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Papers by abdellah belkacem

Proceedings of the 4th International Conference of Fluid Flow, Heat and Mass Transfer, May 1, 2016

The effect of steady-state natural convection in undulation wall is presented. The two-dimensiona... more The effect of steady-state natural convection in undulation wall is presented. The two-dimensional numerical analysis is carried out with a method called CVFEM thermally coupled. Incompressible flow formulation written in terms of primitive variables ,this method uses the interpolation equal order velocity-pressure to the resolution of the Navier-Stokes equations, and is applied to the laminar flow problems in natural convection in a vertical channel heated symmetrically, one case is for a single undulation, the other case with several undulations. The thermal boundaries conditions used are uniform wall temperature. The profiles of the local and average Nusselt number are presented for all the studied cases. FORTRAN code is elaborated in this paper.

Advances and Applications in Fluid Mechanics, Sep 8, 2016

International Review of Mechanical Engineering-IREME, May 31, 2016

In this paper a numerical Study of natural convection-Surface radiation coupling in a differentia... more In this paper a numerical Study of natural convection-Surface radiation coupling in a differentially heated 2D square cavity, while the horizontal walls are insulated and all walls have the same emissivity filled with air is presented. The governing equations are formulated in Helmholtz variables (ψ, ω).The study has been investigated by a numerical method; the basic principle of this method is the Gauss’s theorem (integrals over a closed line around an area). The current method was developed for being used on triangular meshes. The paper presents the main convective and radiative Nusselt numbers distributions for various Rayleigh number and for various emissivity values, the isothermal and streamlines are also presented. The effect of emissivity on the net radiative flux, temperature and velocity profiles has been analyzed. The increasing of emissivity increases the net radiative flux at the top horizontal wall (the top wall loses the heat depending the emissivity's value) and decreases the net radiative flux at the bottom horizontal wall (the bottom wall receives the heat depending the emissivity's value).

International Review of Mechanical Engineering-IREME, May 31, 2016

In this paper a numerical Study of natural convection-Surface radiation coupling in a differentia... more In this paper a numerical Study of natural convection-Surface radiation coupling in a differentially heated 2D square cavity, while the horizontal walls are insulated and all walls have the same emissivity filled with air is presented. The governing equations are formulated in Helmholtz variables (ψ, ω).The study has been investigated by a numerical method; the basic principle of this method is the Gauss’s theorem (integrals over a closed line around an area). The current method was developed for being used on triangular meshes. The paper presents the main convective and radiative Nusselt numbers distributions for various Rayleigh number and for various emissivity values, the isothermal and streamlines are also presented. The effect of emissivity on the net radiative flux, temperature and velocity profiles has been analyzed. The increasing of emissivity increases the net radiative flux at the top horizontal wall (the top wall loses the heat depending the emissivity's value) and decreases the net radiative flux at the bottom horizontal wall (the bottom wall receives the heat depending the emissivity's value).

The present study focuses on the effect of nanofluid for heat transfer on laminar forced convecti... more The present study focuses on the effect of nanofluid for heat transfer on laminar forced convection internal flow. Square duct with constant wall temperature is considered, and newtonian fluid model for fully hydrodynamically and thermally developed flow is applied. Variable thermophysical properties for the fluid and negligible viscous dissipation are assumed. The numerical solution of the problem is based on the finite volume method for quadrilaterals unstructured mesh. In this scheme, based on the integration around the polygonal control volume, the derivatives of the flow equations must be converted into closed line integrals using similar formulation of the Stokes theorem. The profiles of velocity and temperature are determined, the friction factors and the Nusselt number are predicted for different nanoparticle concentration (0 ≤ φ ≥ 10%) for both nanofluids (Water-γAl2O3 and Ethylene Glycol-γAl2O3). The results show that the average velocity decreases and the friction factor increases when the nanoparticle concentration rises. The use of a nanofluid has a beneficial effect on the heat transfer. The results obtained have clearly revealed that the inclusion of nanoparticles has produced a considerable improvement of the heat transfer, which clearly becomes important with an augmentation of the particle concentration. The solution method is verified for absence of the nanoparticle concentration case.

