Abstract A numerical algorithm is presented for studying laminar convection flow and heat transfer over an isothermal vertical horizontal plate embedded in a saturated porous medium. 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 are illustrated graphically. Heat transfer parameters are derived. Keywords
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.
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
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
Implementation of finite volume method in creeping flow around a circular cyl...eSAT Journals
Abstract
A Finite Volume Method have been performed in simulation of creeping flow around a circular cylinder contained between plates. By adopting the SIMPLE algorithm the governing equations are solved together with Papanastasious regularization. Apparent viscosity is calculated on each iteration by using forward difference operation. Yield surfaces are studied over the range of Oldroyd number 10≤Od≤〖10〗^4. The model results are found to be in good agreement with obtained results of the other method.
Keywords: Creeping flow, Finite Volume Method, Yielded and unyielded zone, Bingham number.
Couette type mhd flow with suction and injection under constant pressure grad...eSAT Journals
Abstract The unsteady magnetohydrodynamic Couette-type flow of an electrically conducting, viscous and incompressible fluid bounded by two parallel non- conducting porous plates under the influence of a constant pressure gradient and a transversely applied uniform magnetic field is studied with heat transfer. A uniform suction on the upper plate and an injection on the lower plate are applied perpendicularly to the plates keeping the rates of suction and injection the same. The two plates are maintained at different but constant temperatures. The governing nonlinear partial differential equations are solved by both analytical as well as numerical methods. An exact solution for the velocity of the fluid has been obtained by Laplace transform method. The Crank-Nicholson implicit method is used to obtain the unsteady fluid velocity profile. The transient part of the fluid velocity tends to zero as the time t tends to infinity. The energy equation is solved by the finite difference method .The effect of the magnetic field coupled with suction and injection on the velocity and temperature distributions is examined graphically and discussed in the present work. Keywords: Magnetohydrodynamics, Transverse magnetic field, Suction and injection, Constant pressure gradient, Transient state flow, Crank-Nicholson implicit method, Finite difference method.
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.
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
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
Implementation of finite volume method in creeping flow around a circular cyl...eSAT Journals
Abstract
A Finite Volume Method have been performed in simulation of creeping flow around a circular cylinder contained between plates. By adopting the SIMPLE algorithm the governing equations are solved together with Papanastasious regularization. Apparent viscosity is calculated on each iteration by using forward difference operation. Yield surfaces are studied over the range of Oldroyd number 10≤Od≤〖10〗^4. The model results are found to be in good agreement with obtained results of the other method.
Keywords: Creeping flow, Finite Volume Method, Yielded and unyielded zone, Bingham number.
Couette type mhd flow with suction and injection under constant pressure grad...eSAT Journals
Abstract The unsteady magnetohydrodynamic Couette-type flow of an electrically conducting, viscous and incompressible fluid bounded by two parallel non- conducting porous plates under the influence of a constant pressure gradient and a transversely applied uniform magnetic field is studied with heat transfer. A uniform suction on the upper plate and an injection on the lower plate are applied perpendicularly to the plates keeping the rates of suction and injection the same. The two plates are maintained at different but constant temperatures. The governing nonlinear partial differential equations are solved by both analytical as well as numerical methods. An exact solution for the velocity of the fluid has been obtained by Laplace transform method. The Crank-Nicholson implicit method is used to obtain the unsteady fluid velocity profile. The transient part of the fluid velocity tends to zero as the time t tends to infinity. The energy equation is solved by the finite difference method .The effect of the magnetic field coupled with suction and injection on the velocity and temperature distributions is examined graphically and discussed in the present work. Keywords: Magnetohydrodynamics, Transverse magnetic field, Suction and injection, Constant pressure gradient, Transient state flow, Crank-Nicholson implicit method, Finite difference method.
Effect of Magnetic Field on Peristaltic Flow of Williamson Fluid in a Symmetr...IOSRJM
This paper deals with the influence of magnetic field on peristaltic flow of an incompressible Williamson fluid in a symmetric channel with heat and mass transfer. Convective conditions of heat and mass transfer are employed. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...IJERA Editor
This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law
fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations
are reduced to non-linear ordinary differential equations by means of similarity transformations. These
equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various
flow parameters in the form of dimensionless quantities on the flow field are discussed and presented
graphically.
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.
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.
Thermal Stress in a Half-Space with Mixed Boundary Conditions due to Time Dep...iosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Application of CAD and SLA Method in Dental ProsthesisIDES Editor
Placement of dental implants requires precise
planning that accounts for anatomic limitations and
restorative goals. Diagnosis can be made with the assistance
of computerized tomographic scanning, but transfer of
planning to the surgical field is limited. Precise implant
placement no longer relies upon so called mental-navigation
but rather can be computer guided, based on a three
dimensional prosthetically directed plan. Recently, novel CAD/
CAM techniques such as stereolithographic rapid prototyping
have been developed to build surgical guides in an attempt to
improve precision of implant placement. The purpose of this
paper is to discuss the use of scanning equipments to transfer
clinically relevant prosthetic information which can be used
for fabrication of stereolithographic medical models and
surgical guides. The proposed method provides solid evidence
that computer-aided design and manufacturing technologies
may become a new avenue for custom-made dental implants
design, analysis, and production in the 21st century.
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.
Effect of Magnetic Field on Peristaltic Flow of Williamson Fluid in a Symmetr...IOSRJM
This paper deals with the influence of magnetic field on peristaltic flow of an incompressible Williamson fluid in a symmetric channel with heat and mass transfer. Convective conditions of heat and mass transfer are employed. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...IJERA Editor
This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law
fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations
are reduced to non-linear ordinary differential equations by means of similarity transformations. These
equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various
flow parameters in the form of dimensionless quantities on the flow field are discussed and presented
graphically.
