Advances in Applied Mathematics and Mechanics Adv. Appl. Math. Mech., Vol. 6, No. 3, pp. 359-375 DOI: 10.4208/aamm.2013.m303 June 2014 Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer Over a Stretching Sheet Antonio Mastroberardino ∗ School of Science, Penn State Erie, The Behrend College, Erie, Pennsylvania 16563, USA Received 25 July 2013; Accepted (in revised version) 9 January 2014 Available online 21 May 2014 Abstract. An investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretch- ing surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equa- tions for the fluid flow and temperature are reduced to a nonlinear system of ordi- nary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that pre- viously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct. AMS subject classifications: 76D10, 76W05 Key words: Viscoelastic fluid, non-uniform heat source/sink, viscous dissipation, thermal radia- tion, homotopy analysis method. 1 Introduction More than 100 years after Blasius equation was formulated to describe the boundary layer present in uniform viscous flow over a semi-infinite plate [2], researchers in engi- neering and applied mathematics continue to investigate the nonlinear differential equa- tions that describe boundary layer flow. Since the landmark work of Blasius, variations of the classical problem have been formulated that consider different flow scenarios and incorporate relevant physical phenomena. In practically all cases considered, the differ- ential equations governing the flow are nonlinear, and the existence of exact solutions is ∗ Corresponding author. Email: axm62@psu.edu (A. Mastroberardino) http://www.global-sci.org/aamm 359 c 2014 Global Science Press