This document summarizes a study examining the slow steady motion of a second-order thermo-viscous fluid between two parallel plates with constant pressure and temperature gradients. The study obtains closed-form solutions for the velocity and temperature distributions for two cases: when the upper plate is in relative motion and when it is thermally insulated. Graphs show the effects of various parameters on the velocity, temperature, and transverse forces.
Slow steady motion of a thermo viscous fluid between two parallel plates with...eSAT Journals
Abstract
In this paper, the slow steady motion of a second order thermo-viscous fluid between two parallel plates is examined. The closed form
solutions of the velocity and temperature distributions are obtained when thermo-stress coefficient is far less compared to strain
thermal conductivity coefficient and coefficient of cross viscosity for the following two cases: (i) when the upper plate is in relative
motion and (ii) when the upper plate is thermally insulated. The heat transfer coefficient on the upper plate , The mean Bulk
temperature and the transverse force perpendicular to the flow direction are also calculated. It is observed that forces are generated
in transverse directions which are special feature of these types of fluids. The effect of various flow parameters on the flow field have
been discussed with the help of graphical illustrations.
Keywords: Thermo-viscous fluids, Strain thermal conductivity coefficient and Thermo stress Coefficient.
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
Numerical simulation on laminar free convection flow and heat transfer over a...eSAT Journals
Abstract
In the present numerical study, laminar free-convection flow and heat transfer over an isothermal vertical plate is presented. By
means of similarity transformation, the original nonlinear coupled partial differential equations of flow are transformed to a pair
of simultaneous nonlinear ordinary differential equations. Then, they are reduced to first order system. Finally, NewtonRaphson
method and adaptive Runge-Kutta method are used for their integration. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity and temperature profiles for various Prandtl number are illustrated graphically. Flow
and heat transfer parameters are derived as functions of Prandtl number alone. The results of the present simulation are then
compared with experimental data published in literature and find a good agreement.
Keywords: Free Convection, Heat Transfer, Matlab, Numerical Simulation, Vertical Plate.
Numerical simulation of marangoni driven boundary layer flow over a flat plat...eSAT Journals
Abstract
A numerical algorithm is presented for studying Marangoni convection flow over a flat plate with an imposed temperature
distribution. Plate temperature varies with x in the following prescribed manner: where A and k are constants.
By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a pair of
nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton
Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab
environment. Velocity profiles for various values of k, and temperature profiles for various Prandtl number and k are illustrated
graphically. The results of the present simulation are then compared with the previous works available in literature with good
agreement.
Keywords: Matlab, Marangoni Convection, Numerical Simulation, Surface Tension, Flat Plate.
Numerical study of natural convection in an enclosed square cavity using cons...eSAT Journals
Abstract In the present study, Constrained Interpolated Profile (CIP) method was used to simulate the natural convection heat transfer and fluid flow in an enclosed square cavity with differentially heated side walls. The fundamental idea of this method is to solve the advection phase equation with CIP method and the non-advection phase equation is calculated with finite difference method. CIPNSE is applied to predict the temperature and velocity profiles in a square cavity for various Rayleigh number: Ra=103, 104 and 105. The streamline and isotherms obtained under these conditions were then compared with those published in literature and found a good agreement. Keywords: Constrained Interpolated Profile (CIP), Finite Difference Method (FDM) and Lattice Boltzmann Method (LBM), Natural Convection, Square Cavity, Stream-Function Vorticity
Numerical study of mhd boundary layer stagnation point flow and heat transfer...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
Slow steady motion of a thermo viscous fluid between two parallel plates with...eSAT Journals
Abstract
In this paper, the slow steady motion of a second order thermo-viscous fluid between two parallel plates is examined. The closed form
solutions of the velocity and temperature distributions are obtained when thermo-stress coefficient is far less compared to strain
thermal conductivity coefficient and coefficient of cross viscosity for the following two cases: (i) when the upper plate is in relative
motion and (ii) when the upper plate is thermally insulated. The heat transfer coefficient on the upper plate , The mean Bulk
temperature and the transverse force perpendicular to the flow direction are also calculated. It is observed that forces are generated
in transverse directions which are special feature of these types of fluids. The effect of various flow parameters on the flow field have
been discussed with the help of graphical illustrations.
