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

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=1.0β=1.0) at the fin tip and a triangular shape (wedge) flow (β=0.015β=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 (PrPr), the elastic number (EE), the free convection parameter (GG) and the conduction–convection coefficient (NccNcc) 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 Ncc,G,ENcc,G,E and PrPr.