Effects of non‐Darcian and temperature dependent heat source on two‐phase flow in a vertical porous space with thermal radiation

In this article, influences of viscous dissipation and thermal radiation on MHD flow of two immiscible fluids in a vertical channel filled with porous materials have been studied theoretically. The equations governing the problem are transformed to a system of ODE and are solved by homotopy analysis method (HAM). The effects of physical parameters on flow and heat transfer characteristics have been discussed with the help of graphs. It is found that viscous dissipation parameter, heat source parameter, thermal parameter lead to enhance velocity as well as temperature field. Also, increasing Brinkmann number and heat source parameter lead to suppress Coefficient of skin friction at the left wall but the opposite is true at the other wall. However, these parameters give reverse trend on Nusselt number distribution. Further, increasing thermal conductivity ratio and fluids height ratio leads to increase heat transfer coefficient significantly at the left wall. In addition, we have compared present HAM solution with analytical solution of the problem (ie, absence of radiation parameter and Brinkmann number).     

Effect of nonlinear thermal radiation on silver and copper water nanofluid flow due to a rotating disk with variable thickness in the presence of nonuniform heat source/sink using the homotopy analysis method

An analysis of a steady axisymmetric heat transfer nanofluid flow due to a rotating disk having variable thickness in the presence of nonlinear radiation and nonuniform heat source/sink is presented. Water with Copper (Cu) and Silver (Ag) nanoparticles are utilized in the investigation. The governing equations along with boundary conditions are solved using the homotopy analysis method. A parametric study of the physical parameters is done and results are displayed in the form of graphs. The findings indicate that nonlinear radiation has a significant effect on temperature as well as on wall heat transfer when compared with linear case, which is more useful in few engineering processes.