Effect of Conjugate Heat Transfer on Entropy Generation in Slip-Driven Microflow of Power Law Fluids

Abstract

ABSTRACTWe analyze the entropy generation characteristics in a non-Newtonian microflow under the influence of interfacial slip as modulated by the conjugate transport of heat. We consider power law model to represent the constitutive behavior of the non-Newtonian fluid. In this analysis, we analytically solve the transport equations employing the thermal boundary condition of the third kind at the exterior wall surface accounting for the effect of conjugate heat transfer. We demonstrate that the slip flow–driven alteration in convective transport of heat and its nonlinear interaction with viscous dissipation, as modulated by fluid rheology and conjugate transport of heat, gives rise to a minimum entropy generation rate of the system. We determine the optimum value of the geometrical parameter—that is, the channel wall thickness and the thermophysical parameters, such as the Biot number and Peclet number—leading to a minimum entropy generation rate in the system. The results of this analysis could be of helpful in designing microsystems/devices typically used for electronic cooling, micro-heat pipes, and micro-heat exchangers.