In the present work, we present a numerical method able to capture the optimum thermal performanc... more In the present work, we present a numerical method able to capture the optimum thermal performances of finned surfaces of high and low conductivity. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by restoring to the finite volumes method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. In this study it is shown that a finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation, in order to determine the sinusoidal parameter values which optimize the fin effectiveness. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the 'Stokes theorem'. The heat flux dissipated by generic profile fin is compared with the heat flux removed by rectangular profile with the same length and volume. The numerical method is then applied to the case of sinusoidal profiles fin that represent problems with complex geometries, which make the heat transfer fluxes as high as possible under different conditions. The optimum profile is finally shown for different sinusoidal profiles.

In the present work, we present a numerical method able to capture the optimum thermal performanc... more In the present work, we present a numerical method able to capture the optimum thermal performances of finned surfaces of high and low conductivity. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by restoring to the finite volumes method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. In this study it is shown that a finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation, in order to determine the sinusoidal parameter values which optimize the fin effectiveness. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the ‘Stokes theorem’. The heat flux dissipated by generic profile fin is compared with the hea...

The present study focuses on the effect of nanofluid for heat transfer on laminar forced convecti... more The present study focuses on the effect of nanofluid for heat transfer on laminar forced convection internal flow. Square duct with constant wall temperature is considered, and newtonian fluid model for fully hydrodynamically and thermally developed flow is applied. Variable thermophysical properties for the fluid and negligible viscous dissipation are assumed. The numerical solution of the problem is based on the finite volume method for quadrilaterals unstructured mesh. In this scheme, based on the integration around the polygonal control volume, the derivatives of the flow equations must be converted into closed line integrals using similar formulation of the Stokes theorem. The profiles of velocity and temperature are determined, the friction factors and the Nusselt number are predicted for different nanoparticle concentration (0 ≤ φ ≥ 10%) for both nanofluids (Water-γAl2O3 and Ethylene Glycol-γAl2O3). The results show that the average velocity decreases and the friction factor ...

The present paper deals with the approximation of the solutions of partial differential equations... more The present paper deals with the approximation of the solutions of partial differential equations that describe the phenomena of heat transfer and fluid flow, using a method based on Stokes' theorem and applied an unstructured computational mesh. The thus developed method will be applied in a problem of heat transfer charactiristics of laminar fully developed flow. After developing a code for calculating quantitative tests are planned to determine the accuracy of the method by the comparison with analytical solution or other studies that are already done. Keywords—Numerical method, unstructured grid, heat transfer, fully developed flow, complex geometry.

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 2020

The objective of this work is the mathematical modelling and the numerical simulation of the stat... more The objective of this work is the mathematical modelling and the numerical simulation of the stationary, laminar, and natural convection, in a confined square cavity (H = L) filled with two fluids (a mixture of nanoparticles of aluminum oxide and Al2O3 water) in one partition and pure water in the other partition. A porous conductive wall of thickness w (w = L/e) and thermal conductivity Keff constitutes the exchange surface between these two partitions. The fluid movement is modeled by the Navier-Stokes equations in the two partitions, while the porous medium is modelled by the Darcy–Brinkman equation. Comsol Multiphysics software is used to solve the system of differential equations that is based on the finite element method. The results are discussed with particular attention to the mean and local Nusselt number (Nu), streamlines and isotherms. A parametric study for Rayleigh number Ra (102 to 106), volume fraction j (0% to 10%), and Darcy number Da (10-7 to 10-2) is performed. T...

