Conjugate Heat Transfer of Forced Convection with Viscous Dissipation for Visco-Elastic Fluid Past a Flat Plate Fin

Abstract

Summary A conjugate forced convection with viscous dissipation heat transfer problem of a second-grade visco-elastic fluid past a flat plate fin has been studied. Governing equations include heat conduction equation of the fin, and continuity equation, momentum equationand energy equationofthe fluid,were analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite-difference method. Solutions of a stagnation flow (β = 1.0) at the fin tip and a flat plate shape (wedge flow β = 0.0) on the fin surface were obtained by a generalized Falkner-Skan flow derivation. These solutionswere used to iterate with the heat conduction equation of the fin to obtain distributionsof the local convective heat transfer coefficient and the fin temperature. Ranges of dimensionless parameters, the Prandtl number (Pr), the elastic number (E), the viscous dissipation parameter (Ec) and the conduction-convection coefficient (Ncc) are from 0.1 to 100, 0.001 to 0.01, 0 to 0.1 and 0.05 to 2.0, respectively. Results indicated that Results indicated that elastic effect in the flow can increase the local heat transfer coefficient and enhance the heat transfer of a flat plate fin. Also, same as results from Newtonian fluid flow and conduction analysis of a flat plate fin, a better heat transfer is obtained with a larger Ncc, E, Ec and Pr.