Laminar Entry Flow in a Pipe or Channel: Effect of Variable Viscosity Due to Heat Transfer Across the Wall

A combined asymptotic and numerical (finite-difference) method is applied to solve the full Navier-Stokes and energy equations. The approach is based on the Taylor series expansion of viscosity with respect to temperature. The basic flow (zero order) is that of constant viscosity. Higher order equations successively account for the influence of variable viscosity. The viscosity corrections have to be calculated only once for a specific Reynolds and Prandtl number. They asymptotically hold for all viscosity laws and for all heat transfer rates.