Entrance pipe flow and heat transfer for a Bingham plastic

The problem of the simultaneous development of the hydrodynamic and thermal fields in the entrance region of a circular pipe for a non-Newtonian Bingham-type fluid is solved numerically using the fully elliptic governing continuity, momentum and energy equations. A simultaneous variable solution technique for the system of finite difference equations is employed which has already been proven to efficiently and accurately predict Newtonian flows. Laminar flow and constant fluid properties are assumed. The solutions obtained are for a wide range of Reynolds. Yield, Prandtl and Brinkman numbers and are compared with other existing solutions based on reduced forms of the governing equations.