Keywords: Thermo-viscous fluids, Strain thermal conductivity coefficient and Thermo stress Coefficient.
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
Numerical simulation on laminar free convection flow and heat transfer over a...eSAT Journals
Abstract
In the present numerical study, laminar free-convection flow and heat transfer over an isothermal vertical plate is presented. By
means of similarity transformation, the original nonlinear coupled partial differential equations of flow are transformed to a pair
of simultaneous nonlinear ordinary differential equations. Then, they are reduced to first order system. Finally, NewtonRaphson
method and adaptive Runge-Kutta method are used for their integration. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity and temperature profiles for various Prandtl number are illustrated graphically. Flow
and heat transfer parameters are derived as functions of Prandtl number alone. The results of the present simulation are then
compared with experimental data published in literature and find a good agreement.
Keywords: Free Convection, Heat Transfer, Matlab, Numerical Simulation, Vertical Plate.
Numerical simulation of marangoni driven boundary layer flow over a flat plat...eSAT Journals
Abstract
A numerical algorithm is presented for studying Marangoni convection flow over a flat plate with an imposed temperature
distribution. Plate temperature varies with x in the following prescribed manner: where A and k are constants.
By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a pair of
nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton
Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab
environment. Velocity profiles for various values of k, and temperature profiles for various Prandtl number and k are illustrated
graphically. The results of the present simulation are then compared with the previous works available in literature with good
agreement.
Keywords: Matlab, Marangoni Convection, Numerical Simulation, Surface Tension, Flat Plate.
Numerical study of natural convection in an enclosed square cavity using cons...eSAT Journals
Abstract In the present study, Constrained Interpolated Profile (CIP) method was used to simulate the natural convection heat transfer and fluid flow in an enclosed square cavity with differentially heated side walls. The fundamental idea of this method is to solve the advection phase equation with CIP method and the non-advection phase equation is calculated with finite difference method. CIPNSE is applied to predict the temperature and velocity profiles in a square cavity for various Rayleigh number: Ra=103, 104 and 105. The streamline and isotherms obtained under these conditions were then compared with those published in literature and found a good agreement. Keywords: Constrained Interpolated Profile (CIP), Finite Difference Method (FDM) and Lattice Boltzmann Method (LBM), Natural Convection, Square Cavity, Stream-Function Vorticity
Numerical study of mhd boundary layer stagnation point flow and heat transfer...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
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...IJERA Editor
This paper presents a study of MHD free convection flow of an electrically conducting incompressible fluid with
variable viscosity about an isothermal truncated cone in the presence of heat generation or absorption. The fluid
viscosity is assumed to vary as a inverse linear function of temperature. The non-linear coupled partial
differential equations governing the flow and heat transfer have been solved numerically by using an implicit
finite - difference scheme along with quasilinearization technique. The non-similar solutions have been obtained
for the problem, overcoming numerical difficulties near the leading edge and in the downstream regime. Results
indicate that skin friction and heat transfer are strongly affected by, both, viscosity-variation parameter and
magnetic field. In fact, the transverse magnetic field influences the momentum and thermal fields, considerably.
Further, skin friction is found to decrease and heat transfer increases near the leading edge. Also, it is found that
the direction of heat transfer gets reversed during heat generation.
Some Mixed Quadrature Rules for Approximate Evaluation of Real Cauchy Princip...IJERD Editor
In this paper some mixed quadrature rules have been constructed for numerical integration of real
Cauchy principal value integrals and their asymptotic error estimates have been derived. The numerical
verification of the rules has been done by considering some standard Cauchy principal value integrals.
Theoretical investigations on standing wave thermoacoustic prime mover using ...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
Yet another statistical analysis of the data of the ‘loophole free’ experime...Richard Gill
I presented novel statistical analyses of the data of the famous Bell-inequality experiments of 2015 and 2016: Delft, NIST, Vienna and Munich. Every statistical analysis relies on statistical assumptions. I’ll make the traditional, but questionable, i.i.d. assumptions. They justify a novel (?) analysis which is both simple and (close to) optimal.
It enables us to fairly compare the results of the two main types of experiments: NIST and Vienna CH-Eberhard “one-channel” experiment with target settings and state chosen to optimise the handling of the detection loophole (detector efficiency > 66.7%); Delft and Munich CHSH “two channel” experiments based on entanglement swapping, with the target state and settings which achieve the Tsirelson bound (detector efficiency ≈ 100%).
