Free convection in a square porous cavity using a thermal nonequilibrium model

http://www.oocities.org/eblgn/ebthinfin.pdf

Natural convection in cavities with a thin fin on the hot wall

MHD boundary layer flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with Navier slip

MHD nanofluid bioconvection due to gyrotactic microorganisms over a convectively heat stretching sheet

http://www.geocities.ws/eblgn/ebhakanhmt05.pdf

Natural convection heat transfer in partially open inclined square cavities

Multiple solutions for double-diffusive convection in a vertical porous enclosure

Convective heat transfer in a vertical anisotropic porous layer

The Galerkin and the finite element methods are used to study the onset of the double-diffusive convective regime in a rectangular porous cavity. The two vertical walls of the cavity are subject to constant fluxes of heat and solute while the two horizontal ones are impermeable and adiabatic. The analysis deals with the particular situation where the buoyancy forces induced by the thermal and solutal effects are opposing each other and of equal intensity. For this situation, a steady rest state solution corresponding to a purely diffusive regime is possible. To demonstrate whether the solution is stable or unstable, a linear stability analysis is carried out to describe the oscillatory and the stationary instability in terms of the Lewis number, Le, normalized porosity, e, and the enclosure aspect ratio, A. Using the Galerkin finite element method, it is shown that there exists a supercritical Rayleigh number, RsupTC, for the onset of the supercritical convection and an overstable Rayleigh number, RoverTC, at which overstability may arise. Furthermore, the overstable regime is shown to exist up to a critical Rayleigh number, RoscTC, at which the transition from the oscillatory to direct mode convection occurs. By using an analytical method based on the parallel flow approximation, the convective heat and mass transfer is studied. It is found that, below the supercritical Rayleigh number, RsupTC, there exists a subcritical Rayleigh number, RsubTC, at which a stable convective solution bifurcates from the rest state through finite-amplitude convection. In the range of the governing parameters considered in this study, a good agreement is observed between the analytical predictions and the finite element solution of the full governing equations. In addition, it is found that, for a given value of the governing parameters, the converged solution can be permanent or oscillatory, depending on the porous-medium porosity value, e.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112098001591

Double-diffusive convection instability in a vertical porous enclosure

This paper presents an analytical and numerical study of natural convection of a double-diffusive fluid contained in a rectangular slot subject to uniform heat and mass fluxes along the vertical sides. Governing parameters of the problem under study are the thermal Rayleigh number, Ra T ; buoyancy ratio, N; Lewis number, Le; Prandtl number, Pr and aspect ratio of the cavity, A. In the first part of the analytical study a scale analysis is applied to the two extreme cases of heat-transfer and mass-transfer-driven flows. In the second part, an analytical solution, based on the parallel flow approximation, is reported for tall enclosures (A<1). Solutions for the flow fields, temperature and concentration distributions and Nusselt and Sherwood numbers are obtained in terms of the governing parameters of the problem. In the limits of heat-driven and solute-driven flows a good agreement is obtained between the prediction of the scale analysis and those of the analytical solution. The numerical solutions are based on the complete governing equations for two-dimen- sional flows, and cover the range 14Ra T 4107 ,0 4 N 4105, 10~34Le4103 ,1 4 A 420 and Pr\7. A good agreement is found between the analytical predictions and the numerical simulation. Analytische und numerische Untersuchung der durch Doppeldiffusion ausgelo‹ sten Konvektion in einem vertikalen Schacht Zusammenfassung In der Arbeit wird analytisch und

E. Bilgen

Papers

Natural convection heat transfer in partially open inclined square cavities

Multiple solutions for double-diffusive convection in a vertical porous enclosure

Convective heat transfer in a vertical anisotropic porous layer

Double-diffusive convection instability in a vertical porous enclosure

Analytical and numerical study of double diffusive convection in a vertical enclosure