Numerical analysis of natural convection heat transfer and entropy generation in a porous quadrantal cavity

The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall.

Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected to uniform heating on the bottom wall. The governing transport equations are solved using the finite element method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 10³ to 10⁶ and Darcy number (Da) in the range of 10⁻⁵-10⁻².

A complex interaction between the buoyant and viscous forces that govern the transport of heat and entropy generation and the permeability of the porous medium plays a significant role on the same. The effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (10³, 10⁴), while there is a significant alteration in Nusselt number for Ra ≥10⁵ and moreover, the change is more intense for larger values of Da. For lower values of Ra (≤10⁴), the main contributor of irreversibility is the thermal irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player at higher values of Ra (=10⁶) and Da (=10⁻²).

From an industrial point of view, the present study will have applications in micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and lubrication systems.

This research examines numerically the buoyancy driven heat transfer irreversibility in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that was not investigated in the literature before.