Entropy Generation Minimization in a Pressure-Driven Microflow of Viscoelastic Fluid With Slippage at the Wall: Effect of Conjugate Heat Transfer

We focus on the entropy generation minimization for the flow of a viscoelastic fluid through a parallel plate microchannel under the combined influences of applied pressure gradient, interfacial slip, and conjugate heat transfer. We use the simplified Phan–Thien–Tanner model (s-PTT) to represent the rheological behavior of the viscoelastic fluid. Using thermal boundary conditions of the third kind, we solve the transport equations analytically to obtain the velocity and temperature distributions in the flow field, which are further used to calculate the entropy generation rate in the analysis. In this study, the influential role of the following dimensionless parameters on entropy generation rate is examined: the viscoelastic parameter $(εDe2)$⁠, slip coefficient $(k¯)$⁠, channel wall thickness $(δ)$⁠, thermal conductivity of the wall $(γ)$⁠, Biot number $(Bi)$ and Peclet number $(Pe)$⁠. We show that there exists a particular value of the abovementioned parameters that lead to a minimum entropy generation rate in the system. We believe the results of this analysis could be of helpful in the optimum design of microfluidic system/devices typically used in thermal management, such as micro-electronic devices, microreactors, and microheat exchangers.