Abstract Viscosity of fluid keeps its leading role in the polymer process, biological fluids, mayonnaise, colloidal suspensions, melt solutions and lubrication models. The Carreau nanofluid viscosity model can explain features of non-Newtonian fluids in the shear-thinning/thickening regions. This article describes the Lorentz force effects with the use of the infinite shear rate of the Carreau viscosity model and thermal radiation along with the influence of non-uniform heat source/sink transportation phenomenon of heat over the surface. The transformations of dimensionless variables are implemented to convert the partial differential equations into nonlinear coupled ordinary differential equations (ODEs). The solution of these ODEs is performed using the Runge–Kutta Fehlberg method along with the shooting scheme. The effects of the We, Pr,M,Nr, β * * * , β,B parameters denote the Weissenberg number, Prandtl number, radiation parameter, temperature ratio parameter, viscosity ratio parameter, stretching parameter, coefficients of space and temperature-dependent heat source/sink. For the correctness and exactness of the scheme, a comparison study is also provided based on the present results and the published results. and A