Temperature-Dependent Viscosity and Viscous Dissipation Effects in Simultaneously Developing Flows in Microchannels With Convective Boundary Conditions

Abstract

The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels are studied with reference to convective boundary conditions. Two different geometries, namely the circular tube and the parallel plate channel, are considered. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor are presented with reference to both heating and cooling conditions for two different values of the Biot number. Examples of radial temperature profiles at different axial locations and of axial distributions of centerline velocity and temperature are also shown.