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.
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.
Thermal Stress in a Half-Space with Mixed Boundary Conditions due to Time Dep...iosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Application of CAD and SLA Method in Dental ProsthesisIDES Editor
Placement of dental implants requires precise
planning that accounts for anatomic limitations and
restorative goals. Diagnosis can be made with the assistance
of computerized tomographic scanning, but transfer of
planning to the surgical field is limited. Precise implant
placement no longer relies upon so called mental-navigation
but rather can be computer guided, based on a three
dimensional prosthetically directed plan. Recently, novel CAD/
CAM techniques such as stereolithographic rapid prototyping
have been developed to build surgical guides in an attempt to
improve precision of implant placement. The purpose of this
paper is to discuss the use of scanning equipments to transfer
clinically relevant prosthetic information which can be used
for fabrication of stereolithographic medical models and
surgical guides. The proposed method provides solid evidence
that computer-aided design and manufacturing technologies
may become a new avenue for custom-made dental implants
design, analysis, and production in the 21st century.
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.
Similarity Solution of an Unsteady Heat and Mass Transfer Boundary Layer Flow...iosrjce
The unsteady hydromagnetic boundary layer flow of an incompressible and electrically conducting
fluid through a porous medium bounded by a moving surface has been considered. It is assumed that the moving
surface has a velocity profile with respect to time and fluid flow is taken under the influence of a transverse
magnetic field. The similarity solution is used to transform the system of partial differential equations,
describing the problem under consideration, into a boundary value problem of coupled ordinary differential
equations and an efficient numerical technique is implemented to solve the reduced system. The effects of the
parameters such as Magnetic parameter, Prandtl number and Eckert number are discussed graphically on
velocity and temperature distributions
GDQ SIMULATION FOR FLOW AND HEAT TRANSFER OF A NANOFLUID OVER A NONLINEARLY S...AEIJjournal2
This paper presents the generalized differential quadrature (GDQ) simulation for analysis of a nanofluid
over a nonlinearly stretching sheet. The obtained governing equations of flow and heat transfer are
discretized by GDQ method and then are solved by Newton-Raphson method. The effects of stretching
parameter, Brownian motion number (Nb), Thermophoresis number (Nt) and Lewis number (Le), on the
concentration distribution and temperature distribution are evaluated. The obtained results exhibit that
Chemical Reaction on Heat and Mass TransferFlow through an Infinite Inclined ...iosrjce
The numerical studies are performed to examine the mass transfer flow with thermal diffusion and
diffusion thermo effect past an infinite, inclined vertical plate in a porous medium in the presence of chemical
reaction. First of all, the governing equations are transformed to a system of dimensionless coupled partial
equations. Explicit finite difference method has been used to solve these dimensionless equations for momentum,
concentration and energy equations. During the course of discussion, it is found that various parameters related
to the problem influence the calculated result. Finally, the profiles of velocity, concentration and temperature
are analyzed and illustrated with graphs.
The effect of magnetic field on the boundary layer flow over a stretching she...IAEME Publication
The boundary layer flow created due to a linearly stretching sheet in a nanofluid is studied numerically. The boundary value problem consisting of nonlinear partial differential equations are converted into nonlinear ordinary differential equations, using similarity transformation and are solved numerically using Runge-Kutta Fourth order method, with shooting technique. The transport equations include the effects of Brownian motion and thermophoresis.
Unsteady Mhd free Convective flow in a Rotating System with Dufour and Soret ...IOSRJM
Numerical analysis is used to examine the unsteady MHD free convection and mass transfer fluid flow through a porous medium in a rotating system. Impulsively started plate moving its individual plane is considered. Similarity equations of the corresponding momentum, energy, and concentration equations are derived by introducing a time dependent length scale which infect plays the role of a resemblance parameter. The velocity component is taken to be inversely proportional to this parameter. The effects on the velocity, temperature, concentration, local skin-friction coefficients, Nusselt number, Prandl number, Dufour, Soret number and the Sherwood number of the various important parameters entering into the problem separately are discussed with the help of graphs.
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
Pressure Gradient Influence on MHD Flow for Generalized Burgers’ Fluid with S...IJERA Editor
This paper presents a research for magnetohydrodynamic (MHD) flow of an incompressible generalized
Burgers’ fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the
no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is
introduced to establish the constitutive relationship of the generalized Burgers’ fluid. By using the discrete
Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear
stress are obtained in terms of Fox H- function for the following two problems: (i) flow due to a constant
pressure gradient, and (ii) flow due to due to a sinusoidal pressure gradient. The solutions for no – slip condition
and no magnetic field, can be derived as special cases of our solutions. Furthermore, the effects of various
parameters on the velocity distribution characteristics are analyzed and discussed in detail. Comparison between
the two cases is also made.
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...theijes
A steady two-dimensional MHD free convection and mass transfer flow past an inclined vertical surface in the presence of heat generation and a porous medium have been studied numerically when the fluid viscosity and thermal conductivity are assumed to be vary as inverse linear function of temperature. The governing partial differential equations are reduced to a system of ordinary differential equations by introducing similarity transformations. The non-linear similarity equations are solved numerically by applying the Runge-Kutta method of fourth order with shooting technique. The numerical results are presented graphically to illustrate influence of different values of the parameters on the velocity, temperature and concentration profiles. Skin friction, Nusselt number and Sherwood number are also completed and presented in tabular form.
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.
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.
