Cheikh Mbow

Numerical analysis of the effect of radiation on laminar steady natural convection in a two-dimensional participating medium between two horizontal confocal elliptical cylinders

Combined radiation and natural convection in a participating medium between two horizontal confocal elliptical cylinders is investigated numerically. The equations of steady, laminar two-dimensional natural convection are written by using an elliptic-cylinder coordinates system, the stream function, and the vorticity. The finite volume radiation solution method and the control volume technique are used to discretize the coupled equations of momentum, energy, and radiative transfer. Numerical solutions are obtained for Rayleigh numbers in the range 104 to 2x105 and the radiation-conduction parameter ranging from 0 to infinity. The special case corresponding to the convective flow within the annulus formed by an elliptical cylinder surrounding a flat plate is also considered.

Numerical analysis of combined radiation and unsteady natural convection within a horizontal annular space

The effect of radiation on unsteady natural convection in a two‐dimensional participating medium between two horizontal concentric and vertically eccentric cylinders is investigated numerically. The equations of transfer are written by using a bicylindrical coordinates system, the stream function, and the vorticity. The finite volume radiation solution method and the control volume approach are used to discretize the coupled equations of radiative transfer, momentum, and energy. Original results are obtained for three eccentricities, Rayleigh number equal to 104, 105, and a wide range of radiation‐conduction parameter. The effects of optical thickness, wall emissivity, and scattering on flow intensity and heat transfer are discussed.

Étude numérique du couplage rayonnement-convection naturelle en régime permanent dans des secteurs et des espaces annulaires à l'aide de la méthode des volumes finis

Abstract Combined radiation and natural convection within annular spaces and sectors are investigated numerically. The medium is considered as gray, emitting, absorbing, and isotropically scattering gas. The finite volume radiation solution method and the control volume approach are used to discritize the coupled equations of momentum, energy, and radiative transfer. The effects of the boundary conditions (for annular sectors) and the position of inner cylinder (for annular spaces) on the intensity and the stability of the flow are analyzed. Numerical solutions are obtained fo Pr = 0.7, Ra ≤ 2·10 5 , and the radiation-conduction parameter ranging from 0 to ∞.

Etude numérique de l'influence du transfert radiatif sur la convection naturelle laminaire, bidimensionnelle, permanente, dans un espace annulaire d'axe horizontal, délimité par deux cylindres circulaires isothermes

Abstract Combined radiation and natural convection in a participating medium between concentric or vertically eccentric horizontal cylinders is investigated numerically. The annular medium is considered as a gray, emitting, absorbing, and isotropically scattering gas. The equations of steady, laminar, two-dimensional, thermal, natural convection are written by using a two-cylindrical coordinate system, the stream function, and the vorticity. The finite volumes method is used to discretize the coupled equations of momentum, energy, and radiative transfer. To solve the global nonlinear algebraic equations the successive-over-relaxation iterating scheme is applied. Numerical solutions are obtained for a Rayleigh number in the range 10 3 –10 5 and radiation-conduction parameter ranging from 0 to ∞. The influences of radiation-conduction parameter, Rayleigh number and other parameters on flow and temperature distributions and heat transfer are discussed.

NUMERICAL STUDY OF MIXED CONVECTION AROUND A SPHERE ROTATING ABOUT ITS VERTICAL AXIS IN A NEWTONIAN FLUID AT REST AND SUBJECT TO A HEAT FLUX

We study numerically the steady state laminar mixed convection around a sphere heated by a nonuniform flux in a Newtonian fluid. The sphere rotates around its vertical axis. The governing transfer equations in this three-dimensional problem are solved by using the method of Cebeci-Keller. Three types of convection are considered: pure rotation, pure natural convection, and mixed convection. The profiles of the coefficients of heat transfer and local friction, as well as the profiles of temperature, will be determined for various distributions of a heat flux. In the case of a two-dimensional problem, our results agree with those in the literature.

Étude numérique du modèle de Boussinesq de convection naturelle laminaire transitoire dans un ellipsoide de révolution de grand axe vertical rempli d'air

Abstract The authors observed the transition of the system between two states of equilibrium by solving, with the help of a finite-difference method, the thermal unsteady laminar natural convection equations in an axisymmetric ellipsoid with vertical great axis filled with air. They showed that the number of convective cells varies from one to one by passing through a maximal value that depends on the Grashof number and on the aspect ratio. Simultaneously, the instantaneous average Nusselt number decreases in a monotonous way with time when the flow is unicellular and increases or decreases abruptly with each appearance or disappearance of cells.