In this article we present an experimental and numerical study of the behavior of the boundary layer type viscous flow in the presence of the thermal effect. The flow was held in a three-dimensional field with a uniform infinite velocity in the case of an adiabatic wall with heat input. The presented experimental work was performed in the Thermal Laboratory (LET) of the Prime Institute of Poitiers (France). It describes the analysis of a turbulent boundary layer created in a wind tunnel on the surface of a flat plate covered with epoxy resin. An HP 6012A power supply system was used to provide circulating heat flux to heat the flat plate to 80°C by the Joule effect. The numerical result shows a clear difference in the evolution of the thermal boundary layer between the three temperatures of the wall.
technoloTwo dimensional numerical simulation of the combined heat transfer in...ijmech
A numerical investigation was conducted to analyze the flow field and heat transfer characteristics in a vertical channel withradiation and blowing from the wall. Hydrodynamic behaviour and heat transfer results are obtained by the solution of the complete Navier–Stokesand energy equations using a control volume finite element method. Turbulent flow with "Low Reynolds Spalart-Allmaras Turbulence Model" and radiation with "Discrete Transfer Radiation Method" had been modeled. In order to have a complete survey, this article has a wide range of study in different domains including velocity profiles at different locations, turbulent viscosity, shear stress, suctioned mass flow rate in different magnitude of the input
Rayleigh number, blowing Reynoldsnumber, radiation parameter, Prandtl number, the ratio of length to width and also ratio of opening thickness to width of the channel. In addition, effects of variation in any of the above non-dimensional numbers on parameters of the flow are clearly illustrated. At the end resultants had been compared with experimental data which demonstrated that in the present study, results have a great accuracy, relative errors are very small and the curve portraits are in a great
agreement with real experiments.
A three-dimensional numerical analysis of laminar natural convection with entropy generation in an open trapezoidal cavity filled with water has been carried out. In this investigation, the inclined wall is maintained at isothermal hot temperature while cold water enters into the cavity from its right open boundary and all other walls are assumed to be perfect thermal insulators. Attention is paid on the effects of buoyancy forces on the flow structure and temperature distribution inside the open enclosure. Rayleigh number is the main parameter which changes from 103 to 105 and Prandtl number is fixed at Pr =6.2. Obtained results have been presented in the form of particles trajectories, iso-surfaces of temperature and those of entropy generated as well as the average Nusselt number. It has been found that the flow structure is sensitive to the value of Rayleigh number and that heat transfer increases with increasing this parameter.
Effects of Hall and thermal on MHD Stokes’ second problem for unsteady second...IJERA Editor
In this paper, we investigated the combined effects of Hall and thermal on MHD Stokes’ second problem for
unsteady second grade fluid flow through porous medium. The expressions for the velocity field and the
temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and
temperature field are studied in detail with the aid of graphs.
Second Law Analysis of Fluid Flow and Heat Transfer through Porous Channel wi...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The document summarizes key concepts in heat transfer by conduction. It defines Fourier's law of conduction, thermal conductivity, and provides equations for one-dimensional steady-state heat conduction through a slab and hollow cylinder. It also defines thermal resistance, overall heat transfer coefficient, critical thickness of insulation, fins, fin effectiveness, and fin efficiency. Examples of heat generation and the difference between transient and steady heat transfer are provided. The lumped system analysis method and Biot number are introduced along with their applicability conditions.
Exploring the Use of Computation Fluid Dynamics to Model a T-Junction for UM ...Doug Kripke
1) This document discusses using computational fluid dynamics (CFD) to model a T-junction where hot and cold fluid flows combine. Specifically, it will compare the realizable and standard k-ε turbulence models in replicating experimental velocity field measurements of water in a T-junction.
2) Extensive previous water experiments on a T-junction characterized the thermal striping phenomenon and measured velocity and temperature distributions. This project will use those experimental conditions and measurements for validation of CFD simulations.
3) Reynolds number calculations confirmed the flows are fully turbulent, validating the use of turbulence models. The CFD model setup and boundary conditions aimed to replicate the previous experimental conditions for validation purposes.
This document summarizes a study that examines heat and mass transfer over a vertical plate in a porous medium with Soret and Dufour effects, a convective surface boundary condition, chemical reaction, and magnetic field. The governing equations for the fluid flow, heat transfer, and mass transfer are presented. Similarity solutions are used to transform the governing partial differential equations into ordinary differential equations, which are then solved numerically. The results are presented graphically to show the influence of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number.
International Journal of Computational Engineering Research(IJCER)ijceronline
The document summarizes a study on the effect of thermal radiation on boundary layer flow of a second-grade fluid over a stretching sheet through a porous medium, where the fluid's viscosity and thermal conductivity are temperature dependent. The governing equations are non-dimensionalized using similarity transformations and then solved numerically. Results show the effects of various parameters like radiation, viscosity, thermal conductivity, and porosity on the fluid's velocity and temperature profiles, as well as the skin friction coefficient and Nusselt number.
technoloTwo dimensional numerical simulation of the combined heat transfer in...ijmech
A numerical investigation was conducted to analyze the flow field and heat transfer characteristics in a vertical channel withradiation and blowing from the wall. Hydrodynamic behaviour and heat transfer results are obtained by the solution of the complete Navier–Stokesand energy equations using a control volume finite element method. Turbulent flow with "Low Reynolds Spalart-Allmaras Turbulence Model" and radiation with "Discrete Transfer Radiation Method" had been modeled. In order to have a complete survey, this article has a wide range of study in different domains including velocity profiles at different locations, turbulent viscosity, shear stress, suctioned mass flow rate in different magnitude of the input
Rayleigh number, blowing Reynoldsnumber, radiation parameter, Prandtl number, the ratio of length to width and also ratio of opening thickness to width of the channel. In addition, effects of variation in any of the above non-dimensional numbers on parameters of the flow are clearly illustrated. At the end resultants had been compared with experimental data which demonstrated that in the present study, results have a great accuracy, relative errors are very small and the curve portraits are in a great
agreement with real experiments.
