In current framework, an analytical treatment for mixed convection flow of an electrically conducting Oldroyd-B fluid adjacent to a vertical stretchable surface is provided. A non-Fourier heat flux approach is employed to formulate the energy balance relation. Using similarity approach, the governing equations are changed to a set of non-linear differential equations which are tackled by well-known analytical approach called homotopy analysis method (HAM). Appropriate range of auxiliary parameter is obtained by plotting the so called h-curves. Velocity and temperature profiles are computed and elucidated in the existence of new physical mechanism, that is, thermal relaxation time in current research. The main implication of this research is that the relaxation and retardation times considerably alter the flow behavior near the surface. The results predict that heat penetration into the fluid reduces as the relaxation time of heat flux enlarges. Furthermore, the change in temperature gradient at the surface with increasing thermal relaxation time appears similar in magnitude at all considered Prandtl numbers. In assisting flow regime, we noticed a growth in velocity and temperature profiles for increasing strength of buoyancy force. (C) 2017 Elsevier Ltd. All rights reserved.