Nader Ben Cheikh - Academia.edu (original) (raw)
Papers by Nader Ben Cheikh
Computational Thermal Sciences: An International Journal, 2020
We present a study of Rayleigh-Benard natural convection to highlight the effects of some boundar... more We present a study of Rayleigh-Benard natural convection to highlight the effects of some boundary conditions about heat transfer in a cubic cavity filled with air. Three boundary conditions relative to temperature and velocity of fluid particles on walls of the cavity are considered. The obtained results are compared to the 2D problem. We prove that tridimensional effects are negligible for a particular boundary condition, consequently, we conclude that such configuration can be assimilated to its equivalent in 2D. Mots clefs : Transfert de chaleur, Convection naturelle, Simulation numerique directe, Cavite carre/cubique, Refroidissement composant electronique.
La presente investigation porte sur une etude numerique de convection naturelle bidimensionnelle ... more La presente investigation porte sur une etude numerique de convection naturelle bidimensionnelle dans une cavite de type Rayleigh-Benard. La methode numerique est basee sur un schema de type volumes finis du second ordre et une methode de projection. Une approche multigrille est utilisee pour accelerer la convergence de lequation de Poisson. Nous allons etudier dans une premiere partie leffet des conditions initiales relatives a la temperature (eint) sur lecoulement du fluide. Dans une deuxieme etape, nous determinons le nombre de Rayleigh critique (Rac)I au-dela duquel les particules fluides se mettent en mouvement et lecoulement devient instationnaire. Enfin une application physique portant sur letude de leffet des parametres de controle de notre configuration, a savoir le rapport de forme (A) et la nature du fluide(Pr) sera par la suite presentee.
International Journal of Thermal and Environmental Engineering, 2018
Fluid flow structures and heat transfer rates in a rectangular enclosure of aspect ratio of two c... more Fluid flow structures and heat transfer rates in a rectangular enclosure of aspect ratio of two containing two heated cylindrical blocks and filled with various water-based nanofluids is investigated. The free space between the cylindrical blocks and the enclosure walls is filled with four nanofluids: Cu-water, Ag-water, Al 2 O 3-water and TiO 2-water. The controlling parameters to be considered are: the Rayleigh number 6 3 04. 0 . Additionally, the inclination angle can be used as a control parameter for rectangular enclosures housing two equal heated blocks which are cooled with waterbased nanofluids.
International Journal of Thermal Sciences, 2020
Three-dimensional numerical simulations were conducted for the natural convection phenomena which... more Three-dimensional numerical simulations were conducted for the natural convection phenomena which occurs between an inner hot body and its outer enclosure. The physical model considered here is that a body of cubical shape is located at the center of an isothermal cooled spherical enclosure. Therefore, the fluid flow inside the enclosure results from the temperature difference between the cooled spherical enclosure and the heated cube. The governing equations are solved using a second-order accurate finite volume approach on a staggered grid system and multi-grid acceleration. Three different fluids, an air (Pr = 0.71), a water (Pr = 6.2) and the other a dielectric liquid (Pr = 25) are employed encompassing descriptive Rayleigh numbers Ra that range three orders of magnitude from 10 4 to 10 7. The conducted benchmark study leads to excellent accordance with previous findings. Detailed three-dimensional flow and thermal structures in the enclosure were analyzed using the distribution of iso-contours of temperature, iso-surfaces of the standard velocity vector and streamtraces for different Rayleigh numbers. The variation of the local and the surface-averaged Nusselt numbers at the inner hot cube wall are also presented to exhibit the overall heat transfer characteristics inside the enclosure. At the end, monomial correlations are presented for the quantification of the heat transfer that emanates from the heated cube and the spherical enclosure in harmony with the various Rayleigh number. It was found that the thermal and flow fields eventually reach steady state for Rayleigh numbers ranging from 10 4 to 10 7. Results indicate also that the heat transfer is increasing significantly by increasing Rayleigh numbers and optimal heat transfer rate is obtained for high Rayleigh number set to 10 7 .