A three-dimensional numerical analysis of laminar natural convection with entropy generation in an open trapezoidal cavity filled with water has been carried out. In this investigation, the inclined wall is maintained at isothermal hot temperature while cold water enters into the cavity from its right open boundary and all other walls are assumed to be perfect thermal insulators. Attention is paid on the effects of buoyancy forces on the flow structure and temperature distribution inside the open enclosure. Rayleigh number is the main parameter which changes from 103 to 105 and Prandtl number is fixed at Pr =6.2. Obtained results have been presented in the form of particles trajectories, iso-surfaces of temperature and those of entropy generated as well as the average Nusselt number. It has been found that the flow structure is sensitive to the value of Rayleigh number and that heat transfer increases with increasing this parameter.
Effects of Hall and thermal on MHD Stokes’ second problem for unsteady second...IJERA Editor
In this paper, we investigated the combined effects of Hall and thermal on MHD Stokes’ second problem for
unsteady second grade fluid flow through porous medium. The expressions for the velocity field and the
temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and
temperature field are studied in detail with the aid of graphs.
Second Law Analysis of Fluid Flow and Heat Transfer through Porous Channel wi...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The document summarizes key concepts in heat transfer by conduction. It defines Fourier's law of conduction, thermal conductivity, and provides equations for one-dimensional steady-state heat conduction through a slab and hollow cylinder. It also defines thermal resistance, overall heat transfer coefficient, critical thickness of insulation, fins, fin effectiveness, and fin efficiency. Examples of heat generation and the difference between transient and steady heat transfer are provided. The lumped system analysis method and Biot number are introduced along with their applicability conditions.
Exploring the Use of Computation Fluid Dynamics to Model a T-Junction for UM ...Doug Kripke
1) This document discusses using computational fluid dynamics (CFD) to model a T-junction where hot and cold fluid flows combine. Specifically, it will compare the realizable and standard k-ε turbulence models in replicating experimental velocity field measurements of water in a T-junction.
2) Extensive previous water experiments on a T-junction characterized the thermal striping phenomenon and measured velocity and temperature distributions. This project will use those experimental conditions and measurements for validation of CFD simulations.
3) Reynolds number calculations confirmed the flows are fully turbulent, validating the use of turbulence models. The CFD model setup and boundary conditions aimed to replicate the previous experimental conditions for validation purposes.
This document summarizes a study that examines heat and mass transfer over a vertical plate in a porous medium with Soret and Dufour effects, a convective surface boundary condition, chemical reaction, and magnetic field. The governing equations for the fluid flow, heat transfer, and mass transfer are presented. Similarity solutions are used to transform the governing partial differential equations into ordinary differential equations, which are then solved numerically. The results are presented graphically to show the influence of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number.
International Journal of Computational Engineering Research(IJCER)ijceronline
The document summarizes a study on the effect of thermal radiation on boundary layer flow of a second-grade fluid over a stretching sheet through a porous medium, where the fluid's viscosity and thermal conductivity are temperature dependent. The governing equations are non-dimensionalized using similarity transformations and then solved numerically. Results show the effects of various parameters like radiation, viscosity, thermal conductivity, and porosity on the fluid's velocity and temperature profiles, as well as the skin friction coefficient and Nusselt number.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document presents a numerical solution for unsteady heat and mass transfer flow past an infinite vertical plate with variable thermal conductivity, taking into account Dufour number and heat source effects. The governing equations are non-linear and coupled, and were solved numerically using an implicit finite difference scheme. Various parameters, including Dufour number and heat source, were found to influence the velocity, temperature, and concentration profiles. Skin friction, Nusselt number, and Sherwood number were also calculated.
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 study of mhd boundary layer stagnation point flow and heat transfer...eSAT Publishing House
This document presents a numerical study of magnetohydrodynamic boundary layer stagnation point flow and heat transfer over an exponentially stretching surface with thermal radiation. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations. A Runge-Kutta shooting method is used to solve the coupled non-linear system numerically. The effects of parameters such as the Prandtl number, Grashoff number, Eckert number, and velocity ratio parameter are analyzed through graphs of the velocity and temperature profiles. The results are compared to known solutions to validate the numerical method.
Heat Transfer on Steady MHD rotating flow through porous medium in a parallel...IJERA Editor
We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.
Effects of conduction on magneto hydrodynamics mixed convection flow in trian...Alexander Decker
This document summarizes research on magnetohydrodynamic (MHD) mixed convection flow in triangular enclosures. Key points:
1) The study investigates the effects of conduction on MHD mixed convection flow in triangular enclosures using a finite element method.
2) Parameters like the Hartmann number, Prandtl number, Reynolds number, and Rayleigh number are found to strongly influence the flow and thermal fields.
3) Validation of the numerical code is done by comparing average Nusselt numbers to previous research on natural convection in triangular enclosures.
Asme2009 82287 - Porous Media - Forced Convection FlowHIIO
In this study the flow field and heat transfer properties of a
steady, two-dimensional flow field in a porous domain between
two parallel plates is investigated numerically by using a
discretized numeric code. Analysis has been carried for
Reynolds number based on particle sizes ranging from 60 to
1000. Numerical results are compared with different numerical
methods used for predicting this kind of flow. Results are
obtained for different regime, various p Re numbers and the
effect of Particles size is also investigated. Solutions indicate
that by increasing the
p Re , the flow in the porous media
remains laminar where the flow has turbulence characteristics
for p Re <50. Moreover, by increasing p Re , the value of
average Nusselt number increases. Also, reducing the particle
size affects the Nusselt number and it increases while the
porosity remains the same.
Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
In this paper, we investigated the effects of magnetic field and thermal in Stokes’ second problem for unsteady second grade fluid flow through a porous medium. The expressions for the velocity field and the temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and temperature field are studied through graphs in detail.
