Conjugate heat transfer of mixed convection for visco-elastic fluid past a triangular fin

Abstract

A conjugate mixed-convection heat-transfer problem of a second-grade visco-elastic fluid past a triangular fin was studied. Governing equations include heat-conduction equation of the fin, and continuity equation, momentum equation and energy equation of the fluid, were analysed 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 triangular shape (wedge) flow ( β = 0.015 ) on the fin surface were obtained by a generalized Falkner–Skan flow derivation. These solutions were used to iterate with the heat-conduction equation of the fin to obtain distributions of the local convective heat-transfer coefficient and the fin temperature. Ranges of dimensionless parameters, the Prandtl number ( P r ), the elastic number ( E ), the free convection parameter ( G ) and the conduction–convection coefficient ( N c c ) are from 0.1 to 100, 0.001 to 0.01, 0 to 1.5 and 0.05 to 2.0, respectively. Results indicated that the elastic effect in the flow can increase the local heat-transfer coefficient and enhance the heat transfer of a triangular fin. In addition, same as the results from Newtonian fluid flow and conduction analysis of a triangular fin, a better heat transfer is obtained with a larger N c c , G , E and P r .