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
Unsteady Free Convection MHD Flow of an Incompressible Electrically Conductin...IJERA Editor
In this paper we investigate unsteady free convection MHD flow of an incompressible viscous electrically
conducting fluid through porous medium under the influence of uniform transverse magnetic field between two
heated vertical plate with one plate is adiabatic. The governing equations of velocity and temperature fields with
appropriate boundary conditions are solved by the Integral Transform Technique. The obtained results of
velocity and temperature distributions are shown graphically and are discussed on the basis of it. The effects of
Hartmann number, Darcy parameter, Prandtl number and the decay factor, and effects of adiabatic plate on the
velocity and temperature fields are discussed.
Similar to Numerical simulation on laminar convection flow and heat transfer over an isothermal vertical plate embedded in a saturated porous medium (20)
Mechanical properties of hybrid fiber reinforced concrete for pavementseSAT Journals
Abstract
The effect of addition of mono fibers and hybrid fibers on the mechanical properties of concrete mixture is studied in the present
investigation. Steel fibers of 1% and polypropylene fibers 0.036% were added individually to the concrete mixture as mono fibers and
then they were added together to form a hybrid fiber reinforced concrete. Mechanical properties such as compressive, split tensile and
flexural strength were determined. The results show that hybrid fibers improve the compressive strength marginally as compared to
mono fibers. Whereas, hybridization improves split tensile strength and flexural strength noticeably.
Keywords:-Hybridization, mono fibers, steel fiber, polypropylene fiber, Improvement in mechanical properties.
Material management in construction – a case studyeSAT Journals
Abstract
The objective of the present study is to understand about all the problems occurring in the company because of improper application
of material management. In construction project operation, often there is a project cost variance in terms of the material, equipments,
manpower, subcontractor, overhead cost, and general condition. Material is the main component in construction projects. Therefore,
if the material management is not properly managed it will create a project cost variance. Project cost can be controlled by taking
corrective actions towards the cost variance. Therefore a methodology is used to diagnose and evaluate the procurement process
involved in material management and launch a continuous improvement was developed and applied. A thorough study was carried
out along with study of cases, surveys and interviews to professionals involved in this area. As a result, a methodology for diagnosis
and improvement was proposed and tested in selected projects. The results obtained show that the main problem of procurement is
related to schedule delays and lack of specified quality for the project. To prevent this situation it is often necessary to dedicate
important resources like money, personnel, time, etc. To monitor and control the process. A great potential for improvement was
detected if state of the art technologies such as, electronic mail, electronic data interchange (EDI), and analysis were applied to the
procurement process. These helped to eliminate the root causes for many types of problems that were detected.
Managing drought short term strategies in semi arid regions a case studyeSAT Journals
Abstract
Drought management needs multidisciplinary action. Interdisciplinary efforts among the experts in various fields of the droughts
prone areas are helpful to achieve tangible and permanent solution for this recurring problem. The Gulbarga district having the total
area around 16, 240 sq.km, and accounts 8.45 per cent of the Karnataka state area. The district has been situated with latitude 17º 19'
60" North and longitude of 76 º 49' 60" east. The district is situated entirely on the Deccan plateau positioned at a height of 300 to
750 m above MSL. Sub-tropical, semi-arid type is one among the drought prone districts of Karnataka State. The drought
management is very important for a district like Gulbarga. In this paper various short term strategies are discussed to mitigate the
drought condition in the district.
Keywords: Drought, South-West monsoon, Semi-Arid, Rainfall, Strategies etc.
Life cycle cost analysis of overlay for an urban road in bangaloreeSAT Journals
Abstract
Pavements are subjected to severe condition of stresses and weathering effects from the day they are constructed and opened to traffic
mainly due to its fatigue behavior and environmental effects. Therefore, pavement rehabilitation is one of the most important
components of entire road systems. This paper highlights the design of concrete pavement with added mono fibers like polypropylene,
steel and hybrid fibres for a widened portion of existing concrete pavement and various overlay alternatives for an existing
bituminous pavement in an urban road in Bangalore. Along with this, Life cycle cost analyses at these sections are done by Net
Present Value (NPV) method to identify the most feasible option. The results show that though the initial cost of construction of
concrete overlay is high, over a period of time it prove to be better than the bituminous overlay considering the whole life cycle cost.
The economic analysis also indicates that, out of the three fibre options, hybrid reinforced concrete would be economical without
compromising the performance of the pavement.
Keywords: - Fatigue, Life cycle cost analysis, Net Present Value method, Overlay, Rehabilitation
Laboratory studies of dense bituminous mixes ii with reclaimed asphalt materialseSAT Journals
Abstract
The issue of growing demand on our nation’s roadways over that past couple of decades, decreasing budgetary funds, and the need to
provide a safe, efficient, and cost effective roadway system has led to a dramatic increase in the need to rehabilitate our existing
pavements and the issue of building sustainable road infrastructure in India. With these emergency of the mentioned needs and this
are today’s burning issue and has become the purpose of the study.
In the present study, the samples of existing bituminous layer materials were collected from NH-48(Devahalli to Hassan) site.The
mixtures were designed by Marshall Method as per Asphalt institute (MS-II) at 20% and 30% Reclaimed Asphalt Pavement (RAP).
RAP material was blended with virgin aggregate such that all specimens tested for the, Dense Bituminous Macadam-II (DBM-II)
gradation as per Ministry of Roads, Transport, and Highways (MoRT&H) and cost analysis were carried out to know the economics.
Laboratory results and analysis showed the use of recycled materials showed significant variability in Marshall Stability, and the
variability increased with the increase in RAP content. The saving can be realized from utilization of recycled materials as per the
methodology, the reduction in the total cost is 19%, 30%, comparing with the virgin mixes.
