gives after using the
Laplace transform the following conditions
( )
( ) 0s 1
0,s
s
−β θ
θ = , (53)
and
( )f 0
0,s
s
βθ
θ = , (54)
(2) The mechanical conditions
We will consider the bounding plane surface of the medium at x = 0 has been connected to a rigid
surface which prevents any displacement to accrue on that surface, i.e.
( )u 0,t 0= , (55)
and
( )U 0,t 0= , (56)
which gives after using the Laplace transform the following conditions
( )u 0,s 0= , (57)
and
( )U 0,s 0= . (58)
After using the boundary conditions in (53), (54), (57) and (58), we get the following system
4
i
i 1
0
=
α =∑ , (59)
4
i
i
i 1 i
H
0
W=
α =∑ , (60)
( )4
0i
i
i 1 i
1G
W s=
−β θ
α =∑ , (61)
4
0i
i
i 1 i
F
W s=
βθ
α =∑ , (62)
Then we get
10. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
36
( )
( )
( )
2 3 4 4 3 3 4 4 3 3 4 4 3
0 1
1 3 2 4 4 2 2 4 4 2 2 4 4 2
4 2 3 3 2 2 3 3 2 2 3 3 2
W (F H - F H +G H G H )-F H F H -
W
= W (F H - F H +G H G H )-F H F H
s
W (F H - F H +G H G H )-F H F H
β − +
θ
α β − + +
∆
β − +
,
( )
( )
( )
1 3 4 4 3 3 4 4 3 3 4 4 3
0 2
2 3 1 4 4 1 1 4 4 1 1 4 4 1
4 1 3 3 1 1 3 3 1 1 3 3 1
W (F H - F H +G H G H )-F H F H -
W
= W (FH - F H +G H G H )-FH F H
s
W (FH - F H +G H G H )-FH F H
β − +
θ
α − β − + +
∆
β − +
,
( )
( )
( )
1 2 4 4 2 2 4 4 2 2 4 4 2
0 3
3 2 1 4 4 1 1 4 4 1 1 4 4 1
4 1 2 2 1 1 2 2 1 1 2 2 1
W (F H - F H +G H G H )-F H F H -
W
= W (FH - F H +G H G H )-FH F H
s
W (FH - F H +G H G H )-FH F H
β − +
θ
α β − + +
∆
β − +
,
( )
( )
( )
1 2 3 3 2 2 3 3 2 2 3 3 2
0 4
4 2 1 3 3 1 1 3 3 1 1 3 3 1
3 1 2 2 1 1 2 2 1 1 2 2 1
W (F H - F H +G H G H )-F H F H -
W
= W (FH - F H +G H G H )-FH F H
s
W (FH - F H +G H G H )-FH F H
β − +
θ
α − β − + +
∆
β − +
,
where
1 2 3 4 4 3 3 4 2 2 4 4 2 3 3 2
2 1 3 4 4 3 3 4 1 1 4 4 1 3 3 1
3 1 2 4 4 2 2 4 1 1 4 4 1 2 2 1
4 1 2 3 3 2
= - W (F (G H - G H ) + F (G H - G H ) + F (G H - G H )) +
W (F (W H - G H ) + F (G H - G H ) + F (G H - G H )) -
W (F (G H - G H ) + F (G H - G H ) + F (G H - G H )) +
W (F (G H - G H ) +
∆
2 3 1 1 3 3 1 2 2 1F (G H - G H ) + F (G H - G H ))
,
Those complete the solution in the Laplace transform domain.
NUMERICAL INVERSION OF THE LAPLACE TRANSFORMS
In order to invert the Laplace transforms, we adopt a numerical inversion method based on a
Fourier series expansion [27].
By this method the inverse )t(f of the Laplace transform ( )sf is approximated by
( ) ( )
ct N
1
k 11 1 1
e 1 i k i k t
f t f c R1 f c exp , 0 t 2t,
t 2 t t=
π π
= + + < <
∑
Where N is a sufficiently large integer representing the number of terms in the truncated Fourier
series, chosen such that
( ) 1
1 1
i N i N t
exp c t R1 f c exp
t t
π π
+ ≤ ε
,
where ε1 is a prescribed small positive number that corresponds to the degree of accuracy
required. The parameter c is a positive free parameter that must be greater than the real part of all
the singularities of ( )sf . The optimal choice of c was obtained according to the criteria described
11. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
37
in [27].
NUMERICAL RESULTS AND DISCUSSION
The Ferrari's method has been constructed by using the FORTRAN program to solve equation
(41). The material properties of asphaltic material saturated by water have been taken as follow
[28], [29]:
*
o 11 2 11 2 11 2
0
11 2 s -5 o 1 s* 3 3
11
s 1 o 1 s 1 o 1 s
E o
T 27 C, Q 0.4853 10 dyne.cm , R 0.0362 10 dyne.cm , 0.2160 10 dyne.cm
0.0926 10 dyne.cm , 2.16 10 C , 2.35 gm.cm , 0.002 gm.cm
k 0.8W m k , C 800 J.kg . C , 0.02s, k 0.001
− − −
− − − −
− − − −
= = × = × λ = ×
µ = × α = × ρ = ρ =
= = τ = = 1 o 1
W m k− −
*
f sf fs o 1 f * 3 f 1 o 1 f 1 o 1
E
f
o
0.0001 C , 0.82 gm.cm , k 0.3W m k , C 1.9cal.gm . C ,
0.00001s,
− − − − − −
α = α = α = ρ = = =
τ =
We will take the non-dimensional x variable to be in interval 0 x 1≤ ≤ and all the results will be
calculated at the same instance t 0.1= for two different values of the porosity β of the material
when 0.25β = and 0.35β = .
The temperature, the stress, the strain and the displacement for the solid and the liquid have been
shown in figures 1-8 respectively. We can see that, the value of the porosity has a significant
effect on all the studied fields.
Figure 1 shows the temperature increment distribution of the solid with two different values of
the porosity; 0.25β = and 0.35β = . It shows that the porosity parameter has a significant effect.
Figure 2 shows the temperature increment distribution of the liquid with two different values of
the porosity; 0.25β = and 0.35β = . We can see that the porosity parameter has a significant
effect where the liquid temperature increases when the porosity increases.
Figure 3 shows the stress distribution of the solid with two different values of the porosity;
0.25β = and 0.35β = . We can see that the porosity parameter has a significant effect where the
absolute value of the stress acts on the solid increases when the porosity increases.
Figure 4 shows the stress distribution of the liquid with two different values of the porosity;
0.25β = and 0.35β = . We can see that the porosity parameter has a significant effect where the
absolute value of the stress acts on the liquid increases when the porosity increases for wide range
of x.
Figures 5-8, show that the porosity parameter has significant effects on the deformation and the
displacement for both medium solid and liquid. The absolute value of the peak points (sharp
points) increase when the value of the porosity parameter increases for the both medium solid and
water.
12. International Journal on Soft Computing (IJSC) Vol.8, No. 1, February 2017
38
CONCLUSION
In studying a mathematical model of generalized porothermoelasticity with one relaxation time
for poroelastic half-space saturated with fluid in the context of Youssef model we found that:
1- The porosity parameter of the poroelastic material has significant effects on the
temperature, the stress, the deformation and the displacement distributions for the both
medium the solid and the liquid.
2- Youssef model of porothermoelasticity with one relaxation time introduce finite speed of
thermal wave propagation which agree with realistic physical behavior for the solid and
the liquid.
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