Temperature Dependent Viscosity and Thermal Conductivity Effects on the Laminar Forced Convection in Straight Microchannels

Abstract

A parametric investigation is carried out on the effects of viscous dissipation and temperature dependent viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight microchannels of constant cross-sections. Uniform heat flux boundary conditions are specified at the heated walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries are considered, corresponding to both axisymmetric (circular) and three-dimensional (square) microchannel geometries. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Brinkman number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain the correct value of the Nusselt number by considering separately the effects of temperature dependent viscosity and viscous dissipation and those of temperature dependent thermal conductivity. In fact, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is independent of the value of the Brinkman number, i.e., it is the same no matter whether viscous dissipation is negligible or not. Finally, it is demonstrated that, in liquid flows, the main effects on pressure drop of temperature dependent fluid properties can be retained even if only viscosity is allowed to vary with temperature, the other properties being assumed constant.