Thermal characteristics of forced convection in combined pressure and shear‐driven flow of a non‐Newtonian third‐grade fluid through parallel plates

Heat transfer in a non‐Newtonian third‐grade fluid, flowing under the action of pressure gradient and shear, through two parallel plates, is considered. The upper plate moves with a constant velocity. Constant wall heat fluxes are applied to the plates. Effect of viscous dissipation is included, which has a major role in heat transfer of non‐Newtonian fluids. The governing equations are nonlinear and are solved semi‐analytically by using the least‐square method (LSM). Then, using the solution for velocity in the energy equation, the solution is obtained by a direct integration process. Further, approximate analytical solutions are obtained by the perturbation method, which validates the results generated by the LSM. The effects of the third‐grade fluid parameter on the velocity and temperature and also on the physical quantity, such as Nusselt's number, are discussed. Further, viscous dissipation effects on the temperature distribution have been analyzed. Observations show that the movement of the upper plate results in a significant decrease in temperature near the upper plate. For the unit heat flux ratio, the temperature difference between the surface and fluid is more at the upper surface due to the enhanced convective heat transfer caused by the moving upper plate. Nusselt's number increases significantly with an increase in the heat flux ratio.