Asymptotic analysis of boundary layer of a thermo-dependent fluid flow

Abstract

In this work, we applied the asymptotic analysis method based on a large Prandtl number for a boundary layer flow over a flat plate, of a thermo-dependent fluid obeying a power law. In order to make sense to the notion of boundary layer, we have to assume that the fluid is shear-thinning. The governing equations of the thermal boundary layer do not admit self-similar solutions but the asymptotic model derived in this work admits one. This approach was also employed to obtain a Nusselt number correlation as a function of the ratio K(T∞)/K(Tw), where K is the consistency index, T∞ and Tw are respectively the free stream and the wall temperature. In particular, we have shown that the shear-thinning nature of the fluid accentuates the effect of thermo-dependence and amplifies the heat transfer at the wall.