Exact solution of the Graetz–Brinkman problem extended to non-Newtonian nanofluids flow in elliptical microchannels

In this study, an exact solution using the Generalized Integral Transform Technique (GITT), for the laminar forced convection problem of non-Newtonian fluid flow in elliptical duct by considering the viscous dissipation effects is provided. The proposed solution has been validated by comparison with the numerical solution based on the Dynamic Alternating Direction Implicit (DADI) method developed in this study and with the results available in literature. Results of the analysis showed that the temperature distribution is highly influenced by the Brinkman number as well as the aspect ratio. The use of elliptical duct enhances the viscous heating and the heat transfer coefficient compared to the circular duct. The analytical solution was used to investigate the polyalkylene–glycol–TiO 2 non-Newtonian nanofluids flow in microchannels. The results showed that the addition of nanoparticles reduces viscous dissipation effect due to the shear-thinning behavior and the increase in thermal conductivity. In addition, the elliptical microchannel showed a significant enhancement in the heat transfer rate and reduction by half of the thermal length compared to the circular microchannel. These two advantages are with high importance in development of micro-electro-mechanical system (MEMS).