International Journal of Numerical Methods for Heat & Fluid Flow, 2019
Purpose Two-dimensional incompressible fluid flows around a rectangular shape placed over a large... more Purpose Two-dimensional incompressible fluid flows around a rectangular shape placed over a larger rectangular shape at low Reynolds numbers (Re) have been numerically analyzed in the present work. The vortex shedding is investigated at different arrangements of the two shapes allowing the investigation of three possible configurations. The calculations are carried out for several values of Re ranging from 1 to 200. The effect of the obstacle geometry on the vortex shedding is analyzed for crawling, steady and unsteady regimes. The analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow becomes unstable and undergoes a bifurcation. This paper aims to observe that the transition of the unsteady regime is performed by a Hopf bifurcation. The critical Re beyond which the flow becomes unsteady is determined for each configuration. A special attention is paid to compute the drag and lift forces acting on the rectangular shapes, which allowed...
International Journal of Numerical Methods for Heat & Fluid Flow, 2017
Purpose The purpose of this paper is to examine numerically the three natural convection of air i... more Purpose The purpose of this paper is to examine numerically the three natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and titled angle of the enclosure from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy, and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature and isosurfaces of velocity eventually reaches a steady state in the range of Rayleigh numbers between 103 and 107 for titled inclination of 90°; however, for the remaining inclinations, Rayleigh number must be in the range 103-106 to avoid unsteady state, which is manifested by the division of the area containing the maximum local heat transfer rate into three parts for a Rayl...
International Journal of Numerical Methods for Heat & Fluid Flow, 2018
Purpose This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on th... more Purpose This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed ...
Computers & Fluids, 2017
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights The unsteady behavior of two-sided lid-driven cubical cavity induced by an obstacle was performed. The flow undergoes a bifurcation with a critical Reynolds number of 1034. Percentage difference of critical Reynolds number between two-and one-sided lid-driven obstructed cavities is 41.714%.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017
x, y Dimensionless coordinates St Strouhal number CD Drag coefficient CL Lift coefficient p Dimen... more x, y Dimensionless coordinates St Strouhal number CD Drag coefficient CL Lift coefficient p Dimensionless pressure φ Generic variable Greek symbols ρ Density of fluid, kg m −3 ν Kinematic viscosity, m 2 s −1 Subscripts Max, Min Maximum, minimum c Critical Keywords Obstacle • Incompressible fluid flow • Finitevolume method • Von Karman vortex street • Lift and drag coefficients • Strouhal number List of symbols Re Reynolds number l Channel width h Channel height (u, v) Velocity components, m s −1
Particulate Science and Technology, 2016
ABSTRACT In this paper, we numerically investigate the steady laminar natural convection in a wat... more ABSTRACT In this paper, we numerically investigate the steady laminar natural convection in a water-filled 2D enclosure containing a rectangular conducting body. Computations are performed for a wide range of dimensionless parameters including the Rayleigh number Ra, the thermal conductivity ratio k, and the location of the inner body δ, while the value of the Prandtl number is maintained constant at 6.8. This simulation spans four decades of Rayleigh number, Ra, from 103 to 106. The influence of these various dimensionless parameters on the flow behavior is investigated. Correlations of the averaged Nusselt numbers are obtained as a function of two parameters (Ra and δ) for each working thermal conductivity ratio. The results indicate that the heat transfer rate through the enclosure can be controlled by the position of the rectangular body. A comparative study was also carried out between a horizontal and a vertical conducting shape inside the enclosure. It is proved that a vertical position leads to a better heat transfer compared to the horizontal case.
International Letters of Chemistry, Physics and Astronomy, 2015
This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. ... more This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bi...
Journal of Applied Mechanical Engineering, 2015
International Letters of Chemistry, Physics and Astronomy, 2015
Three dimensional steady state mixed convection in a lid driven cubical cavity heating from below... more Three dimensional steady state mixed convection in a lid driven cubical cavity heating from below has been investigated numerically. Two sided walls are maintained at a constant ambient temperature Ttop > Tbottom, while the vertical walls are thermally insulated. Governing equations expressing in a dimensionless form are solved by using finite element method. The Reynolds number is fixed at Re=100, while the Richardson number is varied from 0.001 to 10. Parametric studies focusing on the effect of the Richardson number on the fluid flow and heat transfer have been performed. The flow and heat transfer characteristics, expressed in terms of streamlines, isotherms and average wall Nusselt number are presented for the entire range of Richardson number considered. Multiple correlations in terms of the heat transfer rate and Richardson number has been established.
