Study of non-orthogonal time dependent mixed convection Hiemenz flow of viscoelastic Walter's B fluid with thermal radiation is the major focus of this article. The surface intact with the fluid particle is assumed to be oscillating-stretching and heated with sinusoidal surface temperature. This physical process is modeled in mathematical form into system of PDEs, which are simulated numerically by Chebyshev spectral method. The obtained solution is firstly validated for reduced case with already published results, and then further results are achieved for governing physical parameters. The effects of dimensionless emerging constants are described through tables and graphs. In this study, it is concluded that in assisting flow case velocity enhances as compared to opposing flow case. By increasing the Weissenberg number velocity of the fluid decreases in both assisting and opposing flow cases while in opposing flow case these effects are more prominent as compared to assisting flow case. The streamlines in both assisting and opposing flow cases come closer to each other with the passage of time and at t = 3π / 2, they overlap each other and stagnation points also get coincide.