Analysis and modeling of hydromagnetic poiseuille multiphase flow of pseudoplastic fluid: thermal analysis with analytical scheme

The analytical solution is conducted for two two-phase linear flows of Williamson fluid through a porous medium to examine the heat transfer mechanism under the suspension of solid rigid nanoparticles. To produce the two-phase flow, the mathematical model of fluid and particle phases is developed by using the continuity, momentum, and heat equations. The momentum and energy-balanced equations of both phases are solved analytically by employing the perturbation series method. The computational results revealed that the magnetic field parameter diminishes both velocity and temperature profiles while the velocity and thermal fields are increasing in function of density number and Darcy number. Moreover, the fluid phase velocity is much smaller than the particle phase velocity under both suspensions of the particles. The thermal slip parameter generates 10% and 20% more heat transfer in a system with the suspension of gold and silver nanoparticles, respectively. The results of the present analysis are beneficial to designing modern solar cell devices to stock more solar energy due to less heating release under the suspension of gold and silver nanoparticles.