TWO FLUID ELECTROMAGNETO CONVECTIVE FLOW AND HEAT TRANSFER BETWEEN VERTICAL W...IAEME Publication
The mixture of viscous and magneto convective flow and heat transfer between a long vertical wavy wall and a parallel flat wall in the presence of applied electric field parallel to gravity , magnetic field normal to gravity in the presence of source or sink is investigated. The non-linear equations governing the flow are solved using the linearization technique. The effect of Grash of number and width ratio is to promote the flow for both open and short circuits. The effect of Hartmann number is to suppress the flow, the effect of source is to promote and the effect of sink is to suppress the velocity for open and short circuit s. Conducting ratio decreases the temperature where as width ratio increases the temperature.
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...theijes
This document summarizes a study that numerically investigates the effects of variable viscosity and thermal conductivity on magnetohydrodynamic (MHD) free convection and mass transfer flow over an inclined vertical surface in a porous medium with heat generation. The governing equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. The results show that increasing the viscosity variation parameter, thermal conductivity parameter, magnetic parameter, permeability parameter, or Schmidt number decreases the fluid velocity, while increasing the heat generation parameter, local Grashof number, or mass Grashof number increases the fluid velocity. Skin friction, Nusselt number, and Sherwood number are also computed and presented in tabular form.
FINITE ELEMENT THERMAL ANALYSIS OF DEEP BOX-GIRDERSIAEME Publication
A three-dimensional thermal analysis using the finite element method was conducted in this research to evaluate the heat conduction in deep concrete box-girder bridges considering the temperature change of air, the thermal radiation from the sun and the speed of the wind. The current finite element analysis has predicted the concrete temperatures effectively with temperature errors ranged between 0.1 oC and 1.7 oC. The proposed finite element model was then used to evaluate the distribution of temperature in deep concrete box-girders considering the weather conditions of Gaziantep, Turkey. The weather data including solar radiation, air temperature and wind speed for a hot summer day were recorded from a specially installed weather station in the campus of the University of Gaziantep. The results showed that the AASHTO's gradient model was almost identical with the predicted temperature gradients at the top and the bottom surfaces and along the clear depth of the webs. However, the behavior along the top 1 m was different.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
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.
Effect of Radiation on Mixed Convection Flow of a Non-Newtonian Nan fluid ove...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Numerical investigation of heat transfer and fluid flow characteristics insid...doda_1989h
Abstract
The combined effect of waviness and porous media on the convection heat transfer and fluid flow characteristics
is numerically investigated. Two models of wavy walled channel fully filled with homogenous porous material
are assumed. The first was the symmetric converging-diverging channel (case A), and the second was the
channel with concave-convex walls (case B). The governing equations have been solved on non-orthogonal grid,
which is generated by Poisson elliptic equations, based on ADI method. Nusselt number values are used to
indicate whether any cases of corrugation studied may have led to an increase in the rate of heat transferred
compared with the planar surface channel which is the purpose of the study. The results show that case A gives
more enhancement in heat transfer than case B. However, the thermal performance of the wavy channels (cases
A & B) is better than the straight channel (simple duct).
Using Lattice Boltzmann Method to Investigate the Effects of Porous Media on ...A Behzadmehr
1) The document describes a numerical study using the lattice Boltzmann method to investigate heat transfer from a solid block inside a porous media-filled channel.
2) The effects of porosity and thermal conductivity ratio on fluid flow patterns and temperature fields were examined.
3) Higher porosity and lower thermal conductivity ratio resulted in lower fluid temperatures, as increased porosity reduces the effective thermal conductivity and thus heat transfer between the fluid and solid block.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Study on Natural Convection in a Square Cavity with Wavy right vertical wall ...IOSRJMCE
In the present study, natural convection problem has been solved in a cavity having three flat walls and the right vertical wall consisting of one undulation and three undulations. The two vertical and bottom walls are cold walls maintained at a fixed temperature whereas the top wall is heated with spatially varying temperature distribution. Air has been taken as the working fluid with Pr =0.71. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. A wide range of Rayleigh number (103 to 106 ) has been chosen for this study. For small Ra, the heat transfer was dominated by conduction across the fluid layers. With increase of Ra, the process began to be dominated by convection. In the presence of undulation the peak point of the heat rejection (negative local Nusselt number) in the right wall increases by 5.54% than left wall for Ra = 104 . The three undulations case had maximum heat transfer to the uppermost undulation compared to that of the one undulation case
Magneto convective flowand heat transfer of two immiscible fluids between ver...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
This document presents a mathematical analysis of the unsteady free convection and mass transfer flow through a porous medium with variable viscosity and thermal conductivity. The governing equations for momentum, temperature, and concentration are non-dimensionalized and solved using an explicit finite difference method. Key aspects include:
1) The flow is induced by an exponentially accelerated vertical plate with variable temperature and concentration.
2) Viscosity and thermal conductivity are assumed to vary linearly with temperature.
3) The resulting non-dimensional equations are nonlinear partial differential equations solved numerically.
4) Skin friction and Nusselt numbers are defined and analyzed graphically.
Investigation of fracture behavior and mechanical properties of epoxy composi...Barhm Mohamad
Adding of a multi-walled carbon nanotubes (MWCNTs) to epoxy resin has shown
promising results in improving fracture toughness in bulk epoxy and carbon fiber-reinforced
epoxy composites (CFRP). using a hand layup proceeding followed by the so called vacuum
bagging process method, carbon fiber-reinforced polymer multi-wall carbon nanotubes
(MWCNTs) was added to an epoxy resin with a weight percentage mixing of 1% wt., 1.25% wt.,
and 1.5 % wt. MWCNTs. Furthermore, the specimen underwent analysis via Fourier-Transform
Infrared (FTIR) spectroscopy, and X-ray Diffraction (XRD) spectroscopy, the composites were
subjected to a microscopic examination using a Scanning Electron Microscope (SEM). FTIR and
XRD verified the folding and unfolding of the polymer, in addition, the mechanical properties
including tensile strength, bending stress, and impact behavior were investigated as well as the
hardness test. The obtained results showed a significant improvement of about (40 %) in tensile
strength, (53 %) in bending stress at 1 % wt. MWCNTs, and (70 %) percentage increment in the
strength of Impact at 1.25 % wt. MWCNTs. And the gained hardness was about 40.5 HV which
were compared with a reference substance named Carbon Fiber (CF) without any addition of nano
materials. Carbon nanotubes have demonstrated their potential to enhance the mechanical
properties of fiber-reinforced polymers, so this investigative study employs comprehensive
characterization techniques, and demonstrates significant improvements in mechanical properties
for the modified polymeric composite materials supported with nano materials.