Keywords: Reclaimed Asphalt Pavement, Marshall Stability, MS-II, Dense Bituminous Macadam-II
Laboratory investigation of expansive soil stabilized with natural inorganic ...eSAT Journals
Abstract
Soil stabilization has proven to be one of the oldest techniques to improve the soil properties. Literature review conducted revealed
that uses of natural inorganic stabilizers are found to be one of the best options for soil stabilization. In this regard an attempt has
been made to evaluate the influence of RBI-81 stabilizer on properties of black cotton soil through laboratory investigations. Black
cotton soil with varying percentages of RBI-81 viz., 0, 0.5, 1, 1.5, 2, and 2.5 percent were studied for moisture density relationships
and strength behaviour of soils. Also the effect of curing period was evaluated as literature review clearly emphasized the strength
gain of soils stabilized with RBI-81 over a period of time. The results obtained shows that the unconfined compressive strength of
specimens treated with RBI-81 increased approximately by 250% for a curing period of 28 days as compared to virgin soil. Further
the CBR value improved approximately by 400%. The studies indicated an increasing trend for soil strength behaviour with
increasing percentage of RBI-81 suggesting its potential applications in soil stabilization.
Influence of reinforcement on the behavior of hollow concrete block masonry p...eSAT Journals
Abstract
Reinforced masonry was developed to exploit the strength potential of masonry and to solve its lack of tensile strength. Experimental
and analytical studies have been carried out to investigate the effect of reinforcement on the behavior of hollow concrete block
masonry prisms under compression and to predict ultimate failure compressive strength. In the numerical program, three dimensional
non-linear finite elements (FE) model based on the micro-modeling approach is developed for both unreinforced and reinforced
masonry prisms using ANSYS (14.5). The proposed FE model uses multi-linear stress-strain relationships to model the non-linear
behavior of hollow concrete block, mortar, and grout. Willam-Warnke’s five parameter failure theory has been adopted to model the
failure of masonry materials. The comparison of the numerical and experimental results indicates that the FE models can successfully
capture the highly nonlinear behavior of the physical specimens and accurately predict their strength and failure mechanisms.
Keywords: Structural masonry, Hollow concrete block prism, grout, Compression failure, Finite element method,
Numerical modeling.
Influence of compaction energy on soil stabilized with chemical stabilizereSAT Journals
Abstract
Increase in traffic along with heavier magnitude of wheel loads cause rapid deterioration in pavements. There is a need to improve
density, strength of soil subgrade and other pavement layers. In this study an attempt is made to improve the properties of locally
available loamy soil using twin approaches viz., i) increasing the compaction of soil and ii) treating the soil with chemical stabilizer.
Laboratory studies are carried out on both untreated and treated soil samples compacted by different compaction efforts. Studies
show that increase in compaction effort results in increase in density of soil. However in soil treated with chemical stabilizer, rate of
increase in density is not significant. The soil treated with chemical stabilizer exhibits improvement in both strength and performance
properties.
Keywords: compaction, density, subgradestabilization, resilient modulus
Geographical information system (gis) for water resources managementeSAT Journals
Abstract
Water resources projects are inherited with overlapping and at times conflicting objectives. These projects are often of varied sizes
ranging from major projects with command areas of millions of hectares to very small projects implemented at the local level. Thus,
in all these projects there is seldom proper coordination which is essential for ensuring collective sustainability.
Integrated watershed development and management is the accepted answer but in turn requires a comprehensive framework that can
enable planning process involving all the stakeholders at different levels and scales is compulsory. Such a unified hydrological
framework is essential to evaluate the cause and effect of all the proposed actions within the drainage basins.
The present paper describes a hydrological framework developed in the form of a Hydrologic Information System (HIS) which is
intended to meet the specific information needs of the various line departments of a typical State connected with water related aspects.
The HIS consist of a hydrologic information database coupled with tools for collating primary and secondary data and tools for
analyzing and visualizing the data and information. The HIS also incorporates hydrological model base for indirect assessment of
various entities of water balance in space and time. The framework would be maintained and updated to reflect fully the most
accurate ground truth data and the infrastructure requirements for planning and management.
Keywords: Hydrological Information System (HIS); WebGIS; Data Model; Web Mapping Services
Forest type mapping of bidar forest division, karnataka using geoinformatics ...eSAT Journals
Abstract
The study demonstrate the potentiality of satellite remote sensing technique for the generation of baseline information on forest types
including tree plantation details in Bidar forest division, Karnataka covering an area of 5814.60Sq.Kms. The Total Area of Bidar
forest division is 5814Sq.Kms analysis of the satellite data in the study area reveals that about 84% of the total area is Covered by
crop land, 1.778% of the area is covered by dry deciduous forest, 1.38 % of mixed plantation, which is very threatening to the
environmental stability of the forest, future plantation site has been mapped. With the use of latest Geo-informatics technology proper
and exact condition of the trees can be observed and necessary precautions can be taken for future plantation works in an appropriate
manner
Keywords:-RS, GIS, GPS, Forest Type, Tree Plantation
Factors influencing compressive strength of geopolymer concreteeSAT Journals
Abstract
To study effects of several factors on the properties of fly ash based geopolymer concrete on the compressive strength and also the
cost comparison with the normal concrete. The test variables were molarities of sodium hydroxide(NaOH) 8M,14M and 16M, ratio of
NaOH to sodium silicate (Na2SiO3) 1, 1.5, 2 and 2.5, alkaline liquid to fly ash ratio 0.35 and 0.40 and replacement of water in
Na2SiO3 solution by 10%, 20% and 30% were used in the present study. The test results indicated that the highest compressive
strength 54 MPa was observed for 16M of NaOH, ratio of NaOH to Na2SiO3 2.5 and alkaline liquid to fly ash ratio of 0.35. Lowest
compressive strength of 27 MPa was observed for 8M of NaOH, ratio of NaOH to Na2SiO3 is 1 and alkaline liquid to fly ash ratio of
0.40. Alkaline liquid to fly ash ratio of 0.35, water replacement of 10% and 30% for 8 and 16 molarity of NaOH and has resulted in
compressive strength of 36 MPa and 20 MPa respectively. Superplasticiser dosage of 2 % by weight of fly ash has given higher
strength in all cases.
