On account of engineering applications and its complexity, the flows of non-Newtonian fluid caused by stretching/shrinking surface has turned out to be standout amongst the difficult research fields of fluid mechanics. Therefore, the central concern of this article is to identify the simultaneous consequences of viscous dissipation and Ohmic heating on the flow of an electrically conducting Williamson fluid generated by stretching/shrinking sheet. Flow is subject to a time-dependent magnetic field which is applied in transverse direction. The dimensionless variables are used to transform the governing equations including mass, momentum and energy conservation into ordinary differential equations. The reduced equations subject to the given boundary conditions have been solved by employing Runge-Kuta Fehlberg method followed by shooting technique. In addition, the multiple solutions for dimensionless fluid velocity and temperature distributions are captured when certain amount of mass suction is employed through the porous shrinking surface. The dynamic thermo-physical dimensionless parameters controlling the flow and heat transfer features are the magnetic parameter, viscosity ratio parameter, Weissenberg number, suction parameter, Eckert number and Prandtl number. It is visualized from multiple branches that the skin friction enhances with magnetic parameter for the upper branch solution and it reduces for lower branch solution. On the other side, obtained numerical results illustrated that the rate of heat transfer shows an accelerating trend with higher unsteadiness parameter for both the solutions. The obtained results show a better agreement of this model with respect to experimental data, compared to the homogeneous model. (C) 2018 Published by Elsevier Ltd.