An Analytical Investigation of Pressure-Driven Transport and Heat Transfer of Non-Newtonian Third-Grade Fluid Flowing Through Parallel Plates

Flow of a third-grade fluid induced by the difference in pressure, thorough rectangular parallel plates, having different wall temperatures, is revisited considering the effect of viscous dissipation. The governing equations, describing the physical phenomenon, are nonlinear. The non-Newtonian third-grade fluid parameter is considered to be small, and the governing equations are reduced to weakly nonlinear equations. The nonlinear momentum and energy conservation equations, thus obtained, are solved employing perturbation method. Analytical solutions for the velocity and temperature distributions are obtained. Results generated by the perturbation method are compared with that of Danish et al. (Commun Nonlinear Sci Numer Simul 17:1089–1097, 2012 [1]) and an excellent agreement is exhibited within the small range of perturbation parameter (third-grade fluid parameter). Effects of various parameters such as Brinkmann number, non-Newtonian third-grade fluid parameter, temperature ratio of the upper plate and lower plate on the variation of velocity and temperature are discussed. Results indicate that an increase the third-grade fluid parameter results in a decrease in the velocity. Temperature of the fluid decreases with an increase in third-grade fluid parameter and displays an increasing trend with an increase in Brinkman number. The peak temperature is observed to occur not at the upper plate, at a region which is near the upper plate. Results are useful for designing thermal systems applied in the fields of polymer melt flows, food processing, flow of slurry, etc.