Numerical study on combined convection heat transfer flow problem in a porous corrugated enclosure: Fid-Bau Portal

Numerical study on combined convection heat transfer flow problem in a porous corrugated enclosure

Choudhary, Pankaj / Ray, Rajendra K.

In this study, we numerically analyzed the unsteady two‐dimensional combined convection flow problem in a porous‐corrugated enclosure whose upper wall is moving with uniform velocity associated with sinusoidal temperature distribution. The vertical sidewalls of the porous‐corrugated enclosure are kept at constant cold temperature while square‐shaped undulations at the bottom wall are discretely heated. Five different cases are considered depending on the discrete isothermal heating. In this paper, we have used the vorticity‐stream‐function formulation of the Brinkmann‐extended Darcy model to numerically simulate the momentum transfer in a porous‐corrugated enclosure. A transformation‐free higher‐order compact (HOC) scheme is used to discretize the nonlinear coupled transport equations, and an advanced iterative solver, like the hybrid‐bi‐conjugate‐gradient stabilized technique, is used to solve the system of algebraic equations generated from the numerical discretization. The present higher‐order compact scheme is fourth‐order accurate in space coordinates and second‐order accurate in the time variable. The numerically simulated results are analyzed over a range of key parameters, like Darcy number $(1 0^{- 4} \leq D a \leq 1 0^{- 1})$ , Reynolds Number $(100 \leq R e \leq 1000)$ , Prandtl number $(0.015 \leq P r \leq 10)$ , and with fixed high Grashof number $(G r = 1 0^{6})$ , to study the effects of these leading parameters on the characteristics of heat transfer, fluid flow and isothermal distributions in the porous‐corrugated enclosure. These numerically computed results are presented in the form of streamlines, isotherms, Nusselt number plots, and so forth. Our computed results show numerous flow features which have not been studied previously.