Characterization of a flat plate solar water heating system using different n...Barhm Mohamad
Flat-plate solar collectors (FPSCs) are the most effective and environmentally friendly heating systems available. They are frequently used to convert solar radiation into usable heat for a variety of thermal applications. Because of their superior thermo-physical features, the use of Nano-fluids in FPSCs is a useful technique to improve FPSC performance. Nano-fluids are advanced colloidal suspensions containing Nano-sized particles that have been researched over the last two decades and identified a fluid composed of strong nanoparticles with a diameter of smaller than (100 nm). These micro-particles aid in improving the thermal conductivity and convective heat transfer of liquids when mixed with the base fluid. The current study provides an in-depth review of the scientific advances in the field of Nano-fluids on flat-plate solar collectors. Previous research on the usage of Nano-fluids in FPSCs shows that Nano-fluids can be used successfully to improve the efficiency of flat-plate collectors. Though several Nano-fluids have been reviewed as solar collector operatin fluids. Nano-fluids have greater pressure drops than liquids, and their pressure drops andhence pumping power rise as the volume flow rate increases. Additionally, the article discusses the concept of Nano-fluids, the different forms of nanoparticles, the methods for preparing Nano-fluids, and their thermos-physical properties. The article concludes with a few observations and suggestions on the usage of Nano-fluids in flat-plate solar collectors. This article summarizes the numerous research studies conducted in this region, which may prove useful for future experimental studies.
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International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document presents a numerical solution for unsteady heat and mass transfer flow past an infinite vertical plate with variable thermal conductivity, taking into account Dufour number and heat source effects. The governing equations are non-linear and coupled, and were solved numerically using an implicit finite difference scheme. Various parameters, including Dufour number and heat source, were found to influence the velocity, temperature, and concentration profiles. Skin friction, Nusselt number, and Sherwood number were also calculated.
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 study of mhd boundary layer stagnation point flow and heat transfer...eSAT Publishing House
This document presents a numerical study of magnetohydrodynamic boundary layer stagnation point flow and heat transfer over an exponentially stretching surface with thermal radiation. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations. A Runge-Kutta shooting method is used to solve the coupled non-linear system numerically. The effects of parameters such as the Prandtl number, Grashoff number, Eckert number, and velocity ratio parameter are analyzed through graphs of the velocity and temperature profiles. The results are compared to known solutions to validate the numerical method.
Heat Transfer on Steady MHD rotating flow through porous medium in a parallel...IJERA Editor
We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.
Effects of conduction on magneto hydrodynamics mixed convection flow in trian...Alexander Decker
This document summarizes research on magnetohydrodynamic (MHD) mixed convection flow in triangular enclosures. Key points:
1) The study investigates the effects of conduction on MHD mixed convection flow in triangular enclosures using a finite element method.
2) Parameters like the Hartmann number, Prandtl number, Reynolds number, and Rayleigh number are found to strongly influence the flow and thermal fields.
3) Validation of the numerical code is done by comparing average Nusselt numbers to previous research on natural convection in triangular enclosures.
Asme2009 82287 - Porous Media - Forced Convection FlowHIIO
In this study the flow field and heat transfer properties of a
steady, two-dimensional flow field in a porous domain between
two parallel plates is investigated numerically by using a
discretized numeric code. Analysis has been carried for
Reynolds number based on particle sizes ranging from 60 to
1000. Numerical results are compared with different numerical
methods used for predicting this kind of flow. Results are
obtained for different regime, various p Re numbers and the
effect of Particles size is also investigated. Solutions indicate
that by increasing the
p Re , the flow in the porous media
remains laminar where the flow has turbulence characteristics
for p Re <50. Moreover, by increasing p Re , the value of
average Nusselt number increases. Also, reducing the particle
size affects the Nusselt number and it increases while the
porosity remains the same.
Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
In this paper, we investigated the effects of magnetic field and thermal in Stokes’ second problem for unsteady second grade fluid flow through a porous medium. The expressions for the velocity field and the temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and temperature field are studied through graphs in detail.
TWO FLUID ELECTROMAGNETO CONVECTIVE FLOW AND HEAT TRANSFER BETWEEN VERTICAL W...IAEME Publication
The mixture of viscous and magneto convective flow and heat transfer between a long vertical wavy wall and a parallel flat wall in the presence of applied electric field parallel to gravity , magnetic field normal to gravity in the presence of source or sink is investigated. The non-linear equations governing the flow are solved using the linearization technique. The effect of Grash of number and width ratio is to promote the flow for both open and short circuits. The effect of Hartmann number is to suppress the flow, the effect of source is to promote and the effect of sink is to suppress the velocity for open and short circuit s. Conducting ratio decreases the temperature where as width ratio increases the temperature.
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...theijes
This document summarizes a study that numerically investigates the effects of variable viscosity and thermal conductivity on magnetohydrodynamic (MHD) free convection and mass transfer flow over an inclined vertical surface in a porous medium with heat generation. The governing equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. The results show that increasing the viscosity variation parameter, thermal conductivity parameter, magnetic parameter, permeability parameter, or Schmidt number decreases the fluid velocity, while increasing the heat generation parameter, local Grashof number, or mass Grashof number increases the fluid velocity. Skin friction, Nusselt number, and Sherwood number are also computed and presented in tabular form.
