Free Convection with a Viscosity that is Exponentially Dependent Upon Temperature

Using numerical and asymptotic analyses, we explore the situation where viscosity is an exponential function of temperature in free convection in the large Prandtl number limit. We identify two distinct asymptotic limits. For the case of a heated wall, all of the variation in velocity is contained in a thin lubrication layer near the wall. Whereas, for the case of a cooled wall, a conductive plug in which there is no velocity forms near the wall and all velocity variation is confined to a narrow transition region beyond the plug. This work has important applications to diapir dynamics, and to other flows of fluids, like honey, whose viscosity is strongly affected by changes in temperature.