Advances and Applications in Fluid Mechanics, 2016

Journal of Applied Sciences, 2007

International Review of Mechanical Engineering (IREME), 2018

The present work enlightens the study of laminar natural convection in an isosceles right-angled ... more The present work enlightens the study of laminar natural convection in an isosceles right-angled triangular cavity filled with water. The bottom wall of the cavity contains a caterpillar (C)-curve shape wavy wall, having different width (w = 0.20b, 0.25b, 0.33b and 0.50b) and aspect ratio (d) with 0 6 d 6 0.15. Vertical and incline walls of the cavity are considered individually and together for cooling purpose. The physical model is solved to examine the effect of constrained parameters such as hot wall profiles, configurations of cold walls and Rayleigh number (10 5-10 7) on the fluid flow and heat transfer. The study is carried out numerically by commercially available software FLUENT 6.3. The deviation in the flow pattern and temperature profile is displayed by streamlines and isotherms contours whereas the variation in heat transfer rate is presented by local and average Nusselt number. It is found from the investigation that the heat transfer rate is enhanced significantly for caterpillar curved shape wavy wall than the flat hot wall. Moreover, the rate of heat transfer is varied profoundly with the location of cold walls.

Energy Procedia, 2017

District heating networks are commonly addressed in the literature as one of the most effective s... more District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand-outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations.

International Review of Mechanical Engineering (IREME), 2016

In this paper a numerical Study of natural convection-Surface radiation coupling in a differentia... more In this paper a numerical Study of natural convection-Surface radiation coupling in a differentially heated 2D square cavity, while the horizontal walls are insulated and all walls have the same emissivity filled with air is presented. The governing equations are formulated in Helmholtz variables (ψ, ω).The study has been investigated by a numerical method; the basic principle of this method is the Gauss’s theorem (integrals over a closed line around an area). The current method was developed for being used on triangular meshes. The paper presents the main convective and radiative Nusselt numbers distributions for various Rayleigh number and for various emissivity values, the isothermal and streamlines are also presented. The effect of emissivity on the net radiative flux, temperature and velocity profiles has been analyzed. The increasing of emissivity increases the net radiative flux at the top horizontal wall (the top wall loses the heat depending the emissivity's value) and decreases the net radiative flux at the bottom horizontal wall (the bottom wall receives the heat depending the emissivity's value).

Proceedings of the 3rd International Conference of Fluid Flow, Heat and Mass Transfer (FFHMT'16), 2016

The effect of steady-state natural convection in undulation wall is presented. The two-dimensiona... more The effect of steady-state natural convection in undulation wall is presented. The two-dimensional numerical analysis is carried out with a method called CVFEM thermally coupled. Incompressible flow formulation written in terms of primitive variables ,this method uses the interpolation equal order velocity-pressure to the resolution of the Navier-Stokes equations, and is applied to the laminar flow problems in natural convection in a vertical channel heated symmetrically, one case is for a single undulation, the other case with several undulations. The thermal boundaries conditions used are uniform wall temperature. The profiles of the local and average Nusselt number are presented for all the studied cases. FORTRAN code is elaborated in this paper.

EPJ Web of Conferences, 2016

This study focuses on the numerical simulation of heat transfer by natural convection in a rectan... more This study focuses on the numerical simulation of heat transfer by natural convection in a rectangular enclosure, filled with a liquid metal (low Prandtl number) partially heated from below with a sinusoidal temperature. The value of the study lies in its involvement in the crystal growth for the manufacture of semiconductors and electronics cooling. Indeed, the occurrence of convection during crystal growth can lead to in homogeneities that lead to striations and defects that affect the quality of the crystals obtained by the Bridgman techniques or Chochrawlski. Temperature of the oscillations, due to the instabilities of the convective flow in the liquid metal, also induces non-uniform cooling in the solidification front. Convection is then studied in order to reduce it. A modelling of the problem in two dimensions was conducted using Comsol computer code that is based on the finite element method, by varying the configuration of the control parameters, namely, the Rayleigh number, the nature of fluid (Prandtl number) and amplitude of temperature on heat transfer rate (Nusselt number) on convective structures that appear. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits distribution, and reproduction in any medium, provided the original work is properly cited.