International Letters of Chemistry, Physics and Astronomy, 2015
The present work deals with the prediction of a natural convection flow in a square cavity, parti... more The present work deals with the prediction of a natural convection flow in a square cavity, partially heated by an obstacle placed at the bottom wall. The two transverse walls and the top wall of the cavity are supposed to be cold, the remaining walls are kept insulated. The main parameter of numerical investigations is the Rayleigh number (engine convection) varying from 103 to 105. When Ra is fixed at 107, the flow and thermal fields bifurcate and undergoes an unsteady behavior at critical positions. Flow patterns corresponding to the unsteady state are presented and analyzed in the current study. The simulations were conducted using a numerical approach based on the finite volume method and the projection method, which are implemented in a computer code in order to solve the Navier-Stokes equations.
High Temperature, 2014
ABSTRACT This work addresses a numerical approach based on the finite volume method and a full mu... more ABSTRACT This work addresses a numerical approach based on the finite volume method and a full multi-grid technique to study three-dimensional flow structures and heat transfer rates in cubical cavity partially heated from one wall. The working fluid is air so that the Prandtl number equates to 0.71. Numerical solutions are generated for representative values of the controlling Rayleigh number inside the range 103 ≤ Ra ≤ 107. The heating occurs with a heated strip placed inside the enclosure. Three scenarios are investigated: (i) the heated source is mounted on the bottom horizontal wall, (ii) the heated source is mounted horizontally on the lateral wall, and (iii) the heated source is mounted vertically on the lateral wall. Effects of heated strip position in the enclosure on heat transfer are studied. It is shown that suitable configuration which generates highest heat transfer rate through the heated strip is depending on Rayleigh number. Results are presented in the form of projection of flow lines and isotherms plots as well as the variation of the Nusselt number and the average temperature at the heat source surface for all configurations computed in this study.
Proceedings of International Symposium on Convective Heat and Mass Transfer in Sustainable Energy, 2009
The papers deals with a numerical 3D study of natural convection in a finned Rayleigh-Benard (RB)... more The papers deals with a numerical 3D study of natural convection in a finned Rayleigh-Benard (RB) cubical enclosure. A single fin with a thickness of 10% of the cavity side (and a height of 50%) is placed vertically on the bottom hot wall at T H . The working fluid is air with ...
Numerical Heat Transfer, Part B: Fundamentals, 2007
A computational procedure is presented with an accelerated full-multigrid scheme for an efficient... more A computational procedure is presented with an accelerated full-multigrid scheme for an efficient modeling of time-dependent buoyancy-driven flows. The smoother is the iterative red-and-black successive overrelaxation (RBSOR) scheme. In order to improve the convergence, an acceleration parameter, Γ, is implemented in the classical full-multigrid procedure. It is shown that an optimal value of Γ = 3.75 minimizes the number of iterations needed
Numerical Heat Transfer, Part A: Applications, 2009
and-conditions-of-access.pdf This article may be used for research, teaching and private study pu... more and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
Journal of Heat Transfer, 2007
The effect of aspect ratio on natural convection flow in a cavity submitted to periodic temperatu... more The effect of aspect ratio on natural convection flow in a cavity submitted to periodic temperature boundary, is investigated numerically. The temperature of the heated wall is either maintained constant or varied sinusoidally with time while the temperature of the opposite vertical wall is maintained constant. The results are given for a range of varied parameters as Rayleigh number (5×103⩽Ra⩽106), cavity aspect ratio (1∕6⩽A⩽8), and period of the sinusoidally heated wall (1⩽τ⩽1600). The amplitude of oscillation (a=0.8) and the Prandtl number (Pr=0.71) were kept constant. The results obtained in the steady state regime show that the heat transfer averaged over the cold wall is maximum when the aspect ratio is in the range 1⩽A⩽2. In the case of a periodic temperature boundary, it is shown that the deviation between the mean heat transfer and the heat transfer of the constant heated case is larger for shallow cavities.
