Analysis of Laminar Heat Transfer on Thermal Viscous Dissipative Flow of a Newtonian Fluid between Parallel Plates Geometries with Constant Heat Flux Boundary Conditions

Abstract

In the thesis, an investigation has been made to analyze the effects of viscous dissipation on the analytical solutions of temperature distributions and heat transfer rates for both hydro dynamically and thermally fully developed laminar plane Couette flow and flow between two fixed infinitely long parallel plates. On the basis of some routine assumptions made in the literature, a closed form analytical expressions of Nusselt numbers for the flow of Newtonian fluid with constant properties has been developed for three different cases of constant heat flux boundary conditions. The significant effect of the viscous dissipation as compared to other terms in the energy equation is manifested by the Brinkman number. In order to have a generalized idea about the viscous heating effect on the heat transfer analysis, different definitions of the Brinkman number have been used in the present study. For different values of the relative velocity for both flows, the effect of the modified Brinkman number and Brinkman number on the temperature distributions and the Nusselt numbers are discussed. Comparison of the present analytical solutions for the simple constant heat flux boundary conditions with those available in the literature indicates that some of the reported results were different from what we have obtained independently and also suggest a new way of expressing the Nusselt numbers.