FINITE ELEMENT THERMAL ANALYSIS OF DEEP BOX-GIRDERSIAEME Publication
A three-dimensional thermal analysis using the finite element method was conducted in this research to evaluate the heat conduction in deep concrete box-girder bridges considering the temperature change of air, the thermal radiation from the sun and the speed of the wind. The current finite element analysis has predicted the concrete temperatures effectively with temperature errors ranged between 0.1 oC and 1.7 oC. The proposed finite element model was then used to evaluate the distribution of temperature in deep concrete box-girders considering the weather conditions of Gaziantep, Turkey. The weather data including solar radiation, air temperature and wind speed for a hot summer day were recorded from a specially installed weather station in the campus of the University of Gaziantep. The results showed that the AASHTO's gradient model was almost identical with the predicted temperature gradients at the top and the bottom surfaces and along the clear depth of the webs. However, the behavior along the top 1 m was different.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
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
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compared with the planar surface channel which is the purpose of the study. The results show that case A gives
more enhancement in heat transfer than case B. However, the thermal performance of the wavy channels (cases
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2) Viscosity and thermal conductivity are assumed to vary linearly with temperature.
3) The resulting non-dimensional equations are nonlinear partial differential equations solved numerically.
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EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF A TURBULENT BOUNDARY LAYER UNDER VARIABLE TEMPERATURE GRADIENTS
1. Journal of the Serbian Society for Computational Mechanics / Vol. 16 / No. 1, 2022 / pp 1-15
(10.24874/jsscm.2022.16.01.01)
EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF A
TURBULENT BOUNDARY LAYER UNDER VARIABLE
TEMPERATURE GRADIENTS
Amar Berkache1
, Salah Amroune1,2,
*, Ali Golbaf3
, Barhm Mohamad4
1
Faculty of Technology, Mohamed Boudiaf University M’sila Algeria, 28000
e-mail: amar.berkache@univ-msila.dz, salah.amroune@univ-msila.dz
2
Laboratoire de Matériaux et Mécanique des Structures (LMMS), Université de M’sila, Algérie
3
Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran
e-mail: ali.golbaf71@gmail.com
4
Department of Petroleum Technology, Koya Technical Institute, Erbil Polytechnic University,
44001 Erbil, Iraq
e-mail: pywand@gmail.com
*corresponding author
Abstract
In this article we present an experimental and numerical study of the behavior of the boundary
layer type viscous flow in the presence of the thermal effect. The flow was held in a three-
dimensional field with a uniform infinite velocity in the case of an adiabatic wall with heat input.
The presented experimental work was performed in the Thermal Laboratory (LET) of the Prime
Institute of Poitiers (France). It describes the analysis of a turbulent boundary layer created in a
wind tunnel on the surface of a flat plate covered with epoxy resin. An HP 6012A power supply
system was used to provide circulating heat flux to heat the flat plate to 80°C by the Joule effect.
The numerical result shows a clear difference in the evolution of the thermal boundary layer
between the three temperatures of the wall.
Keywords: Infinite velocity, turbulent boundary layer, temperature gradient, heat flux, fluent.
1. Introduction
The analysis of wall turbulence presents significant challenges both experimentally and
numerically. Recently, a novel experimental approach employing hot wire anemometry and
particle image velocimetry has been introduced to investigate the turbulent boundary layer of flat
plates at high Reynolds numbers. These approaches not only have allowed access to classical
results and validation of the device but also have provided the first contribution to the
understanding of the organization of the parietal production zone (Brooks et al., 2018). Although,
the hot wire anemometer has been firstly used to characterize the Reynolds tensor and to present
energy spectra in the turbulent boundary layer, the determination of the average properties by
statistical methods provides little information on the structures participating in the organization
of turbulence. These structures have been discovered mainly by flow visualization methods
(Klebanoff 1955). Theodorsen Theodore (Theodorsen 1959) is the first who proposed the
2. Amar Berkache et al.: EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF A TURBULENT…
2
existence of hairpin vortices. It has been proven that the formation of streaks near the wall and
the bursting phenomenon are the main reasons for the production of turbulence (Kline et al.,
1967).
Falco R. (Falco 1983) observed the presence of vortices bearing his name on the interface of the
turbulent boundary layer. All proposed processes of self-generation of turbulence. In particular,
Falco R. (Falco 1983) considered the interaction of the vortices of (Falco 1983) and the wall, and
(Head et al., 1981) with a distribution of hairpin vortices. (Blackwelder et al., 1976) and (Wallace
et al., 1972) tried using detection methods such as VITA or the Quadrants method to identify and
quantify these coherent structures without really succeeding.
In recent years, the appearance of new techniques has provided the scientific community with
access to new information about turbulence. Firstly, Direct Numerical Simulation (DNS) which,
for low Reynolds numbers, allows a three-dimensional resolution of the flow. Robinson
(Robinson 1991) was thus able, due to the data of Spalart 12, to find the hairpin vortices by
visualizing the isobars. These results can now be compared to those obtained by Particle Image
Velocimetry (PIV). Using this method, Kähler's team (Kähler et al., 1998) observed a cross-
section of these vortices.
The main objectives of the experiment were to calculate the turbulence via the RMS velocity, the
evolution of the aerodynamic and thermal boundary layer and the effect of the temperature
gradient on the thermal boundary layer. Measurements were made along the plate following the
X axis in the downstream direction of the flow. Six measurement stations were chosen, ranging
from X = 0 to X = 180 mm. At inlet conditions (X = 0), the free flow velocity Ue = 2.3m / s, Re
= 33600 and Te = 40 ° C.
2. Dynamic and thermal boundary layer
2.1 Concept of boundary layer
The unsteady full-potential equation written in a body-fitted coordinate system is given to
consider the flow of a fluid with a speed U∞ at velocity at the infinite, and a temperature T∞ on
a flat plate at a temperature Tp. In the vicinity of the wall, the values of the velocity and the
temperature are different from those of the potential flow and vary according to the distance to
the wall y. This zone of speed and temperature gradients is called the boundary layer (Barhm et
al, 2020, Barhm et al, 2019). It results from an exchange of momentum and heat between the
fluid and the wall. Its thickness is generally small compared to the entire flow. There are two
types of boundary layer: the dynamic boundary layers and the thermal boundary layer.
