VISCOUS DISSIPATION EFFECTS ON THE LIMITING VALUE OF NUSSELT NUMBERS FOR A SHEAR DRIVEN FLOW BETWEEN TWO ASYMMETRICALLY HEATED PARALLEL PLATES

摘要

The present paper deals with the analytical investigation for the limiting value of the Nusselt number, including the effect of viscous dissipation on heat transfer for a laminar shear driven flow between two infinite parallel plates, where the bottom plate is fixed and the top plate is moving in an axial direction at a constant speed. The study concentrates on hydro-dynamically fully developed flow of a Newtonian fluid of constant properties without considering the axial conduction in the fluid. To investigate the effect of viscous dissipation on heat transfer by defining the limiting Nusselt number, plates are kept at constant unequal temperatures. Close form expressions for the limiting Nusselt numbers as a function of the Brinkman number and asymmetry parameter are evaluated. Focus is given to the viscous dissipative effect due to the shear produced by the movable top plate over and above the viscous dissipation due to the internal fluid friction. The interactive effects of the Brinkman number and the degree of asymmetry on the limiting Nusselt number are investigated analytically. Specific to the cases considered for this study, the appearance of the point of singularities due to the variation of the Nusselt number with the Brinkman number is observed, and discussion has been made considering the energy balance.