Abstract
In many fields, there are various applications of non-Newtonian fluids. Various complicated fluids (polymer melts, clay coatings and oil) belong to the category of non-Newtonian fluids. The third-grade fluid is one of the most important non-Newtonian fluid models. This paper has the primary object of heat transfer mechanism and boundary layer third-grade fluid flow under the effects of thermal radiation. The time-dependent two-dimensional flow is considered to flow above a permeable stretchable vertical Riga plate. For numerical solutions, the setup of ordinary differential equations (ODEs) is acquired by converting nonlinear governing equations through relevant similarity transformations. The nonlinear setup of ODEs is numerically solved with the aid of a suitable software such as MATLAB via its bvp4c technology. Graphs are sketched to discuss the various flow parameters' significance for the expression of velocity and temperature fields. Tabulated values of surface drag force and heat transfer rate corresponding to the numerous pertinent parameters are described. The current analysis of the concerned flow mechanism concludes that the fluid parameters descend the temperature distribution but amplify the profile of the fluid velocity. The radiation parameter escalates the temperature field.