Natural convection heat transfer and entropy generation in a porous rhombic enclosure: influence of non-uniform heating

Abstract

In this paper, we present a numerical investigation of natural convection heat transfer and entropy generation for a rhombic enclosure with inclination angle, ϕ = 30°, filled with a porous medium. The left and right surface walls of the enclosure are confined to cold temperature bath while we impart non-uniform, varying temperature distribution with unequal phase angles along the top and bottom wall. The flow inside the enclosure is steady, two-dimensional, incompressible and laminar, and the working fluid is air (Pr = 0.71). Numerical experiments have been performed using finite element method-based software COMSOL Multiphysics 5a for Darcy number and Rayleigh number in the extent of 10−4–10−2 and 103–106, respectively, in addition to phase deviation angles varying in the range from 0 to π. The amplitude parameter associated with the temperature delineation of the bottom and top walls is kept constant. The realizations from the numerical investigation are exhibited by streamlines and isotherms, local and average heat transfer Nusselt number along with the local distribution of heat transfer and fluid friction irreversibilities. The rate of heat transfer demonstrates non-monotonic trends and can be considerably influenced by the interplay of the phase shift angle, Rayleigh number and Darcy number. Upon increasing the value of phase shift angle from 0 to π, average Nusselt number initially decreases and thereafter shows an increase in its value. As the Darcy number increases, average Nusselt number for the bottom wall increases, while for the top wall it strongly depends on phase shift angle. In terms of entropy generation, it is found that the significant contributor to irreversibility is induced by heat transfer and the location of maximum entropy varies with the change in phase angle. More specifically, minimum entropy generation for any value of Rayleigh number and Darcy number is obtained for a phase shift angle of π/4 and maximum for 3π/4. The concomitant transport characteristics bear significance from the context of design of thermal systems pertaining to the theme of non-uniform heating with the phase angle being a crucial design parameter.