Computational Thermal Sciences: An International Journal, 2020
We present a study of Rayleigh-Benard natural convection to highlight the effects of some boundar... more We present a study of Rayleigh-Benard natural convection to highlight the effects of some boundary conditions about heat transfer in a cubic cavity filled with air. Three boundary conditions relative to temperature and velocity of fluid particles on walls of the cavity are considered. The obtained results are compared to the 2D problem. We prove that tridimensional effects are negligible for a particular boundary condition, consequently, we conclude that such configuration can be assimilated to its equivalent in 2D. Mots clefs : Transfert de chaleur, Convection naturelle, Simulation numerique directe, Cavite carre/cubique, Refroidissement composant electronique.
La presente investigation porte sur une etude numerique de convection naturelle bidimensionnelle ... more La presente investigation porte sur une etude numerique de convection naturelle bidimensionnelle dans une cavite de type Rayleigh-Benard. La methode numerique est basee sur un schema de type volumes finis du second ordre et une methode de projection. Une approche multigrille est utilisee pour accelerer la convergence de lequation de Poisson. Nous allons etudier dans une premiere partie leffet des conditions initiales relatives a la temperature (eint) sur lecoulement du fluide. Dans une deuxieme etape, nous determinons le nombre de Rayleigh critique (Rac)I au-dela duquel les particules fluides se mettent en mouvement et lecoulement devient instationnaire. Enfin une application physique portant sur letude de leffet des parametres de controle de notre configuration, a savoir le rapport de forme (A) et la nature du fluide(Pr) sera par la suite presentee.
International Journal of Thermal and Environmental Engineering, 2018
Fluid flow structures and heat transfer rates in a rectangular enclosure of aspect ratio of two c... more Fluid flow structures and heat transfer rates in a rectangular enclosure of aspect ratio of two containing two heated cylindrical blocks and filled with various water-based nanofluids is investigated. The free space between the cylindrical blocks and the enclosure walls is filled with four nanofluids: Cu-water, Ag-water, Al 2 O 3-water and TiO 2-water. The controlling parameters to be considered are: the Rayleigh number 6 3 04. 0 . Additionally, the inclination angle can be used as a control parameter for rectangular enclosures housing two equal heated blocks which are cooled with waterbased nanofluids.
International Journal of Thermal Sciences, 2020
Three-dimensional numerical simulations were conducted for the natural convection phenomena which... more Three-dimensional numerical simulations were conducted for the natural convection phenomena which occurs between an inner hot body and its outer enclosure. The physical model considered here is that a body of cubical shape is located at the center of an isothermal cooled spherical enclosure. Therefore, the fluid flow inside the enclosure results from the temperature difference between the cooled spherical enclosure and the heated cube. The governing equations are solved using a second-order accurate finite volume approach on a staggered grid system and multi-grid acceleration. Three different fluids, an air (Pr = 0.71), a water (Pr = 6.2) and the other a dielectric liquid (Pr = 25) are employed encompassing descriptive Rayleigh numbers Ra that range three orders of magnitude from 10 4 to 10 7. The conducted benchmark study leads to excellent accordance with previous findings. Detailed three-dimensional flow and thermal structures in the enclosure were analyzed using the distribution of iso-contours of temperature, iso-surfaces of the standard velocity vector and streamtraces for different Rayleigh numbers. The variation of the local and the surface-averaged Nusselt numbers at the inner hot cube wall are also presented to exhibit the overall heat transfer characteristics inside the enclosure. At the end, monomial correlations are presented for the quantification of the heat transfer that emanates from the heated cube and the spherical enclosure in harmony with the various Rayleigh number. It was found that the thermal and flow fields eventually reach steady state for Rayleigh numbers ranging from 10 4 to 10 7. Results indicate also that the heat transfer is increasing significantly by increasing Rayleigh numbers and optimal heat transfer rate is obtained for high Rayleigh number set to 10 7 .
