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This paper investigates the flow and heat transfer of special third-grade fluid with a viscous dissipation effect over a stretching sheet. This model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids domain. The governing momentum and energy equation are reduced to ordinary nonlinear differential (self-similar) equations via the Lie group transformation method. The Homotopy Perturbation Method (HPM) is applied to solve these obtaining results. For validation, current results have been compared with the fourth-order Runga method (RK4) and shooting technique. The effects of physical parameters on fluid velocity and temperature profile were investigated with the aid of figures and tables by simply altering a single parameter while keeping the others constant. It is observed that both the non-Newtonian parameter and the Prandtl number have the effect of decreasing the temperature of the stretching surface, while the opposite behavior was found for the Eckert number.

The current paper illustrates the consequence of viscous dissipation on the unsteady MHD flow of an incompressible viscous fluid over a vertical permeable surface embedded in a porous medium. The roles of chemical reaction and thermal radiation has made the study more interesting. The Perturbation method has been applied to solve the coupled and nonlinear governing equations. It is found that the present solutions are in very good agreement with the previous solutions. The important findings are: increasing values of Eckert number (Ec) enhances the velocity of the fluid flow. The viscous dissipation convincingly increases the temperature. This analysis is of great interest in many applications such as polymer processing flows, condensation process of metallic plate in cooling bath, aerodynamic extrusion of plastic sheets etc.

The present study elucidates the magnetohydrodynamics boundary layer free convective stagnation-point flow toward an inclined nonlinearly stretching sheet embedded in a porous medium. The recent search explores the consequence of permeability of the medium, thermal as well as mass buoyancy, most importantly obliqueness, and thermal slip at the bounding surface. The solutions of the essential equations are achieved with MATLAB'S inbuilt solver bvp4c. The novelty of the present study is to account for the effect of dissipative heat, nonuniform space-dependent volumetric heat power, and a linear first-order chemical reaction of diffusive species and convective flow phenomena on an inclined plate subjected to thermal slip and space-dependent transverse magnetic field acting at a distance. The important findings are laid down as follows: The oblique-surface reduces the effect of body forces, low permeability of the medium causes instability in the flow due to sudden fall in velocity, Biot number contributes to the Newtonian cooling of the surface, these may be of use in a design requirement of the heat exchanger.

Present analysis elucidates the steady free convective flow of nanofluid over a stretching sheet embedded in a porous medium. Mass transfer analysis with chemical reaction acts a great role in this study. The consideration of viscous dissipation makes the heat transfer analysis more interesting. The governing equations are remodelled as a system of ordinary differential equation adopting similarity transformation and treated numerically by 4th order Runge-Kutta method along with Shooting technique. The present results are compared with the earlier results which gives a good agreement. Some important findings are; porosity acts as aiding force whereas magnetic parameter as resistive force for fluid velocity, larger values of chemical reaction parameter result lower velocity and concentration. The study is relevant in polymer processing, food processing industries and chemical industries.