The melting phenomenon plays a vital role in power storage, electronic cooling, and semiconductor manufacturing. A better understanding of the phenomenon may produce an electronic device with optimal performance. In the present study, the melting effect on the flow of Carreau fluid over a stretchable cylinder is analyzed. Since the temperature difference is huge, quadratic thermal radiation is considered to simulate the real situation. To solve the governing equations, suitable similarity variables are applied to convert the complex nonlinear partial equations into ordinary equations. Semi-analytical homotopic solutions of the equation are then determined using the homotopy analysis method. The melting parameter has increased the heat transfer rate by more than 10% for both Prandhl fluids. As the temperature ratio due to the quadratic radiation increase, the local Nusselt number for the fluid with a Prandtl number, 0.71 has been reduced by 25%, and more reduction is observed for fluid with a Prandtl number, 10.