One cannot say which type of experiment is better without agreeing on how to compromise between the desires to obtain high statistical significance and high physical significance. Moreover, robustness to deviations from traditional assumptions is also an issue.
I also discussed my current opinions on the question: what should we now believe about locality and realism and the foundations of quantum mechanics. My provisional conclusion is "exquisite/angelic spukhafte Fernwerkung" ... but tempered with a quantum Buddhist point of view - nothing is real. This was a talk at the 2019 Växjö conference QIRIF
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.
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
EDGE-NEIGHBOR RUPTURE DEGREE ON GRAPH OPERATIONSmathsjournal
Vulnerability and reliability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links in a communication network. An edge subversion strategy of a graph , say , is a set of edge(s) in whose adjacent vertices which is incident with the removal edge(s) are removed from . The survival subgraph is denoted by . In this paper we give some results for the edge-neighbor-rupture degree of the graph operations and Thorny graph types are examined.
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.
Multiple linear regression for energy efficacy of residential buildingsFahad B. Mostafa
In this project, we use a statistical multiple regression to study the impact of eight various predictors (relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, glazing area distribution) to estimate the cooling load energy efficiency of residential buildings. We try to analyze and visualize the effect of each predictor with each of the response variable using different classical statistical analysis tools used in describing linear models, in such a way so that we can find out the most strongly related predictor variables. Before starting all of this, we used the idea of model selection by stepwise regression technique and compare the AIC of these models and identified a better model between all of them. Then, we compare a classical linear regression approach by simulations on 768 diverse residential buildings show that we can predict CL with low mean absolute error. By using ANOVA we determined variation in the different residuals. Also, we used non constant variance test to verify it. Furthermore, we check leverage and influence points as well as outliers as well as determined cook distance for influential points. By taking box cox transformation and weights, we also introduced WLS technique to fit the model for better results and did all type of important analysis to understand the energy efficiency. Finally, we should 5-fold cross validation to verify our model.
Source of used data:
The dataset was created by Angeliki Xifara (angxifara '@' gmail.com, Civil/Structural Engineer) and was processed by Athanasios Tsanas (tsanasthanasis '@' gmail.com, Oxford Centre for Industrial and Applied Mathematics, University of Oxford, UK).
Transient Laminar MHD Free Convective Heat Transfer past a Vertical Plate wit...theijes
An analytical computation of the problem of nonlinear magneto-hydrodynamic flow with heat transfer characteristics is considered for an incompressible viscous, electrically conducting fluid past a vertical plate with transverse magnetic field applied normal to the surface. The dimensionless transient nonlinear governing boundary layer flow equations which are coupled partial differential equations are obtained. These are transformed to ordinary differential equations and solved using the Laplace transform method. The effect of the resulting parameters are analysed and compared with existing results in literature.
A graph with n vertex and m edges is said to be cubic graceful labeling if its vertices are labeled with distinct integers {0,1,2,3,……..,m3} such that for each edge f*( uv) induces edge mappings are {13,23,33,……,m3}. A graph admits a cubic graceful labeling is called a cubic graceful graph. In this paper, we proved that < K1,a , K1,b , K1c , K1,d>, associate urp with u(r+1)1 of K1,P, fixed vertices vr and ur of two copies of Pn are cubic graceful.
Importance of post processing for improved binarization of text documentseSAT 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.
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.
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
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
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
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...IJERA Editor
This paper presents a study of MHD free convection flow of an electrically conducting incompressible fluid with
variable viscosity about an isothermal truncated cone in the presence of heat generation or absorption. The fluid
viscosity is assumed to vary as a inverse linear function of temperature. The non-linear coupled partial
differential equations governing the flow and heat transfer have been solved numerically by using an implicit
finite - difference scheme along with quasilinearization technique. The non-similar solutions have been obtained
for the problem, overcoming numerical difficulties near the leading edge and in the downstream regime. Results
indicate that skin friction and heat transfer are strongly affected by, both, viscosity-variation parameter and
magnetic field. In fact, the transverse magnetic field influences the momentum and thermal fields, considerably.
Further, skin friction is found to decrease and heat transfer increases near the leading edge. Also, it is found that
the direction of heat transfer gets reversed during heat generation.
