Heatfunction Formulation of Thermal Convection in Rectangular Enclosures Filled with Porous Media

Abstract

Numerical investigations were conducted to study the effects of Rayleigh, Ra, Prandtl, Pr, Darcy, Da, numbers, and the temperature difference ratio, J, on the fluid flow, isotherms, heat transfer, and distributions in a square cavity filled with porous medium. The range of parameters used is 5 Â 10 2 e Ra e 10 6 , 10 23 e Pr e 10 3 , 10 23 e Da e 10 3 , and 0 e J e 2. The flow governing equations including the Brinkman-extended Darcy equations of motion, energy, and heatfunction equations were thereby solved using the finite-difference method.The results show that all the problem governing parameters have strong effect on the convection vigour, isotherms, and heatfunction fields and profiles. An increase in the value of the Darcy number above unity has no more influence on the heatfunction profiles.

Numerical study of natural convection in a vertical porous annulus with discrete heating

“…The quantitative results are compared with the corresponding solutions of Waheed [42] for a rectangular porous cavity and are given in Table 2. As can be seen from Table 2, the results of the present simulation agree well with the results of Waheed [42] over the entire range of Rayleigh and Darcy numbers.…”

“…The quantitative results are compared with the corresponding solutions of Waheed [42] for a rectangular porous cavity and are given in Table 2. As can be seen from Table 2, the results of the present simulation agree well with the results of Waheed [42] over the entire range of Rayleigh and Darcy numbers. Finally, due to lack of suitable theoretical or experimental results for a discretely heated cylindrical annular cavity, the present model has been validated against the discretely heated rectangular cavity investigated by Corcione and Habib [35] in the absence of porous medium.…”

Visualization of heat flow in a vertical channel with fully developed mixed convection

“…Basak et al and Kaluri et al [8][9][10] performed several studies on heat transport field for various domains under different boundary conditions. Waheed [11] studied the problem of the natural laminar convection in square enclosures filled with fluidsaturated porous medium by using the heatfunction formulation approach. The above literature review reveals that most of the studies on visualization of heat flow were performed on the closed spaces such as closed cavities rather than channels and ducts.…”

Finite element simulations on heatline trajectories for mixed convection in porous square enclosures: Effects of various moving walls

“…It was observed that, the heat transfer rate is higher for the moving bottom wall (case 2) for all values of the Darcy numbers. Waheed et al [32] investigated the Darcy-Brinkman-Forchheimer model based mixed convection fluid flow and heat transfer in a rectangular porous enclosure in the presence of a heated lid which moves through the cavity at the mid-horizontal plane.…”

“…Limited number of studies focused on the distributions of the fluid and heat flow fields within the enclosed porous cavity based on various motions of the horizontal [30][31][32] or vertical walls [33][34][35] or both [36]. Muthtamilselvan et al [30] studied the effect of the magnetic field during mixed convection in a square cavity filled with the fluid saturated porous medium using the finite volume method.…”