Proceeding of Proceedings of CHT-15. 6th International Symposium on ADVANCES IN COMPUTATIONAL HEAT TRANSFER , May 25-29, 2015, Rutgers University, New Brunswick, NJ, USA, 2015

Journal of Applied Sciences, 2006

Proceedings of the 4th International Conference of Fluid Flow, Heat and Mass Transfer, May 1, 2016

The effect of steady-state natural convection in undulation wall is presented. The two-dimensiona... more The effect of steady-state natural convection in undulation wall is presented. The two-dimensional numerical analysis is carried out with a method called CVFEM thermally coupled. Incompressible flow formulation written in terms of primitive variables ,this method uses the interpolation equal order velocity-pressure to the resolution of the Navier-Stokes equations, and is applied to the laminar flow problems in natural convection in a vertical channel heated symmetrically, one case is for a single undulation, the other case with several undulations. The thermal boundaries conditions used are uniform wall temperature. The profiles of the local and average Nusselt number are presented for all the studied cases. FORTRAN code is elaborated in this paper.

Advances and Applications in Fluid Mechanics, Sep 8, 2016

International Review of Mechanical Engineering-IREME, May 31, 2016

In this paper a numerical Study of natural convection-Surface radiation coupling in a differentia... more In this paper a numerical Study of natural convection-Surface radiation coupling in a differentially heated 2D square cavity, while the horizontal walls are insulated and all walls have the same emissivity filled with air is presented. The governing equations are formulated in Helmholtz variables (ψ, ω).The study has been investigated by a numerical method; the basic principle of this method is the Gauss’s theorem (integrals over a closed line around an area). The current method was developed for being used on triangular meshes. The paper presents the main convective and radiative Nusselt numbers distributions for various Rayleigh number and for various emissivity values, the isothermal and streamlines are also presented. The effect of emissivity on the net radiative flux, temperature and velocity profiles has been analyzed. The increasing of emissivity increases the net radiative flux at the top horizontal wall (the top wall loses the heat depending the emissivity's value) and decreases the net radiative flux at the bottom horizontal wall (the bottom wall receives the heat depending the emissivity's value).

International Review of Mechanical Engineering-IREME, May 31, 2016

In this paper a numerical Study of natural convection-Surface radiation coupling in a differentia... more In this paper a numerical Study of natural convection-Surface radiation coupling in a differentially heated 2D square cavity, while the horizontal walls are insulated and all walls have the same emissivity filled with air is presented. The governing equations are formulated in Helmholtz variables (ψ, ω).The study has been investigated by a numerical method; the basic principle of this method is the Gauss’s theorem (integrals over a closed line around an area). The current method was developed for being used on triangular meshes. The paper presents the main convective and radiative Nusselt numbers distributions for various Rayleigh number and for various emissivity values, the isothermal and streamlines are also presented. The effect of emissivity on the net radiative flux, temperature and velocity profiles has been analyzed. The increasing of emissivity increases the net radiative flux at the top horizontal wall (the top wall loses the heat depending the emissivity's value) and decreases the net radiative flux at the bottom horizontal wall (the bottom wall receives the heat depending the emissivity's value).

The present study focuses on the effect of nanofluid for heat transfer on laminar forced convecti... more The present study focuses on the effect of nanofluid for heat transfer on laminar forced convection internal flow. Square duct with constant wall temperature is considered, and newtonian fluid model for fully hydrodynamically and thermally developed flow is applied. Variable thermophysical properties for the fluid and negligible viscous dissipation are assumed. The numerical solution of the problem is based on the finite volume method for quadrilaterals unstructured mesh. In this scheme, based on the integration around the polygonal control volume, the derivatives of the flow equations must be converted into closed line integrals using similar formulation of the Stokes theorem. The profiles of velocity and temperature are determined, the friction factors and the Nusselt number are predicted for different nanoparticle concentration (0 ≤ φ ≥ 10%) for both nanofluids (Water-γAl2O3 and Ethylene Glycol-γAl2O3). The results show that the average velocity decreases and the friction factor increases when the nanoparticle concentration rises. The use of a nanofluid has a beneficial effect on the heat transfer. The results obtained have clearly revealed that the inclusion of nanoparticles has produced a considerable improvement of the heat transfer, which clearly becomes important with an augmentation of the particle concentration. The solution method is verified for absence of the nanoparticle concentration case.