Some Mixed Quadrature Rules for Approximate Evaluation of Real Cauchy Princip...IJERD Editor
In this paper some mixed quadrature rules have been constructed for numerical integration of real
Cauchy principal value integrals and their asymptotic error estimates have been derived. The numerical
verification of the rules has been done by considering some standard Cauchy principal value integrals.
Theoretical investigations on standing wave thermoacoustic prime mover using ...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
Yet another statistical analysis of the data of the ‘loophole free’ experime...Richard Gill
I presented novel statistical analyses of the data of the famous Bell-inequality experiments of 2015 and 2016: Delft, NIST, Vienna and Munich. Every statistical analysis relies on statistical assumptions. I’ll make the traditional, but questionable, i.i.d. assumptions. They justify a novel (?) analysis which is both simple and (close to) optimal.
It enables us to fairly compare the results of the two main types of experiments: NIST and Vienna CH-Eberhard “one-channel” experiment with target settings and state chosen to optimise the handling of the detection loophole (detector efficiency > 66.7%); Delft and Munich CHSH “two channel” experiments based on entanglement swapping, with the target state and settings which achieve the Tsirelson bound (detector efficiency ≈ 100%).
One cannot say which type of experiment is better without agreeing on how to compromise between the desires to obtain high statistical significance and high physical significance. Moreover, robustness to deviations from traditional assumptions is also an issue.
I also discussed my current opinions on the question: what should we now believe about locality and realism and the foundations of quantum mechanics. My provisional conclusion is "exquisite/angelic spukhafte Fernwerkung" ... but tempered with a quantum Buddhist point of view - nothing is real. This was a talk at the 2019 Växjö conference QIRIF
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.
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
EDGE-NEIGHBOR RUPTURE DEGREE ON GRAPH OPERATIONSmathsjournal
Vulnerability and reliability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links in a communication network. An edge subversion strategy of a graph , say , is a set of edge(s) in whose adjacent vertices which is incident with the removal edge(s) are removed from . The survival subgraph is denoted by . In this paper we give some results for the edge-neighbor-rupture degree of the graph operations and Thorny graph types are examined.
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.
Multiple linear regression for energy efficacy of residential buildingsFahad B. Mostafa
In this project, we use a statistical multiple regression to study the impact of eight various predictors (relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, glazing area distribution) to estimate the cooling load energy efficiency of residential buildings. We try to analyze and visualize the effect of each predictor with each of the response variable using different classical statistical analysis tools used in describing linear models, in such a way so that we can find out the most strongly related predictor variables. Before starting all of this, we used the idea of model selection by stepwise regression technique and compare the AIC of these models and identified a better model between all of them. Then, we compare a classical linear regression approach by simulations on 768 diverse residential buildings show that we can predict CL with low mean absolute error. By using ANOVA we determined variation in the different residuals. Also, we used non constant variance test to verify it. Furthermore, we check leverage and influence points as well as outliers as well as determined cook distance for influential points. By taking box cox transformation and weights, we also introduced WLS technique to fit the model for better results and did all type of important analysis to understand the energy efficiency. Finally, we should 5-fold cross validation to verify our model.
Source of used data:
The dataset was created by Angeliki Xifara (angxifara '@' gmail.com, Civil/Structural Engineer) and was processed by Athanasios Tsanas (tsanasthanasis '@' gmail.com, Oxford Centre for Industrial and Applied Mathematics, University of Oxford, UK).
Transient Laminar MHD Free Convective Heat Transfer past a Vertical Plate wit...theijes
An analytical computation of the problem of nonlinear magneto-hydrodynamic flow with heat transfer characteristics is considered for an incompressible viscous, electrically conducting fluid past a vertical plate with transverse magnetic field applied normal to the surface. The dimensionless transient nonlinear governing boundary layer flow equations which are coupled partial differential equations are obtained. These are transformed to ordinary differential equations and solved using the Laplace transform method. The effect of the resulting parameters are analysed and compared with existing results in literature.
A graph with n vertex and m edges is said to be cubic graceful labeling if its vertices are labeled with distinct integers {0,1,2,3,……..,m3} such that for each edge f*( uv) induces edge mappings are {13,23,33,……,m3}. A graph admits a cubic graceful labeling is called a cubic graceful graph. In this paper, we proved that < K1,a , K1,b , K1c , K1,d>, associate urp with u(r+1)1 of K1,P, fixed vertices vr and ur of two copies of Pn are cubic graceful.