Keywords: compressive strength, alkaline liquid, fly ash
Experimental investigation on circular hollow steel columns in filled with li...eSAT Journals
Abstract
Composite Circular hollow Steel tubes with and without GFRP infill for three different grades of Light weight concrete are tested for
ultimate load capacity and axial shortening , under Cyclic loading. Steel tubes are compared for different lengths, cross sections and
thickness. Specimens were tested separately after adopting Taguchi’s L9 (Latin Squares) Orthogonal array in order to save the initial
experimental cost on number of specimens and experimental duration. Analysis was carried out using ANN (Artificial Neural
Network) technique with the assistance of Mini Tab- a statistical soft tool. Comparison for predicted, experimental & ANN output is
obtained from linear regression plots. From this research study, it can be concluded that *Cross sectional area of steel tube has most
significant effect on ultimate load carrying capacity, *as length of steel tube increased- load carrying capacity decreased & *ANN
modeling predicted acceptable results. Thus ANN tool can be utilized for predicting ultimate load carrying capacity for composite
columns.
Keywords: Light weight concrete, GFRP, Artificial Neural Network, Linear Regression, Back propagation, orthogonal
Array, Latin Squares
Experimental behavior of circular hsscfrc filled steel tubular columns under ...eSAT Journals
Abstract
This paper presents an outlook on experimental behavior and a comparison with predicted formula on the behaviour of circular
concentrically loaded self-consolidating fibre reinforced concrete filled steel tube columns (HSSCFRC). Forty-five specimens were
tested. The main parameters varied in the tests are: (1) percentage of fiber (2) tube diameter or width to wall thickness ratio (D/t
from 15 to 25) (3) L/d ratio from 2.97 to 7.04 the results from these predictions were compared with the experimental data. The
experimental results) were also validated in this study.
Keywords: Self-compacting concrete; Concrete-filled steel tube; axial load behavior; Ultimate capacity.
Evaluation of punching shear in flat slabseSAT Journals
Abstract
Flat-slab construction has been widely used in construction today because of many advantages that it offers. The basic philosophy in
the design of flat slab is to consider only gravity forces; this method ignores the effect of punching shear due to unbalanced moments
at the slab column junction which is critical. An attempt has been made to generate generalized design sheets which accounts both
punching shear due to gravity loads and unbalanced moments for cases (a) interior column; (b) edge column (bending perpendicular
to shorter edge); (c) edge column (bending parallel to shorter edge); (d) corner column. These design sheets are prepared as per
codal provisions of IS 456-2000. These design sheets will be helpful in calculating the shear reinforcement to be provided at the
critical section which is ignored in many design offices. Apart from its usefulness in evaluating punching shear and the necessary
shear reinforcement, the design sheets developed will enable the designer to fix the depth of flat slab during the initial phase of the
design.
Keywords: Flat slabs, punching shear, unbalanced moment.
Evaluation of performance of intake tower dam for recent earthquake in indiaeSAT Journals
Abstract
Intake towers are typically tall, hollow, reinforced concrete structures and form entrance to reservoir outlet works. A parametric
study on dynamic behavior of circular cylindrical towers can be carried out to study the effect of depth of submergence, wall thickness
and slenderness ratio, and also effect on tower considering dynamic analysis for time history function of different soil condition and
by Goyal and Chopra accounting interaction effects of added hydrodynamic mass of surrounding and inside water in intake tower of
dam
Key words: Hydrodynamic mass, Depth of submergence, Reservoir, Time history analysis,
Evaluation of operational efficiency of urban road network using travel time ...eSAT Journals
Abstract
Efficiency of the road network system is analyzed by travel time reliability measures. The study overlooks on an important measure of
travel time reliability and prioritizing Tiruchirappalli road network. Traffic volume and travel time were collected using license plate
matching method. Travel time measures were estimated from average travel time and 95th travel time. Effect of non-motorized vehicle
on efficiency of road system was evaluated. Relation between buffer time index and traffic volume was created. Travel time model has
been developed and travel time measure was validated. Then service quality of road sections in network were graded based on
travel time reliability measures.
Keywords: Buffer Time Index (BTI); Average Travel Time (ATT); Travel Time Reliability (TTR); Buffer Time (BT).
Estimation of surface runoff in nallur amanikere watershed using scs cn methodeSAT Journals
Abstract
The development of watershed aims at productive utilization of all the available natural resources in the entire area extending from
ridge line to stream outlet. The per capita availability of land for cultivation has been decreasing over the years. Therefore, water and
the related land resources must be developed, utilized and managed in an integrated and comprehensive manner. Remote sensing and
GIS techniques are being increasingly used for planning, management and development of natural resources. The study area, Nallur
Amanikere watershed geographically lies between 110 38’ and 110 52’ N latitude and 760 30’ and 760 50’ E longitude with an area of
415.68 Sq. km. The thematic layers such as land use/land cover and soil maps were derived from remotely sensed data and overlayed
through ArcGIS software to assign the curve number on polygon wise. The daily rainfall data of six rain gauge stations in and around
the watershed (2001-2011) was used to estimate the daily runoff from the watershed using Soil Conservation Service - Curve Number
(SCS-CN) method. The runoff estimated from the SCS-CN model was then used to know the variation of runoff potential with different
land use/land cover and with different soil conditions.