2.2 Dynamic boundary layer
One of the main characteristics of a fluid is viscosity. It varies with temperature and never
vanishes. At the wall, the velocity of the fluid is zero, and friction forces are observed. As it is
depicted in Figure 1, these forces slow the flow in the vicinity of the wall.
3. Journal of the Serbian Society for Computational Mechanics / Vol. 16 / No. 1, 2022 3
Fig. 1. Variation of the thickness and velocity of the dynamic boundary layer on a flat plane.
2.3 Thermal boundary layer
When a fluid, at temperature T∞, flows over a wall at temperature Tp, heat exchange is
established. Fluid particles heat up or cool down in contact with the wall. These particles
exchange heat gradually with their neighbors and as it is shown in Figure 2, a temperature gradient
is formed.
Fig. 2. Thermal boundary layer on a flat plate.
2.4 Characteristic parameters of boundary layer
2.4.1 Dynamic boundary layer thickness
U and Ue(x) are the velocities obtained for a perfect fluid on the flat plate. The conventional
boundary layer thickness is equal to the transverse distance where the longitudinal component of
the velocity reaches 99% of Ue (x). This scale usually varies with the abscissa along the plate.
By denoting it by δ(x), we have (Saeed et al., 2020):
, 0.99 e
U x x U x
(1)
2.4.2 Thermal boundary layer thickness
Similarly to the dynamic boundary layer thickness, the thickness of the thermal boundary layer
δT is defined. Let the dimensionless report be
, p
p
T x y T x
T T x
(2)
Where T (x,y) is the temperature at the current point of the boundary layer, Tp (x) is that of the
wall and T that of fluid away from the wall.
The thermal boundary layer thickness is the transverse distance at the end of which the
temperature gap reaches 99% of the difference (T∞-Tp). So, we have (Saeed et al., 2020)
4. Amar Berkache et al.: EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF A TURBULENT…
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,
0.99
T p
p
T x T x
T T x
(3)
2.4.3 Thickness of displacement
Due to the slowing down of the fluid at the wall, the flow of fluid through the boundary layer
thickness is less than it would be, at equal distances, in perfect fluid, as shown in Fig. 3. By
neglecting the variation of the perfect fluid quantities over a transversal distance of the order of
the boundary layer thickness, this deficit can be approximately evaluated by Saeed et al., 2020.
0
p v E E
q q U U dy
(4)
By convention, it is expressed from a thickness 1 such that:
1
p v E E
q q U
(5)
1
0
1
E E
U
x dy
U
(6)
The thickness δ1 is called displacement thickness. As illustrated in the figure below, this qualifier
refers to the physical interpretation of this quantity, which corresponds to the distance from which
the wall should be moved to preserve, in perfect fluid on the thickness (δ - δ1), the same flow rate
as viscous fluid over the entire boundary layer section.
Fig. 3. Flow rate deficit and displacement thickness.
2.4.5 Momentum thickness
The slowing down of the fluid at the wall also results in a lack of momentum. To account for this
and in a similar way to the displacement thickness, a second scale called the momentum thickness
δ2 is introduced, such as
0
1
E E E
U U
x dy
U U
(7)
As for δ1, this new thickness permits to express the difference in momentum of flow between
perfect fluid and viscous fluid with the same mass flow ρU in the form:
5. Journal of the Serbian Society for Computational Mechanics / Vol. 16 / No. 1, 2022 5
2
2 2
0 0
p v E E E
J J UU dy U dy U
(8)
3. Problem description
3.1 Experimental study
3.1.1 Experimental facility
Our experimental work focuses on the study of an aerodynamic and thermal boundary layer
carried out on a test bench. The temperature of the main flow of air flowing over the flat plate
where the boundary layer is formed is equal to 40 °. To vary the temperature of the plate, three
heat flow densities corresponding respectively to wall temperatures Tp1=35°C, Tp2=45°C and
Tp3=55°C were necessary. These three fluxes were created by an electrical circuit etched on the
flat plate covered with a thin layer of epoxy (Fig. 4). An infrared camera was used to measure the
temperature field of the injection wall, and the plate was painted black to increase its emissivity
p whose value was measured experimentally, and which is equal to 0.95 ± 0.02.
Fig. 4. Experimental facility for measuring the flat plate temperatures.
3.1.2 Study field
The field of study is a rectangular section pipe consisting of four plates: two back and front plates
and two lower and upper plates. The back plate that represents the subject injection wall of our
study contains perforations. The front wall is a transparent wall to allow measurements. This
transparent wall also called the "sounding wall" was pierced and equipped with a porthole to
allow the introduction of probes or adjustment measures. The two lower and upper plates connect
the other two plates to create the pipe. (Fig. 5).
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Fig. 5. Schematic representation of the test vein.
The study wall is a plate with dimensions 880x185 mm2 and 1.6 mm thick epoxy resin. (Fig. 6)
Fig. 6. Photograph of the perforated plate (partial view).
3.1.3 Temperature measurements of the flat plate
To achieve this experimental measurement on the flat plate (not perforated plate), the perforations
(81 holes of diameter D) were sealed to prevent the injection flow through the perforations.
The surface temperature measurements of our wall are made by infrared thermography. The
infrared camera used is a CEDIP Itanium dot matrix camera. The wall temperatures are computed
by a matrix of 320x256 detectors giving us matrices of 256 lines and 320 columns. The position
of the infrared camera in our tests is about 0.5 m from the test plate giving a resolution of about
0.25x0.25 mm2 per pixel (Fig. 7)
Fig. 7. Camera arrangement for measuring temperatures of the flat plate.