Importance of post processing for improved binarization of text documentseSAT 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.
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.
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
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
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
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
Congestion control based on sliding mode control and scheduling with prioriti...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.
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
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.
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
Lab view based self tuning fuzzy logic controller for sterilizing equipments ...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.
Enhancement in power delay product by driver and interconnect optimizationeSAT 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.
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
The green aggregates for sustainable development in construction industryeSAT 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
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.
Product quality improved using triz a case study in increasing innovative opt...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
Experimental design to determine thermal diffusivity of a material an anal...eSAT Journals
Abstract Thermal diffusivity of any object is of prime importance as it decides the amount of heat energy required to be provided or removed from an object for it to attain the required temperature on its surface at a particular instant of time. Little has been done so far in devising a way of determining the thermal diffusivity directly without having to use costlier setups or be plagued by errors being piled up by multiplication of individual parameter errors. This paper suggests a simple experimental setup which can deduce the thermal diffusivity of a material directly instead of having to calculate the thermal conductivity and specific heat capacity of the materials. The setup model can be effectively used for determining relationship between heat energy stored within and the rate of heat transfer through the outer surface of specimen when there is no heat generation. An illustrative example for the use of the model is also presented with the material in cylindrical geometry with the subsequent differential equations derived. Apart from being simple and accurate, the setup is also highly economic making it a more viable choice. This experimental model could be used for alloys, ceramics and composite materials of various combination ratios. Keywords: Thermal diffusivity, Experimental model.
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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.
Computational Analysis of Natural Convection in Spherical Annulus Using FEVIJMER
HEAT transfer by natural convection from a body to its finite enclosure is of importance
in nuclear reactor technology, electronic instrumentation packaging, aircraft cabin design, the
analysis of fluid suspension gyrocompasses, and numerous other practical situations. The steady
natural convection heat transfer of fluids between two concentric isothermal spheres is investigated
computationally with the help of FEV in ANSYS 14.5. The inner wall is subjected to a higher
temperature and outer is at room temperature. The steady behavior of the flow field and its
subsequent effect on the temperature distribution for different Rayleigh numbers and radius ratios
are analyzed.
Bossious boundary condition is taken for natural convection and which is solved in fluent
module. Steady solutions of the entire flow field is obtained for Rayleigh number (5x101<ra><105),><rr><3). The result shows that the Rayleigh number and
radius ratio have a profound influence on the temperature and flow fields and Prandlt number has
very negligible effect. The results of average Nusselt numbers are also compared with those of
previous numerical investigations. Excellent agreement is obtained.
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.
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An analysis is carried out to investigate the influence of the prominent magnetic effect on mixed convection heat and mass transfer in the boundary layer region of a semi-infinite vertical flat plate in a nanofluid under the convective boundary conditions. The transformed boundary layer,ordinary differential equations are solved numerically using Runge-Kutta Fourth order method.
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...IJERA Editor
This paper presents a study of MHD free convection flow of an electrically conducting incompressible fluid with
variable viscosity about an isothermal truncated cone in the presence of heat generation or absorption. The fluid
viscosity is assumed to vary as a inverse linear function of temperature. The non-linear coupled partial
differential equations governing the flow and heat transfer have been solved numerically by using an implicit
finite - difference scheme along with quasilinearization technique. The non-similar solutions have been obtained
for the problem, overcoming numerical difficulties near the leading edge and in the downstream regime. Results
indicate that skin friction and heat transfer are strongly affected by, both, viscosity-variation parameter and
magnetic field. In fact, the transverse magnetic field influences the momentum and thermal fields, considerably.
Further, skin friction is found to decrease and heat transfer increases near the leading edge. Also, it is found that
the direction of heat transfer gets reversed during heat generation.
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...IJERA Editor
An analysis is made for the two-dimensional laminar boundary layer flow of a viscous, incompressible
fluid,along an infinite porous hot horizontal continuous moving plate. The governing system of partial
differential equations was transformed into ordinary differential equations before being solve by Natural
transformation. The effects of various physical parameters, such as Eckert number Ec , Prandtlnumber Pr ,
plate velocity α and heat source/sink parameter Sare presented and discussed. It is found that the plate velocity
significantly effects the flow and heat transfer.
