An analytical investigation of pressure-driven flow and heat transfer of a Sisko fluid flowing through parallel plates with viscous dissipation

Pressure driven flow of a Sisko fluid through rectangular parallel plates, having different wall temperatures is investigated considering the effect of viscous dissipation. The nonlinear momentum and energy conservation equations are solved employing homotopy perturbation method (HPM) and analytical solutions for the velocity, flow rate and temperature distributions are obtained. The analytical solution of pressure-driven flow and heat transfer characteristics of Sisko fluids flowing through parallel plates, taking into account viscous dissipation effect, has not been addressed earlier. For a special case of a typical Sisko fluid, the HPM solution exhibits an excellent agreement with the exact solution. Effects of various parameters such as Sisko fluid parameter, non-Newtonian index and Brinkman numbers on the variation of velocity and temperature are discussed. Further, temperature distribution in flow of Sisko fluids through parallel plates with both the plates maintained at same temperature is also obtained by a suitable substitution in the expression for temperature distribution. It is observed that the velocity decreases significantly with an increase in Sisko fluid parameter. Temperature of the fluid decreases with an increase in Sisko fluid parameter and displays an increasing trend with an increase in Brinkman number. Results of the present study are useful for designing thermal systems handling polymer flows. For the typical case of two plates having same temperature, the maximum temperature is observed to occur at the centre, which is attributed to the effect of viscous dissipation acting as an internal source. The theoretical framework developed and analytical solution provided for the problem under consideration may be taken as benchmark result for validation of future work.