International Journal of Numerical Methods for Heat & Fluid Flow, 2019
Purpose Two-dimensional incompressible fluid flows around a rectangular shape placed over a large... more Purpose Two-dimensional incompressible fluid flows around a rectangular shape placed over a larger rectangular shape at low Reynolds numbers (Re) have been numerically analyzed in the present work. The vortex shedding is investigated at different arrangements of the two shapes allowing the investigation of three possible configurations. The calculations are carried out for several values of Re ranging from 1 to 200. The effect of the obstacle geometry on the vortex shedding is analyzed for crawling, steady and unsteady regimes. The analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow becomes unstable and undergoes a bifurcation. This paper aims to observe that the transition of the unsteady regime is performed by a Hopf bifurcation. The critical Re beyond which the flow becomes unsteady is determined for each configuration. A special attention is paid to compute the drag and lift forces acting on the rectangular shapes, which allowed...
International Journal of Numerical Methods for Heat & Fluid Flow, 2017
Purpose The purpose of this paper is to examine numerically the three natural convection of air i... more Purpose The purpose of this paper is to examine numerically the three natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and titled angle of the enclosure from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy, and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature and isosurfaces of velocity eventually reaches a steady state in the range of Rayleigh numbers between 103 and 107 for titled inclination of 90°; however, for the remaining inclinations, Rayleigh number must be in the range 103-106 to avoid unsteady state, which is manifested by the division of the area containing the maximum local heat transfer rate into three parts for a Rayl...
International Journal of Numerical Methods for Heat & Fluid Flow, 2018
Purpose This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on th... more Purpose This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed ...
Computers & Fluids, 2017
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights The unsteady behavior of two-sided lid-driven cubical cavity induced by an obstacle was performed. The flow undergoes a bifurcation with a critical Reynolds number of 1034. Percentage difference of critical Reynolds number between two-and one-sided lid-driven obstructed cavities is 41.714%.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017
x, y Dimensionless coordinates St Strouhal number CD Drag coefficient CL Lift coefficient p Dimen... more x, y Dimensionless coordinates St Strouhal number CD Drag coefficient CL Lift coefficient p Dimensionless pressure φ Generic variable Greek symbols ρ Density of fluid, kg m −3 ν Kinematic viscosity, m 2 s −1 Subscripts Max, Min Maximum, minimum c Critical Keywords Obstacle • Incompressible fluid flow • Finitevolume method • Von Karman vortex street • Lift and drag coefficients • Strouhal number List of symbols Re Reynolds number l Channel width h Channel height (u, v) Velocity components, m s −1
Particulate Science and Technology, 2016
ABSTRACT In this paper, we numerically investigate the steady laminar natural convection in a wat... more ABSTRACT In this paper, we numerically investigate the steady laminar natural convection in a water-filled 2D enclosure containing a rectangular conducting body. Computations are performed for a wide range of dimensionless parameters including the Rayleigh number Ra, the thermal conductivity ratio k, and the location of the inner body δ, while the value of the Prandtl number is maintained constant at 6.8. This simulation spans four decades of Rayleigh number, Ra, from 103 to 106. The influence of these various dimensionless parameters on the flow behavior is investigated. Correlations of the averaged Nusselt numbers are obtained as a function of two parameters (Ra and δ) for each working thermal conductivity ratio. The results indicate that the heat transfer rate through the enclosure can be controlled by the position of the rectangular body. A comparative study was also carried out between a horizontal and a vertical conducting shape inside the enclosure. It is proved that a vertical position leads to a better heat transfer compared to the horizontal case.
International Letters of Chemistry, Physics and Astronomy, 2015
This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. ... more This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bi...
Journal of Applied Mechanical Engineering, 2015
International Letters of Chemistry, Physics and Astronomy, 2015
Three dimensional steady state mixed convection in a lid driven cubical cavity heating from below... more Three dimensional steady state mixed convection in a lid driven cubical cavity heating from below has been investigated numerically. Two sided walls are maintained at a constant ambient temperature Ttop > Tbottom, while the vertical walls are thermally insulated. Governing equations expressing in a dimensionless form are solved by using finite element method. The Reynolds number is fixed at Re=100, while the Richardson number is varied from 0.001 to 10. Parametric studies focusing on the effect of the Richardson number on the fluid flow and heat transfer have been performed. The flow and heat transfer characteristics, expressed in terms of streamlines, isotherms and average wall Nusselt number are presented for the entire range of Richardson number considered. Multiple correlations in terms of the heat transfer rate and Richardson number has been established.