Keywords: Watershed, Nallur watershed, Surface runoff, Rainfall-Runoff, SCS-CN, Remote Sensing, GIS.
Estimation of morphometric parameters and runoff using rs & gis techniqueseSAT Journals
Abstract
Land and water are the two vital natural resources, the optimal management of these resources with minimum adverse environmental
impact are essential not only for sustainable development but also for human survival. Satellite remote sensing with geographic
information system has a pragmatic approach to map and generate spatial input layers of predicting response behavior and yield of
watershed. Hence, in the present study an attempt has been made to understand the hydrological process of the catchment at the
watershed level by drawing the inferences from moprhometric analysis and runoff. The study area chosen for the present study is
Yagachi catchment situated in Chickamaglur and Hassan district lies geographically at a longitude 75⁰52’08.77”E and
13⁰10’50.77”N latitude. It covers an area of 559.493 Sq.km. Morphometric analysis is carried out to estimate morphometric
parameters at Micro-watershed to understand the hydrological response of the catchment at the Micro-watershed level. Daily runoff
is estimated using USDA SCS curve number model for a period of 10 years from 2001 to 2010. The rainfall runoff relationship of the
study shows there is a positive correlation.
Keywords: morphometric analysis, runoff, remote sensing and GIS, SCS - method
-
Effect of variation of plastic hinge length on the results of non linear anal...eSAT Journals
Abstract The nonlinear Static procedure also well known as pushover analysis is method where in monotonically increasing loads are applied to the structure till the structure is unable to resist any further load. It is a popular tool for seismic performance evaluation of existing and new structures. In literature lot of research has been carried out on conventional pushover analysis and after knowing deficiency efforts have been made to improve it. But actual test results to verify the analytically obtained pushover results are rarely available. It has been found that some amount of variation is always expected to exist in seismic demand prediction of pushover analysis. Initial study is carried out by considering user defined hinge properties and default hinge length. Attempt is being made to assess the variation of pushover analysis results by considering user defined hinge properties and various hinge length formulations available in literature and results compared with experimentally obtained results based on test carried out on a G+2 storied RCC framed structure. For the present study two geometric models viz bare frame and rigid frame model is considered and it is found that the results of pushover analysis are very sensitive to geometric model and hinge length adopted. Keywords: Pushover analysis, Base shear, Displacement, hinge length, moment curvature analysis
Effect of use of recycled materials on indirect tensile strength of asphalt c...eSAT Journals
Abstract
Depletion of natural resources and aggregate quarries for the road construction is a serious problem to procure materials. Hence
recycling or reuse of material is beneficial. On emphasizing development in sustainable construction in the present era, recycling of
asphalt pavements is one of the effective and proven rehabilitation processes. For the laboratory investigations reclaimed asphalt
pavement (RAP) from NH-4 and crumb rubber modified binder (CRMB-55) was used. Foundry waste was used as a replacement to
conventional filler. Laboratory tests were conducted on asphalt concrete mixes with 30, 40, 50, and 60 percent replacement with RAP.
These test results were compared with conventional mixes and asphalt concrete mixes with complete binder extracted RAP
aggregates. Mix design was carried out by Marshall Method. The Marshall Tests indicated highest stability values for asphalt
concrete (AC) mixes with 60% RAP. The optimum binder content (OBC) decreased with increased in RAP in AC mixes. The Indirect
Tensile Strength (ITS) for AC mixes with RAP also was found to be higher when compared to conventional AC mixes at 300C.
Keywords: Reclaimed asphalt pavement, Foundry waste, Recycling, Marshall Stability, Indirect tensile strength.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
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.
• 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.
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.
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
Fundamentals of Electric Drives and its applications.pptx
Numerical simulation on laminar convection flow and heat transfer over an isothermal vertical plate embedded in a saturated porous medium
1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 10 | OCT-2015, Available @ http://www.ijret.org 207
NUMERICAL SIMULATION ON LAMINAR CONVECTION FLOW
AND HEAT TRANSFER OVER AN ISOTHERMAL VERTICAL PLATE
EMBEDDED IN A SATURATED POROUS MEDIUM
Asish Mitra
Associate Prof. and HOD, Basic Science and Humanities Department, College of Engineering & Management,
Kolaghat. East Midnapur, India
mitra_asish@yahoo.com
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over an isothermal vertical horizontal
plate embedded in a saturated porous medium. 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 are illustrated graphically. Heat transfer
parameters are derived.
Keywords: Free Convection, Heat Transfer, Isothermal Vertical Plate, Matlab, Numerical Simulation, Porous
Medium.
---------------------------------------------------------------***---------------------------------------------------------------
List of Symbolsa1, a2 initial values eq (21)
f function defined in eq (13)
g gravitational acceleration, 9.81 m/s2
K permeability of the fluid, dimensionless
Nux Nusselt number at x, dimensionless
qw heat flux of the plate, W/m2
Ra Rayleigh number, dimensionless
T temperature, K
Tw surface temperature, K
T∞ free streams temperature, K
u velocity component in x, m/s
v velocity component in y, m/s
x coordinate from the leading edge, m
y coordinate normal to plate, m
z1, z2, z3, z4 variables, eq (18)
Greek Symbols
θ function defined in eq (12), dimensionless
β coefficient of thermal expansion, 1/K
δ boundary layer thickness, m
αa apparent thermal diffusivity, m2
/s
μf dynamic viscosity, N.s/m2
νf kinematic viscosity, m2
/s
η similarity variables, eq (14)
ψ stream function, m2
/s
ρf density, kg/m3
1. INTRODUCTION
There have been a number of studies on natural convection
over an isothermal vertical plate in a porous medium due to
its relevance to a variety of industrial applications and
naturally occurring processes, such as heat insulation by
fibrous materials, spreading of pollutants and convection
in the earth’s mantle, storage of agricultural products such
as fruits, vegetables and grains, ground water hydrology,
disposal of wastes, petroleum reservoir engineering,
mineral extraction and oil recovery system, recovery of
water for drinking and irrigation, salt water
encroachment into fresh water reservoirs, in biophysics-
life processes such as flow in the lungs and kidneys etc.
