Study of a Shear-Driven Flow between Two Infinitely Long Moving Parallel Plates

Abstract

The present work stud1ies the effect of viscous dissipation on the limiting value of Nusselt number for a laminar shear-driven flow of Newtonian fluid between two infinite parallel plates. In order to make the flow occur, both the plates are assumed to move in the axial direction at a constant speed. The study considers the flow to be hydro-dynamically fully developed, while both the plates are kept at unequal constant temperatures. A few assumptions, which are commonly employed in the literature, are considered only to obtain the solution in an analytical framework. In order to delve deep into the effect of viscous hearting on the thermal transport characteristics of forced convective heat transfer, the closed-form expressions of limiting Nusselt numbers are evaluated in terms of the Brinkman number. The study concentrates on the viscous dissipation with the heat transfer characteristics, and, thus, emphasis is given to the viscous heating arising out of the movement of both the plates relative to each other. The effects of the viscous heating and degree of asymmetric wall heating on the heat transfer characteristics are found to be significant following the variation of the Nusselt number. The variation of Nusselt number portrays the existence of the point of singularities at different locations. The point of singularity, as seen on the variation, is the outcome of the equilibrium between the heat generated owing to the viscous heating and the heat supplied by the wall.