Mixed convection in microchannels: Effect of viscous dissipation

In this study, mixed convection in two different vertical micro geometries (mainly parallel-plane microduct and microtube) is investigated numerically. For fully developed flow condition, either the continuum flow regime or slip flow regime is analyzed, respectively, considering the rarefaction (Kn) and viscous dissipation (Br). Two different thermal boundary conditions are applied at the walls: uniform temperature and uniform heat flux. Perturbation method, a semi-analytical method, is used in solution of conservations of mass, momentum and energy equations. For determining the rarefaction level, velocity slip and temperature jump are taken into account. Generally, it is determined that Nusselt number decreases with an increase in Knudsen number for each micro geometry. It is also disclosed that Nusselt number generally decreases with an increase in viscous dissipation. In addition, a singularity is observed for some specific values of Brinkman number and ratio of wall heat flux.