Non-linear drag induced entropy generation analysis in a microporous channel: The effect of conjugate heat transfer

The entropy generation analysis in a viscous dissipative flow of a Newtonian fluid through a hyper-porous microchannel formed between two heated parallel plates is conferred. Employing an analytical method, which is consistent with the perturbation analysis, the transport equations governing the thermo-hydrodynamics are studied. The effects of nonlinear Forchheimer drag and conjugate heat transfer on the thermal transport characteristics of heat are considered, while the thermal boundary conditions of third kind have been employed at the outer boundaries of channel for the conjugate heat transfer analysis. The explicit alterations are made in the thermal transport of heat in the system as attributable to the effect of dissipative heat generated due to the non-linear effect Forchheimer drag, Darcy frictional effect and the viscous shearing stress in the flow field. To account these effects, the explicit variation of Forchhiemer constant, Darcy number, porosity, thickness and conductivity of upper wall and Biot number of upper wall are carried out to shows the changes in the available energy of the system. Also, it is shown that the effect of non-linear drag mainly stemming from the presence of complex porous structure in the flow field and its interaction with the conjugate transport of heat alters the heat transfer rate in the system non-trivially, which, in turn, gives rise to the entropy generation in the system. The individual contribution of two different effects viz., the heat transfer and viscous dissipation on the system entropy generation rate for different cases are studied. It is believed that the implications of the present analysis may have direct bearing on the design of micro devices/systems typically used in electronic cooling, micro-heat pipes.