Abstract: In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a transverse uniform magnetic field using the homotopy analysis method (HAM) for two general types of non-isothermal boundary conditions. In addition, we demonstrate that the previously reported analytical solutions for the temperature field given in terms of Kummer’s function do not converge at the boundary. We provide a graphical and numerical demonstration of the convergence of the HAM solutions and tabulate the effects of various parameters on the skin friction coefficient and wall heat transfer.

Key words: R-filter, HP-filter, spectral properties, Fourier analysis, Hess-matrix, operator theory, magnetohydrodynamic (MHD) flow, homotopy analysis method (HAM), viscoelastic fluid, nonuniform heat source/sink, stretching sheet