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.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
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Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
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When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
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Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
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Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Cosmetic shop management system project report.pdf
Slow steady motion of a thermo viscous fluid between
1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 294
SLOW STEADY MOTION OF A THERMO-VISCOUS FLUID BETWEEN
TWO PARALLEL PLATES WITH CONSTANT PRESSURE AND
TEMPERATURE GRADIENTS
J.Srinivas1
, N.Pothanna2
, P. Nageswara Rao3
, N. Ch. Pattabhi Ramacharyulu4
1, 2, 3
Department of Humanities & Science, VNRVJIET, A.P. India
4
Former faculty, Department of Mathematics, NIT, Warangal, A.P, India.
joshi_seenu@yahoo.com, pothareddy81@gmail.com, nageswararao_p@vnrvjiet.in, pattabhi1933@yahoo.com
Abstract
In this paper, the slow steady motion of a second order thermo-viscous fluid between two parallel plates is examined. The closed form
solutions of the velocity and temperature distributions are obtained when thermo-stress coefficient is far less compared to strain
thermal conductivity coefficient and coefficient of cross viscosity for the following two cases: (i) when the upper plate is in relative
motion and (ii) when the upper plate is thermally insulated. The heat transfer coefficient on the upper plate , The mean Bulk
temperature and the transverse force perpendicular to the flow direction are also calculated. It is observed that forces are generated
in transverse directions which are special feature of these types of fluids. The effect of various flow parameters on the flow field have
been discussed with the help of graphical illustrations.
Keywords: Thermo-viscous fluids, Strain thermal conductivity coefficient and Thermo stress Coefficient.
----------------------------------------------------------------------***------------------------------------------------------------------------
1. INTRODUCTION
The non-Newtonian nature of materials has been the subject of
extensive study for over one and half centuries. It is only in
last seven decades that serious attempts have been made to
extend these investigations in the realm of non-linearity. The
failure of the linear theories in predicting to a reasonable
extent the mechanical behavior of materials such as liquid
polymers, fluid plastic, the molten metal’s etc subjected to
stresses has been the motivating force behind study of the non-
linear theories for material description. A non- linear
generalization of the Voigt type materials was proposed by
Rivlin [16] and Eringen [4]. Some of the non-liner theories
proposed so far (listed in references) have not taken into
account the strong dependence of visco-elastic behaviour upon
thermal conduction i.e. interaction/interrelation between
mechanical and non mechanical (such as thermal, chemical,
electromagnetic etc.) effects even though the large amount
data of experimental evidence indicate a strong dependence of
visco-elastic nature of the fluid upon thermal behavior ( Ferry
[5] ).
The development of non-linear theory reflecting the
interaction/interrelation between thermal and viscous effects
has been preliminarily studied by Koh and Eringen [9] and
Coleman and Mizel [3] . A systematic rational approach for
such a class of fluids has been developed by Green and
Nagdhi [6]. In 1965 Kelly [10] examined some simple shear
flows of second order thermo-viscous fluids . Nageswara Rao
and Pattabhi Ramacharyulu [14] later studied some steady
state problems dealing with certain flows of thermo-viscous
fluids. Some more problems K.Anuradha [1] and
E.Nagaratnam [12] studied in plane, cylindrical and spherical
geometries.
Flows of incompressible homogenous thermo-viscous fluids
satisfy the following basic equations.
Equation of Continuity:
, = 0
Equation of Momentum:
jjiikik
i
tFvv
t
v
,, +=
+
∂
∂
ρρ
Equation of Energy:
ργθρ +−= iiijij qdtc ,
&
Where
th
i iF = Component of external force per unit mass
=c Specific heat
2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 295
=γ Thermal energy source per unit mass
and
th
i iq = Component of heat flux bivector = 2/jkijk h∈
Solving a specific boundary value problem would mean,
finding the solution of these equations with appropriate
boundary conditions such as the no slip condition (i.e. the
velocity of fluid relative to the boundary is zero) and the
prescription of the wall temperature. The later condition may
be replaced by the prescription of heat flux on the boundary.
