Thermal development for a pseudoplastic fluid in simple duct with consideration of viscous dissipation

Abstract

In this work, we treat the thermal development problem, for a pseudoplastic fluid in a single pipe. A fully developed flow is supposed at the pipe inlet, with an imposed temperature at the surface in the case of a heating and cooling. In addition, the effect of viscous dissipation is considered. Finite difference method with an implicit scheme is used to solve the energy equation. The main objective of the work is to provide results, enabling to well understand the effect of viscous dissipation associated with that of rheological behavior. For this, different values of the Brinkman (Br) number characterizing the heat generation by viscous friction, and the rheological index (n) have been taken for in heating situation as well as cooling. It has been found that the fluid shear-thinning (n↓) significantly reduces the dissipative effect, by reducing the friction between the fluid layers