7. Journal of the Serbian Society for Computational Mechanics / Vol. 16 / No. 1, 2022 7
4. Numerical study
A numerical study associated with the experimental study was carried out in order to have more
results that could not be realized experimentally, and to be able to compare the numerical results
with the experimental results.
4.1 Basic Equations
Two evolution equations are used to describe the flow of an incompressible fluid in its motion.
One reflects the mass conservation, the other is the conservation of momentum. The third
equation concerns the heat transfer: the energy equation.
4.1.1 Conservation of mass
i
i
u
O
x
(9)
4.1.2 Navier-Stokes incompressible
1
(2 )
i i
i j ij
j i j
u f
u u S
t x x x
(10)
4.1.3 Heat equation
j f f
j j j
T T
u T α Q
t x x x
(11)
The software utilized is fluent software. FLUENT is a Computational Fluid Dynamics (CFD)
code for modelling fluid flow, heat transfer, mass transfer and chemical reactions.
4.2 Model of turbulence
The turbulence model used in our study is the Reynolds Stress Model (RSM), also known as the
Reynolds Stress Transport Model, which is a high-level turbulence closure model and represents
the classical turbulence model, the most completed one. The closure method employed is usually
called a second-order closure. In Reynolds stress models, the turbulent viscosity approach is
avoided and the individual components of the Reynolds stress tensor are directly calculated.
These models are based on the exact Reynolds constraint transport equation. They can take into
account complex interactions in turbulent flow fields, such as the directional effects of Reynolds
constraints.
The exact transport equations for the transport of the Reynolds stresses, 𝜌𝑢𝑖
,
𝑢𝑗
,
̅̅̅̅̅ may be written as
follows:
i j i j j kj i kj
i j j i
( u' u' ) ( u' u' u' ) [ u' u' u' ) p( u' u' )] [ ( ' ' )]
( ' ' ' ' ) (g u' g u' ) p( 2
2 ( ' ' ' ' )
k i k j i j
t k k k k
j j j j
i i
i k k k
k k j i j i
k j m ikm i m jkm user
u u
x x x x
u u u u
u u
u u u u
x x x x x x
u u u u S
(12)
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Where:
i j
( u' u' )
t
Local Time Derivative
i j
( u' u' u' )
k
k
x
𝐶𝑖𝑗 ≡ Convection
j kj i kj
[ u' u' u' ) p( u' u' )]
i k j
k
x
𝐷𝑇𝑖𝑗 ≡ Turbulent Diffusion
[ ( ' ' )]
i j
k k
u u
x x
𝐷𝐿𝑖𝑗 ≡ Molecular Diffusion
( ' ' ' ' )
j j
i k k k
k k
u u
u u u u
x x
𝑃𝑖𝑗 ≡ Molecular Diffusion
i j j i
(g u' g u' )
𝐺𝑖𝑗 ≡ Buoyancy Production
p( 2
j j
i i
j i j i
u u
u u
x x x x
p(
j
i
j i
u
u
x x
)
∅𝑖𝑗 ≡ Pressure Strain and 𝜖𝑖𝑗 ≡
Dissipation
2 ( ' ' ' ' )
k j m ikm i m jkm
u u u u
𝐹𝑖𝑗 ≡ Production by System Rotation
user
S 𝐹𝑖𝑗 ≡ User-Definec Term
The various terms in these exact equations, 𝐶𝑖𝑗, 𝐷𝐿𝑖𝑗 do nоt require any modeling. However,
𝐺𝑖𝑗, ∅𝑖𝑗 and 𝜖𝑖𝑗 need to be modeled to close the equations.
4.3 Calculation domain and boundary conditions
The computational domain and the adopted boundary conditions are shown in Fig. 8.
Fig. 8. Computational domain and boundary conditions.
Speed Ue = 2.3 m / s
Temperature Te = 40 ° C
Flow output: Outflow
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Flat plate: Wall with 3 temperatures: Tp = 35 ° C; Tp = 45 ° C and Tp = 55 ° C
The other faces of the test vein: Wall with a temperature Tw = 22 ° C
4.4Mesh and choice of Y +
The mesh adopted is a tight tetrahedral mesh at the wall and coarse in the far-off environment.
Our close wall mesh is correctly chosen to ensure accurate simulation of the flow field. As a
result, the height of the first mesh above the necessary plate is calculated to obtain a suitable Y+
using the theory of the boundary layer of the flat plate. The calculations adopted are based on
Frank M. White Fluid Mechanics' flat plate boundary layer theory (Frank 2011).
.
e
x
U L
Re
(13)
1/7
0.026
f
x
C
Re
(14)
2
2
f e
wall
C U
T
(15)
wall
fric
T y
U
(16)
s
fric
C
U
(17)
For y+ = 30 and:
Main flow velocity Ue=2.3 m/s
Density ρ = 1.225 kg/m3
Dynamic viscosity μ = 0.000018375 kg/(m•s)
Reference length L = 0.2 m
We will have
Height of the first stitch Δs = 0.003 m
Number of Reynold Rex = 30667
5. Presentation of experimental and numerical results
5.1 Exploitation of experimental results.
5.1.1 Boundary layer thickness and momentum thickness
Figure 9 illustrates the evolution of the geometric thickness of the boundary layer and the
thickness of the momentum along the X axis. The thickness of the boundary layer tends to
remain constant at the beginning of the flat plate up to X/D = 6, then it begins to increase in a fast
manner with the direction of flow from X/D = 6 to X/D = 10. From this position, the increase of
is smaller to nevertheless reach a value of 5 mm at X/D = 30. Concerning the thickness of the
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momentum, it tends to have the same behavior as the boundary layer thickness because it is
proportional to it with some small differences at the beginning of the increase. In the case of the
quantity of movement, it begins its increase to X/D = 6 up to X/D = 10 where it changes its rate
of increase. From X/D = 10 the evolution of loses its rhythm of the increase until reaching a
value of 5 kg/s in X/D = 30.
