effect of viscous heating on heat transfer and entropy generation inside a partially filled porous channel

The second laws of thermodynamics were investigated analytically for a two-dimensional partially filled porous channel. the porous layer is attached to the channel walls in the first test case and inserted in the channel core in the second one. the flow is laminar, incompressible, and steady with constant wall temperature. considering viscous dissipation effects, new analytical solutions for temperature, velocity, bejan, and entropy generation number profiles were obtained. the results of the new analytical solutions were validated against the numerical results of the lattice boltzmann method (lbm) which show very good agreement. using these analytical solutions, a detailed analysis of the effects of the brinkman number, darcy number, and the porous layer thickness on entropy generation and bejan numbers were carried out for the mentioned test cases. the results show that with the increase of br and da numbers for all investigated porous geometries, entropy generation, and bejan numbers increase.