In the present work, we present a numerical method able to capture the optimum thermal performanc... more In the present work, we present a numerical method able to capture the optimum thermal performances of finned surfaces of high and low conductivity. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by restoring to the finite volumes method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. In this study it is shown that a finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation, in order to determine the sinusoidal parameter values which optimize the fin effectiveness. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the 'Stokes theorem'. The heat flux dissipated by generic profile fin is compared with the heat flux removed by rectangular profile with the same length and volume. The numerical method is then applied to the case of sinusoidal profiles fin that represent problems with complex geometries, which make the heat transfer fluxes as high as possible under different conditions. The optimum profile is finally shown for different sinusoidal profiles.

In the present work, we present a numerical method able to capture the optimum thermal performanc... more In the present work, we present a numerical method able to capture the optimum thermal performances of finned surfaces of high and low conductivity. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by restoring to the finite volumes method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. In this study it is shown that a finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation, in order to determine the sinusoidal parameter values which optimize the fin effectiveness. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the ‘Stokes theorem’. The heat flux dissipated by generic profile fin is compared with the hea...

The present study focuses on the effect of nanofluid for heat transfer on laminar forced convecti... more The present study focuses on the effect of nanofluid for heat transfer on laminar forced convection internal flow. Square duct with constant wall temperature is considered, and newtonian fluid model for fully hydrodynamically and thermally developed flow is applied. Variable thermophysical properties for the fluid and negligible viscous dissipation are assumed. The numerical solution of the problem is based on the finite volume method for quadrilaterals unstructured mesh. In this scheme, based on the integration around the polygonal control volume, the derivatives of the flow equations must be converted into closed line integrals using similar formulation of the Stokes theorem. The profiles of velocity and temperature are determined, the friction factors and the Nusselt number are predicted for different nanoparticle concentration (0 ≤ φ ≥ 10%) for both nanofluids (Water-γAl2O3 and Ethylene Glycol-γAl2O3). The results show that the average velocity decreases and the friction factor ...

The present paper deals with the approximation of the solutions of partial differential equations... more The present paper deals with the approximation of the solutions of partial differential equations that describe the phenomena of heat transfer and fluid flow, using a method based on Stokes' theorem and applied an unstructured computational mesh. The thus developed method will be applied in a problem of heat transfer charactiristics of laminar fully developed flow. After developing a code for calculating quantitative tests are planned to determine the accuracy of the method by the comparison with analytical solution or other studies that are already done. Keywords—Numerical method, unstructured grid, heat transfer, fully developed flow, complex geometry.

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 2020

The objective of this work is the mathematical modelling and the numerical simulation of the stat... more The objective of this work is the mathematical modelling and the numerical simulation of the stationary, laminar, and natural convection, in a confined square cavity (H = L) filled with two fluids (a mixture of nanoparticles of aluminum oxide and Al2O3 water) in one partition and pure water in the other partition. A porous conductive wall of thickness w (w = L/e) and thermal conductivity Keff constitutes the exchange surface between these two partitions. The fluid movement is modeled by the Navier-Stokes equations in the two partitions, while the porous medium is modelled by the Darcy–Brinkman equation. Comsol Multiphysics software is used to solve the system of differential equations that is based on the finite element method. The results are discussed with particular attention to the mean and local Nusselt number (Nu), streamlines and isotherms. A parametric study for Rayleigh number Ra (102 to 106), volume fraction j (0% to 10%), and Darcy number Da (10-7 to 10-2) is performed. T...

