Conjugate heat transfer of a triangular fin in the flow of a second-grade fluid

Abstract

A conjugate heat transfer problem of a second-grade fluid past a triangular fin was studied. Governing equations, including heat conduction equation of a fin, continuity, momentum and energy equations of a second-grade 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 wedge flow ( β =0.015) on the fin surface were obtained. These solutions were then 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 (Pr), the elastic number ( E ) and the conduction–convection coefficient ( N cc ) were from 0.1–50, 0.001–0.1, and 0.5–2.0, respectively. Results indicated that elastic effect in the flow can increase the local heat transfer coefficient and thus enhance the heat transfer capability of a fin. Also, just as the results from Newtonian fluid flow and conduction analysis of a fin, a better heat transfer is obtained with a larger N cc and Pr.