Viscous dissipation effects on the limiting value of Nusselt numbers for a shear-driven flow through an asymmetrically heated annulus

Abstract

In this study, an analytical investigation for analyzing the effects of viscous dissipation on the limiting Nusselt number for a hydro-dynamically fully developed laminar shear-driven flow through an asymmetrically heated annulus of two infinitely long concentric cylinders has been made, where the inner cylindrical rod is moving in an axial direction at a constant speed. On the basis of some common assumptions, an analytical framework has been devised to explore the effects of viscous dissipation on the heat transfer characteristics for the flow of Newtonian fluid, and, consequently, closed-form expressions for the limiting Nusselt numbers are evaluated. In the analysis, focus has been given on the viscous dissipative effect due to the shear produced by the movable inner cylindrical rod apart from the viscous dissipation due to internal fluid friction for the flow of a Newtonian fluid. The interactive effects of the Brinkman number and degree of asymmetry on the limiting Nusselt number are analytically investigated. It is observed from this study that the limiting Nusselt number becomes independent of Brinkman number when both the walls of the annulus are kept at an equal temperature. Moreover, the temperature profile in the conduction limit obtained with the consideration of viscous dissipation effect provides a boundary condition required for solving energy equation including the axial conduction in the fluid.

Keywords

Viscous dissipation limiting Nusselt number Newtonian fluid Brinkman number shear-driven flow asymmetrically heated annulus axial conduction

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