Advances and Applications in Fluid Mechanics, 2016

Journal of Applied Sciences, 2007

International Review of Mechanical Engineering (IREME), 2018

The present work enlightens the study of laminar natural convection in an isosceles right-angled ... more The present work enlightens the study of laminar natural convection in an isosceles right-angled triangular cavity filled with water. The bottom wall of the cavity contains a caterpillar (C)-curve shape wavy wall, having different width (w = 0.20b, 0.25b, 0.33b and 0.50b) and aspect ratio (d) with 0 6 d 6 0.15. Vertical and incline walls of the cavity are considered individually and together for cooling purpose. The physical model is solved to examine the effect of constrained parameters such as hot wall profiles, configurations of cold walls and Rayleigh number (10 5-10 7) on the fluid flow and heat transfer. The study is carried out numerically by commercially available software FLUENT 6.3. The deviation in the flow pattern and temperature profile is displayed by streamlines and isotherms contours whereas the variation in heat transfer rate is presented by local and average Nusselt number. It is found from the investigation that the heat transfer rate is enhanced significantly for caterpillar curved shape wavy wall than the flat hot wall. Moreover, the rate of heat transfer is varied profoundly with the location of cold walls.

Energy Procedia, 2017

District heating networks are commonly addressed in the literature as one of the most effective s... more District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand-outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations.

International Review of Mechanical Engineering (IREME), 2016

In this paper a numerical Study of natural convection-Surface radiation coupling in a differentia... more In this paper a numerical Study of natural convection-Surface radiation coupling in a differentially heated 2D square cavity, while the horizontal walls are insulated and all walls have the same emissivity filled with air is presented. The governing equations are formulated in Helmholtz variables (ψ, ω).The study has been investigated by a numerical method; the basic principle of this method is the Gauss’s theorem (integrals over a closed line around an area). The current method was developed for being used on triangular meshes. The paper presents the main convective and radiative Nusselt numbers distributions for various Rayleigh number and for various emissivity values, the isothermal and streamlines are also presented. The effect of emissivity on the net radiative flux, temperature and velocity profiles has been analyzed. The increasing of emissivity increases the net radiative flux at the top horizontal wall (the top wall loses the heat depending the emissivity's value) and decreases the net radiative flux at the bottom horizontal wall (the bottom wall receives the heat depending the emissivity's value).

Proceedings of the 3rd International Conference of Fluid Flow, Heat and Mass Transfer (FFHMT'16), 2016

The effect of steady-state natural convection in undulation wall is presented. The two-dimensiona... more The effect of steady-state natural convection in undulation wall is presented. The two-dimensional numerical analysis is carried out with a method called CVFEM thermally coupled. Incompressible flow formulation written in terms of primitive variables ,this method uses the interpolation equal order velocity-pressure to the resolution of the Navier-Stokes equations, and is applied to the laminar flow problems in natural convection in a vertical channel heated symmetrically, one case is for a single undulation, the other case with several undulations. The thermal boundaries conditions used are uniform wall temperature. The profiles of the local and average Nusselt number are presented for all the studied cases. FORTRAN code is elaborated in this paper.

EPJ Web of Conferences, 2016

This study focuses on the numerical simulation of heat transfer by natural convection in a rectan... more This study focuses on the numerical simulation of heat transfer by natural convection in a rectangular enclosure, filled with a liquid metal (low Prandtl number) partially heated from below with a sinusoidal temperature. The value of the study lies in its involvement in the crystal growth for the manufacture of semiconductors and electronics cooling. Indeed, the occurrence of convection during crystal growth can lead to in homogeneities that lead to striations and defects that affect the quality of the crystals obtained by the Bridgman techniques or Chochrawlski. Temperature of the oscillations, due to the instabilities of the convective flow in the liquid metal, also induces non-uniform cooling in the solidification front. Convection is then studied in order to reduce it. A modelling of the problem in two dimensions was conducted using Comsol computer code that is based on the finite element method, by varying the configuration of the control parameters, namely, the Rayleigh number, the nature of fluid (Prandtl number) and amplitude of temperature on heat transfer rate (Nusselt number) on convective structures that appear. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits distribution, and reproduction in any medium, provided the original work is properly cited.

Proceeding of Proceedings of CHT-15. 6th International Symposium on ADVANCES IN COMPUTATIONAL HEAT TRANSFER , May 25-29, 2015, Rutgers University, New Brunswick, NJ, USA, 2015

Journal of Applied Sciences, 2006