The earliest analytical investigation in this regard was a
similarity analysis of the boundary layer equations by P.
Cheng and W. J. Minkowycz, J. [1]. The problem is also
discussed by several authors [2-5]. The problem was
discussed in several text books [6-10].
In the present numerical investigation, a simple accurate
numerical simulation of laminar free-convection flow and
heat transfer over an isothermal horizontal plate is
developed.
The paper is organized as follows: Mathematical model of
the problem, its solution procedure, development of code in
Matlab, interpretation of the results, comparison with
Previous work.
2. MATHEMATICAL MODEL
We consider the natural convection about an isothermal
vertical impermeable flat plate immersed in a saturated
porous medium with constant permeability K. We
2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 10 | OCT-2015, Available @ http://www.ijret.org 208
assume the natural convection flow to be steady, laminar,
two-dimensional, having no dissipation, and the flow
through the porous medium is governed by Darcy’s law,
with constant properties, including density, with one
exception: the density difference
is to be
considered since it is this density difference between the
inside and the outside of the boundary layer that gives rise to
buoyancy force and sustains flow, known in the literature as
Boussinesq approximation. We take the direction along the
plate to be x, and the direction normal to surface to be y, as
shown in Fig 1.
Fig. 1 Physical Model and its coordinate system
The equations governing the flow are
u
x
v
y
0
1
u
gK T Tf
f
( )
2
u
T
x
v
T
y
T
y
a
2
2
3
The boundary conditions on the solution are:
At y=0: v=0, T=Tw
For large y: u→0, T→T∞ 4
The continuity equation (1) is automatically satisfied
through introduction of the stream function:
u
y
v
x
5
Eqs (2) and (3) can be written in terms of stream function:
y
gK T Tf
f
( )
6
y
T
x x
T
y
T
y
a
2
2
7
From (6), we can write
2
2
T
y
gK T
y
f
f
8
From scale analysis, it can be shown that
x
o Ra
( ).0 5
9
And
o Raa( ).0 5
10
Where
Ra
gK T T gK T T xf w
a f
w
a f
( ) ( )
11
is Darcy-modified Rayleigh number.
We expect that in the boundary layer, the stream function
and temperature profiles are similar:
T T
T T
y y
x
Ra
w
( ) ( ) ( ).0 5
12
and
a Ra
f0 5.
( )
13
where η is the similarity solution given by
y
x
Ra0 5.
14
With the help of eqs (12) and (13), eqs (8) and (7) can be
written as (with a prime denoting differentiation with
respect to η)
f 15
and
f
2 16
Hence the velocity boundary layer problem is reduced to an
ordinary differential equation (15) and energy eq (3) is also
reduced to an ordinary differential equation (16). This
confirms the assumption that velocity and temperature
profiles are similar. The appropriate boundary conditions (4)
are now:
y = 0: v = 0, T=Tw i.e., at η = 0: f = 0, θ = 1
large y: u→0, T→T∞ i.e., η large: f 0, 0
17
3. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 10 | OCT-2015, Available @ http://www.ijret.org 209
3. SOLUTION PROCEDURE
Eqs (15) and (16) are simultaneous nonlinear ordinary
differential equations for the velocity and temperature
functions, f and θ. No analytical solution is known, so
numerical integration is necessary. Values of f and θ at the
surface of the plate (y = 0), and that of f and far away
from the surface (y → ∞) are known.
3.1 Reduction of Equations to First-order System
This is done easily by defining new variables:
z f1
z z f2 1
z3
z z4 3 18
Therefore from eqs (15) and (16), we get the following set
of differential equations
z f1
z z f z2 1 4
z z3 4
z z
f z z
4 3
1 4
2 2
19
with the following boundary conditions:
z f1 0 0 0( ) ( )
z z f2 1 0( ) ( ) ( )
z3 0 0 1( ) ( )
z3 0( ) ( ) 20
Eqs (15) and (16) are second-order each and are replaced by
two first-order equations (21).
3.2 Solution to Initial Value Problems
To solve eqs (21), we denote the two unknown initial values
by a1 and a2, the set of initial conditions is then:
z f1 0 0 0( ) ( )
z z f a2 1 10 0 0( ) ( ) ( )
z3 0 0 1( ) ( )
z z a4 3 20 0 0( ) ( ) ( ) 21
If eqs (19) are solved with adaptive Runge-Kutta method
using the initial conditions in eq (21), the computed
boundary values at depend on the choice of a1 and
a2 respectively. We express this dependence as
z z f f a2 1 1 1( ) ( ) ( ) ( )
z f a3 2 2( ) ( ) ( ) 22
The correct choice of a1 and a2 yields the given boundary
conditions at ; that is, it satisfies the equations
f a1 1 0( )
f a2 2 0( ) 23
These nonlinear equations can be solved by the Newton-
Raphson method. A value of 10 is fine for infinity, even if
we integrate further nothing will change.
3.3 Program Details
This section describes a set of Matlab routines for the
solution of eqs (19) along with the initial conditions (21).
They are listed in Table 1.
Table 1. A set of Matlab routines used sequentially to solve
Equations (24).