Fig. 9. Evolution of the boundary layer thickness and the momentum thickness along the X
axis.
5.1.2 Intensity of turbulence
Turbulence intensity statistics are presented in terms of rms. The turbulence intensity is
represented by the availability of the standard deviations according to X (left column) and Y
(right column) in the experiments that were reconstructed by measuring the two components of
the fluctuating velocity. The values at the central plane obtained by the experiment are shown in
Fig. 10. The maximum value entered for the reduced standard deviation x/Ue is X/D = 6 where
its value reaches 0.23 and y/Ue = 0.12. From X/D = 18, we notice slight stability of the standard
deviations x and y.
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Fig. 10. Profiles of standard deviations in longitudinal and vertical directions depending on the
position of X/D = 0 to X/D = 30.
Figure 11 shows the contours of the standard deviations in the longitudinal (a) and vertical (b)
directions as a function of the position of X/D=0 to X/D=30. Two main areas of turbulence
generation are identified in this figure. The first zone is just above the wall, with turbulence levels
from about 40% at about Y/D = 2 of X/D = 5 at X/D = 30 for x and X/D = 0 to X/D = 30 for
y.
Fig. 11. Contours of standard deviations in two directions: longitudinal (a)and vertical (b) as a
function of the position of X/D = 0 to X/D = 30.
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5.2 Exploitation of numerical results.
5.2.1 Sensitivity to mesh: Profiles of average speeds U. Comparison with experience
Figure 12 shows the results of the longitudinal velocity profiles obtained by three distinct meshes:
Large mesh (251656 meshes), Medium Mesh (703333 meshes) and fine Mesh (1696077 meshes)
in different longitudinal stations (X/D=0 mm, X/D=6, X/D=12, X/D=18, X/D=24, X/D=30)
along the X axis in the central longitudinal plane. The mesh is tight at the wall and the injection
ports. Note that the coarse mesh gives poor results far from the experimental results, while the
mean mesh and the fine mesh give almost the same result closer to those obtained by the
experiment in all computation stations, especially in the near-wall. For this reason, we used the
average mesh for the following calculations in order to save computing time.
Fig. 12. Longitudinal velocity profiles obtained by three distinct meshes.
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5.2.2 Static temperature profiles for three different flat plate temperatures
Figure 13 shows the variation of the thermal boundary layer in terms of the variation of the
reduced static temperature T(δT)/Te for three different values of the temperature of the flat plate,
subject of our study; Tp=35°C (308K), Tp=45°C (318K) and Tp=55°C (328K) depending on the
reduced height of our test vein Y Where H=0.2m represents the total height of the vein. The
temperature Te of the main flow or temperature at infinity T∞ has been set at 40°C (313K). A
gradual increase in the thickness of the thermal boundary layer is recorded from X/D=0, the
beginning of its appearance. It reaches its maximum value (Y/D=8%) for X/D=6, then it begins
to progress parabolically until reaching a value of (Y/D = 20%) for X/D=30. For Tp=35°C, the
evolution of the temperature increases until reaching the maximum value of the main flow. While
for the other two values T=45°C and Tp=55°C, the evolution of the temperature tends to decrease
but with different starting values; the curve of the first temperature starts at T(δT)/Te=1.018 and
reaches the value 1, while for the second value of the temperature; it starts at T(δT) /Te=1.05 to
reach the same value 1. This difference is due to the difference in the amount of heat flux between
the two temperatures.
Fig. 13. Temperature profiles for Tp=35°C; Tp=45°C; Tp=55°C.
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5.2.3 Static temperature contours for three different flat plate temperatures
In the last step, Fig. 14, the contours of the static temperature are represented. This representation
gives us a clear overview of the thickness of the thermal boundary layer. There is a clear
difference in the evolution of this boundary layer between the three different temperatures of the
wall. For Tp=35°C, the boundary layer starts with a slight variation at the beginning of the plate
and then begins to progress slowly to X/D=24 to wait for its maximum value at X/D=30.
Concerning the two other values of Tp, one inscribes an almost identical and constant evolution
from the beginning of the plate until its end with the clear and very visible remark of the height
of this boundary layer which appears bigger in the case of Tp=55°C.
Fig. 14. Temperature contours for Tp=35°C; Tp=45°C; Tp=55°C.
6. Conclusions
The experimental and numerical investigations conducted in this study were performed on a
turbulent boundary layer of a flat plate subjected to different heat fluxes. Calculations and tests
led to the calculation of some parameters of this boundary layer, such as dynamic and thermal
thicknesses.
The inscribed remarks concerning the dynamic thickness of the boundary layer indicate that
this thickness tends to remain constant at the beginning of the plane plate, and then it begins to
15. Journal of the Serbian Society for Computational Mechanics / Vol. 16 / No. 1, 2022 15
increase in a fast manner with the direction of the flow. From a certain position, the increase of
is less, but nevertheless reaches a value of 5 mm at the end of the flat plate.
With regard to the thermal thickness , a progressive growth of it is registered from the beginning
of the plate, the beginning of its appearance, then it begins to progress parabolically until reaching
a value of (Y / D = 20%) at the end of the flat plate.
The numerical study tells us about the contours of the static temperature. A clear difference is
noticed in the evolution of the thermal boundary layer between the three temperatures of the wall.
For Tp = 35 ° C, the boundary layer starts with a slight variation at the beginning of the plate and
then begins to progress slowly to reach its maximum value at the end of the plate.
Concerning the two other values Tp=45°C and Tp=55°C, we register a nearly identical and
constant evolution from the beginning of the plate until its end with the clear and well-visible
note of the height of this boundary layer which appears larger in the case of Tp=55°C.
Acknowledgement The reported work was performed within the ENSMA Schools (P′ institute),
the University of Poitiers in France. The welcome received for conducting the experiments is
gratefully acknowledged by the author. The author would like to warmly acknowledge Prof. Eva
Dorignac and Dr. Gildas Lalizel for their precious and fundamental support in this activity.
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