2. MATHEMATICAL FORMULATION AND
SOLUTION OF THE PROBLEM
With reference to the Cartesian coordinates system O(x, y, z)
with origin on the lower plate, the X-axis in the direction of
flow. The flow is characterized by the velocity field
[ ( ), 0, 0 ] and temperature by (y).
Y = , =
Temperature )(yθ
Pressure Gradient h Fluid Velocity ( )
= 0 =
X
Fig 1: Flow Configuration
In the absence of any external force in the direction of flow,
the equations of motion reduces to
0 = - + - 6 (1)
c + Fy = 0 (2)
8 + Fz = 0 (3)
In the absence of any heat source, the energy equation reduces
to
c u = - 6 +k + 3
(4)
together with the boundary conditions:
(0) = 0 , (0) = (5)
(ℎ) = , (ℎ) = (6)
Introducing the following non-dimensional quantities,
= ℎ , = ( / ℎ) , =
! "
#! "
, = #! "
$
%
and - =
&
'$( %
The equation (1) and (4) can be reduced to
0 =% +
) *
)+
-,-%
) .
)+
(7)
and
% = , /
01
02
− ,-4
)*
)+
).
)+
5 +
6
) .
)+
+ 784
) *
)+
(8)
With
9: =
;&
<
(Prandtle number), S=
'$="
&
, B3 =
>(
'$ ;
,
A1 =
&
'$ ;( #! ")
and A6 =
?@(A#BA")
&
where
4 is Non-Dimensional constant pressure gradient and
4 is Non-Dimensional constant temperature gradient.
The boundary conditions are U(0) = 0 , U(1) =
T(0) = 0 , T(1) = 1
3. CASE-I: WHEN UPPER PLATE IS IN
RELATIVE MOTION
Assuming that the thermo – stress coefficient 6 is far less
when compared to strain thermal conductivity coefficient 8
and coefficient of cross viscosity c.
The equations (7) and (8) reduces to
0 = % +
) *
)+
(9)
% = ,
01
02
+
6
) .
)+
+784
) *
)+
(10)
The boundary conditions reduces to
U(0) = 0 , T(0) = 0 (11)
U(1) = , T(1) = 1 (12)
3. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 296
i.e. the upper plate is moving with a given velocity and the
two plates are maintained at different temperatures.
The equations (9) and (10) together with the boundary
conditions (11) and (12) yield the velocity
( ) =
4
2
(1 − ) +
And the temperature
( ) = + , F: G
H#
I
(2 − 2 + 1) +
*"
−
0416 2 −1 1− +429K 4124 2− −1−
06 1+ − 73422 1−
The heat transfer coefficient i.e. Nussult number “Nu” on the
upper plate is
Nu=
).
)+ +N
= −
O#P6
I
Q(4 − 2 ) + 8 S +
H P6
I
Q4 + 8 + 12784 S + 1
Which depends on constant pressure gradient4 , the relative
velocity of upper plate and 78 the strain thermal
conductivity coefficient, constant temperature gradient 4 and
the prandtle number 9:.
Also the mean Bulk temperature =
T *. )+
#
"
T * )+
#
"
=
U
V
V
V
V
V
V
V
W
X
1
3Y + , 9: Z
4
480
Y + 24
Y −
4
360Y [
−4 9:
4
240Y − 45
Y +
784
24Y
]
+4 X
1
24Y + , 9: Z
4
2520
Y + 120
Y −
4
360Y [
−4 9:
174
20160Y − 240Y +
784
240Y
]
_
`
`
`
`
`
`
`
a
+
4
6
b
The forces generated in transverse direction are
c = 2 ;
&
' $d G +
H#
(2 − 1)e 4
cf =
?g & ( #! ")
$d'
=
h
i
i
i
i
i
i
i
j
i
i
i
i
i
i
i
k
%
h
i
i
i
i
j
i
i
i
i
k
1 + , 9: X
4
6
(1 + 6 − 8 8)
+
4
3
2 − 9
+9
]
4 9:
h
i
j
i
k−
4
24
(1 + 6 − 24 + 16 8)
+
6
(1 + 3 − 9 )
−
784
2
(−1 + + 2 )
m
i
n
i
o
m
i
i
i
i
n
i
i
i
i
o
− 9:
h
i
i
j
i
i
k
, X
4
4
(1 − 4 + 4 ) −
−3 4 (−1 + 2 )
]
+4 p
4
2
( − ) −
+784
q
m
i
i
n
i
i
o
m
i
i
i
i
i
i
i
n
i
i
i
i
i
i
i
o
It is observed that these forces generated in transverse
directions depends on the cross viscosity ; and on r the
thermo stress viscosity.
