Analytical study of flow field and heat transfer of a non-Newtonian fluid in an axisymmetric channel with a permeable wall

In this study, the momentum and energy equations of laminar flow of a non-Newtonian fluid are solved in an axisymmetric porous channel using the least square and Galerkin methods. The bottom plate is heated by an external hot gas, and a coolant fluid is injected into the channel from the upper plate. The arising nonlinear coupled partial differential equations are reduced to a set of coupled nonlinear ordinary differential equations using stream function.These equations can be solved using the different numerical method. The numerical solution is conducted using fourth order Rung-Kutta method. With comparing the results obtained from the analytical and numerical methods, a good adaptation can be seen between them. It can also be observed that the results of the Galerkin method have further conformity with the numerical results and the Galerkin method is simpler than the least square method and requires fewer computations. The effects of Reynolds number, Prandtl number and power law index of non-Newtonian fluid is examined on flow field and heat transfer. The results show that Nusselt number increases by increasing Reynolds number, Prandtl number, and power law index.