International Letters of Chemistry, Physics and Astronomy, 2015
The present work deals with the prediction of a natural convection flow in a square cavity, parti... more The present work deals with the prediction of a natural convection flow in a square cavity, partially heated by an obstacle placed at the bottom wall. The two transverse walls and the top wall of the cavity are supposed to be cold, the remaining walls are kept insulated. The main parameter of numerical investigations is the Rayleigh number (engine convection) varying from 103 to 105. When Ra is fixed at 107, the flow and thermal fields bifurcate and undergoes an unsteady behavior at critical positions. Flow patterns corresponding to the unsteady state are presented and analyzed in the current study. The simulations were conducted using a numerical approach based on the finite volume method and the projection method, which are implemented in a computer code in order to solve the Navier-Stokes equations.
High Temperature, 2014
ABSTRACT This work addresses a numerical approach based on the finite volume method and a full mu... more ABSTRACT This work addresses a numerical approach based on the finite volume method and a full multi-grid technique to study three-dimensional flow structures and heat transfer rates in cubical cavity partially heated from one wall. The working fluid is air so that the Prandtl number equates to 0.71. Numerical solutions are generated for representative values of the controlling Rayleigh number inside the range 103 ≤ Ra ≤ 107. The heating occurs with a heated strip placed inside the enclosure. Three scenarios are investigated: (i) the heated source is mounted on the bottom horizontal wall, (ii) the heated source is mounted horizontally on the lateral wall, and (iii) the heated source is mounted vertically on the lateral wall. Effects of heated strip position in the enclosure on heat transfer are studied. It is shown that suitable configuration which generates highest heat transfer rate through the heated strip is depending on Rayleigh number. Results are presented in the form of projection of flow lines and isotherms plots as well as the variation of the Nusselt number and the average temperature at the heat source surface for all configurations computed in this study.
Proceedings of International Symposium on Convective Heat and Mass Transfer in Sustainable Energy, 2009
The papers deals with a numerical 3D study of natural convection in a finned Rayleigh-Benard (RB)... more The papers deals with a numerical 3D study of natural convection in a finned Rayleigh-Benard (RB) cubical enclosure. A single fin with a thickness of 10% of the cavity side (and a height of 50%) is placed vertically on the bottom hot wall at T H . The working fluid is air with ...
Numerical Heat Transfer, Part B: Fundamentals, 2007
A computational procedure is presented with an accelerated full-multigrid scheme for an efficient... more A computational procedure is presented with an accelerated full-multigrid scheme for an efficient modeling of time-dependent buoyancy-driven flows. The smoother is the iterative red-and-black successive overrelaxation (RBSOR) scheme. In order to improve the convergence, an acceleration parameter, Γ, is implemented in the classical full-multigrid procedure. It is shown that an optimal value of Γ = 3.75 minimizes the number of iterations needed
Numerical Heat Transfer, Part A: Applications, 2009
and-conditions-of-access.pdf This article may be used for research, teaching and private study pu... more and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
Journal of Heat Transfer, 2007
The effect of aspect ratio on natural convection flow in a cavity submitted to periodic temperatu... more The effect of aspect ratio on natural convection flow in a cavity submitted to periodic temperature boundary, is investigated numerically. The temperature of the heated wall is either maintained constant or varied sinusoidally with time while the temperature of the opposite vertical wall is maintained constant. The results are given for a range of varied parameters as Rayleigh number (5×103⩽Ra⩽106), cavity aspect ratio (1∕6⩽A⩽8), and period of the sinusoidally heated wall (1⩽τ⩽1600). The amplitude of oscillation (a=0.8) and the Prandtl number (Pr=0.71) were kept constant. The results obtained in the steady state regime show that the heat transfer averaged over the cold wall is maximum when the aspect ratio is in the range 1⩽A⩽2. In the case of a periodic temperature boundary, it is shown that the deviation between the mean heat transfer and the heat transfer of the constant heated case is larger for shallow cavities.