Laminar heat transfer for thermally developing flow of a herschel-bulkley fluid in a square duct

Laminar heat transfer of a Herschel-Bulkley fluid in the entrance region of a square duct assuming fully developed velocity profile is investigated numerically. The non linear momentum equation in fully developed region is solved iteratively using a finite difference method to obtain the velocity distribution. Using the velocity profile, the energy equation with viscous dissipation effects is solved by using an implicit Crank-Nicolson method to obtain the temperature distributions. Computations have been obtained for two cases T and H2 thermal boundary conditions. The product of the friction factor and Reynolds number, bulk mean temperatures and local Nusselt numbers for the two cases have been represented for various value of the model parameters and the Brinkman number. The present results have been compared with the known solutions for Newtonian and power-law fluids and are found to be in good agreement.