`Mathematical Problems in EngineeringVolume 2007, Article ID 17058, 21 pageshttp://dx.doi.org/10.1155/2007/17058`
Research Article

## Conjugate Heat Transfer of Mixed Convection for Viscoelastic Fluid Past a Stretching Sheet

1Department of Network and Communication, Diwan College of Management, Diwan University, 87-1, Nansh Li, Madou Jen, Tainan, Taiwan 72153, China
2Department of Computer Science and Information Engineering, Diwan College of Management, Diwan University, 87-1, Nansh Li, Madou Jen, Tainan, Taiwan 72153, China

Received 18 July 2006; Revised 28 October 2006; Accepted 27 December 2006

Academic Editor: Kumbakonam Rajagopal

Copyright © 2007 Kai-Long Hsiao and Guan-Bang Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A conjugate heat transfer problem of a second-grade viscoelastic fluid past a stretching sheet has been studied. Governing equations include heat conduction equation of a stretching sheet, continuity equation, momentum equation, and energy equation of a second-grade fluid, analyzed by a combination of a series expansion method, the similarity transformation, and a second-order accurate finite-difference method. These solutions are used to iterate with the heat conduction equation of the stretching sheet to obtain distributions of the local convective heat transfer coefficient and the stretching sheet temperature. Ranges of dimensionless parameters, the Prandtl number Pr, the elastic number E and the conduction-convection coefficient Ncc are from 0.001 to 10, 0.0001 to 0.01, and 0.5 to 2.0, respectively. A parameter G, which is used to represent the dominance of the buoyant effect, is present in governing equations. Results indicated that elastic effect in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a stretching sheet. In addition, same as the results from Newtonian fluid flow and conduction analysis of a stretching sheet, a better heat transfer is obtained with a larger Ncc, G, and E.