Matlab
code
Brief Description
deqs.m Defines the differential
equations (19).
incond.m Describes initial values for
integration, a1 and a2 are guessed
values, eq (21)
runKut5.m Integrates as initial value
problem using adaptive Runge-
Kutta method.
residual.m Provides boundary residuals and
approximate solutions.
newtonraph
son.m
Provides correct values a1 and a2
using approximate solutions
from residual.m
runKut5.m Again integrates eqs (19) using
correct values of a1 and a2.
The final output of the code runKut5.m gives the tabulated
values of f , f for velocity profile, and and for
temperature profiles as function of η.
4. INTERPRETATION OF THE RESULTS
Physical quantities are related to the dimensionless functions
f and through eqs (12), (13) and (14). f and are now
known.
4.1 Computed Values of the Parameters
Some accurate initial values from this computation are listed
in Table 2. These theoretical computations are in good
agreement with results published in literatures [10].
4. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 10 | OCT-2015, Available @ http://www.ijret.org 210
Table 2. Computed values from eqs (15) & (1)
η f f
0.00000 0.00000 1.00000 1.00000 -0.44390
0.10000 0.09778 0.95565 0.95565 -0.44281
0.56453 0.49467 0.75551 0.75551 -0.41263
1.06139 0.82149 0.56527 0.56527 -0.34971
1.58921 1.07474 0.40121 0.40121 -0.27178
2.17789 1.26863 0.26537 0.26537 -0.19212
2.81160 1.40304 0.16583 0.16583 -0.12561
3.44239 1.48601 0.10208 0.10208 -0.07956
4.03844 1.53462 0.06386 0.06386 -0.05070
4.65045 1.56554 0.03914 0.03914 -0.03154
5.29663 1.58523 0.02316 0.02316 -0.01895
5.99060 1.59747 0.01305 0.01305 -0.01091
6.74612 1.60476 0.00687 0.00687 -0.00596
7.57896 1.60881 0.00325 0.00325 -0.00305
8.50860 1.61079 0.00125 0.00125 -0.00144
9.56051 1.61149 0.00023 0.00023 -0.00062
10.00000 1.61154 0.00000 0.00000 -0.00043
4.2 Dimensionless Stream Function and
Temperature Profiles
Variations of f and obtained from the present computation
are shown in Fig 2.
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
f
Fig. 2 Solutions of f and
4.3 Comparison With Experiments
Fig 3 compares the dimensionless temperature profile θ,
with the experiments of Evans and Plumb [11]. The
agreement is excellent.
Fig 3. Comparison of the computed dimensionless
temperature profile with experimental data.
4.4 Heat Transfer Parameters
Besides the velocity and temperature distributions, it is often
desirable to compute other physically important quantities
associated with the convection flow.
The heat transfer rate at the wall is given by
q k
T
y
w
y
0
24
Hence, using eq (12)
q x
k T T
Raw
a w( )
.
0 5
0
25
From Table 2, we see that
0
0 4439.
Hence,
Nu Rax 0 444 0 5
. .
26
where, Nux is the local Nusselt number based on x. Fig 4
illustrates the comparison of the correlation (26) with the
experimental data of Evans and Plumb [11].
The mean heat transfer rate is then given by using
27
Fig 4. Comparison of the computed correlation with
experimental data.
Eqs (26) and (27) gives
Nu RaL L 0888
0 5
.
.
28
where NuL is the mean Nusselt number based on the length
of the plate, L and RaL is Darcy-modified Rayleigh number
based on L. These empirical correlations are found in the
text books [6-10].
5. CONCLUSION
In the present numerical simulation, laminar convection
flow and heat transfer over an isothermal vertical horizontal
plate embedded in a saturated porous medium is presented.
5. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 10 | OCT-2015, Available @ http://www.ijret.org 211
Details of the solution procedure of the nonlinear partial
differential equations of flow are discussed. The computer
codes are developed for this numerical analysis in Matlab
environment. Velocity profile and temperature profiles are
computed using these codes. The computed and
experimental velocity and temperature distributions are in
very good agreement with results published in literatures.
Heat transfer parameters are derived. A good agreement
between the present results and the past indicates that the
developed numerical simulation as an efficient and stable
numerical scheme in natural convection.
REFERENCES
[1] P. Cheng and W. J. Minkowycz, J. Geophys. Res.
82,2040 (1977).
[2] P. Cheng, Int. J. Heat Mass Transfer 20, 201
(1977).
[3] J. H. Merkin, Int. .I. Heat Mass Transfer 21, 1499
(1978).
[4] J. H. Merkin, .I. Engng. Math. 14, 301 (1980).
[5] Mitra A., “Numerical Simulation on Laminar Free-
Convection Flow and Heat Transfer Over an Isothermal
Vertical Plate,” International Journal of Research in
Engineering & Technology, 04, 2015, pp 488-494.
[6] Hansen, A. G., “Similarity Analysis of Boundary Value
Problems in Engineering”, Prentice-Hall, Englewood
Cliffs, N. J., 1964.
[7] An Introduction to Convective Heat Transfer Analysis
by P O Oosthuizen and D Nalyor, McGraw-Hill, 1999.
[8] Sachdev, P. L., “Self-Similarity and Beyond: Exact
Solutions of Nonlinear Problems”, CRC Press, Boca
Ratton, Fla, 2000
[9] Incropera F.P. and DeWitt D.P., Introduction to Heat
Transfer, Fourth edition, John Wiley, New York, 2002.
[10]Bejan A., Convection Heat Transfer, Fourth Edition,
John Wiley & Sons, Inc. 2013.
[11]Evans, G. H. and Plumb, O. A., Natural convection
from a vertical isothermal surface imbedded in a
saturated porous medium, AIAA-ASME
Thermophysics and Heat Transfer Conf., Paper 78-HT
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