Non-Newtonian fluids encountered in several large-scale industrial applications including blood flows in micro-circulatory system, food and polymer processing, magma and ice flows. Non-Newtonian fluids have applications in chemical materials (polymer liquids, drilling mud, pharmaceutical chemicals, detergents, paints, shampoos), biological materials (animal blood, synovial liquid, vacancies), processing of food (condensed milk, magma, sauces, ketchup, chocolates, ice flows) etc. The study of Carreau fluid has received considerable attention in the recent period, since the traditional Newtonian fluid not able to describe precisely the behavior of fluid flow with suspended particles. This work gives brief summary about the flow attributes of magnetic Carreau and Casson fluids through a paraboloid of revolution under considering convective restrictions along with thermal radiation via porous medium. Similarity functions are useful for renovating the flow governing system to non-linear system. The numerical outcomes are evaluated by enrolling R-K fourth order shooting process. The explicit outcomes are obtained to discuss the reaction of flow and temperature fields for various parameters of interest. The outcomes for skin friction coefficients are exemplified through tables. The Nusselt number’s values are shown via tables. Comparative work with previous outcomes is generated. Four important outcomes are: The Prandtl number’s hiking estimates cause reduction in temperature, the magnifying estimates of magnetic parameter make the velocity profile to decrease, the effect of Casson parameter is to reduce the velocity profile and Nusselt number and enhance temperature profile and skin friction coefficient, Weissenberg number cause reduction in skin friction coefficient and uplift the Nusselt number.