4. CASE-II: WHEN UPPER PLATE IS
INSULATED
Y = ,
)
)
= 0
Temperature )(yθ
Pressure Gradient h Fluid Velocity ( )
= 0 , =
X
Fig.2: Flow Configuration
The equations of motion and energy reduces to
0 = % +
) *
)+
-,-%
) .
)+
(13)
% =A1/
01
02
− A-C
)*
)+
).
)+
5 +
6
) .
)+
+ B3C2
) *
)+
(14)
Together with the boundary conditions:
U(0) = 0 , T(0) = 0 (15)
U(1) = ,
).
)+ +N
= 0 (16)
4. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 297
The velocity field is same as in Newtonian case and is given
by
( ) =
4
2
1 3 E
And the temperature field is given by
9:4 u
4
24
– 8
E 2 3 2 E
6
3 3
w
+, 9: G
H#
I
2 3 3 E 4 3 2 8
3
H#*"
-
3 3
2 E 022 2− + 7341429K2 −2
The forces generated in transverse direction are
c 2 ; I
/ E
4
2
2 3 1 5 4
cf=
4 r
U
V
V
V
V
V
V
V
V
V
V
V
W
9:4 X
%
12
1 3 3 E 6 3 4 8
E
2
1 E 3 3
]
E9:A
U
V
V
W
4
24
32 8
3 48 E 24 3 5
34 35 E 5 3 1 E
2
4 3 3 _
`
`
a
E
9:784 4
2
3 3 4 _
`
`
`
`
`
`
`
`
`
`
`
a
E
U
V
V
V
V
V
W 9:4 x
;#
3 E E y
39:A G
H#
I
4 3 4 E 1 E 4 1 3 2 E e
E 9:784 4 _
`
`
`
`
`
a
Which depends on r , 78 , pressure gradient, given velocity
of upper plate and the constant temperature gradient.
5. RESULTS AND DISCUSSION
Numerical estimates of the velocity and temperature fields
was carried for different values of =(0 ,1) by taking
4 1, A 1, 9: 1 and these are illustrated graphically.
When the upper plate is fixed, thermally insulated or not, the
velocity is parabolic in general. When the upper plate is in
relative motion with a given velocity, the velocity of the fluid
is steadily increased so as to attain the velocity of the upper
plate, this is observed from the Fig 3.
Fig 3: Velocity Profile
The temperature distributions for different values of B3 are
illustrated graphically in Fig. 4, 5 and 6
When the upper plate is not thermally insulated temperature
increases gradually to attain the temperature of the upper plate
and when it is thermally insulated temperature decreases.
Fig 4: Temperature Profile
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
U(Y)
Y
VELOCITY PROFILE
UO=0
U0=1
-0.5 0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
T(Y)
Y
TEMPERATURE PROFILE
UO=0,B3=1
no insulation
with insulation
5. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 298
Fig.5: Temperature Profile
Fig.6: Temperature Profile
When the upper plate is in relative motion, temperature
distributions for different values of B3 are illustrated
graphically in the figures 7, 8 and 9.
When the upper plate is not thermally insulated temperature
increases gradually to attain the temperature of the upper plate
and when it is thermally insulated temperature decreases.
Fig.7: Temperature Profile
Fig 8: Temperature Profile
Fig.9: Temperature Profile
-1.5 -1 -0.5 0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
T(Y)
Y
TEMPERATURE PROFILE
UO=0,B3=3
no insulation
with insulation
-2.5 -2 -1.5 -1 -0.5 0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
T(Y)
Y
TEMPERATURE PROFILE
UO=0,B3=5
no insulation
with insulation
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
T(Y)
Y
TEMPERATURE PROFILE
UO=1,B3=1
no insulation
with insulation
-1.5 -1 -0.5 0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
T(Y)
Y TEMPERATURE PROFILE
UO=1,B3=3
no insulation
with insulation
-2.5 -2 -1.5 -1 -0.5 0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
TEMPERATURE PROFILE
UO=1,B3=5
T(Y)
Y
no insulation
with insulation
6. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 299
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