Effects of viscous dissipation and temperature dependent viscosity in thermally and simultaneously developing laminar flows in microchannels

The effects of viscous dissipation and temperature dependent viscosity in both thermally and simultaneously developing laminar flows of liquids in straight microchannels of arbitrary, but constant, cross-sections are studied. In order to allow a parametric investigation, viscosity is assumed to vary linearly with temperature, while the other fluid properties are held constant. Different cross-sectional geometries are considered, chosen among those usually adopted for microchannels. Reference is made to uniform wall temperature boundary conditions. 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 for ducts of the considered cross-sections are presented with reference to both heating and cooling conditions. Numerical results confirm that, in the laminar forced convection in straight microchannels, both temperature dependence of viscosity and viscous dissipation effects cannot be neglected in a wide range of operative conditions.