Computational modeling of heat transfer in magneto-non-Newtonian material in a circular tube with viscous and Joule heating

Numerous industrial and engineering systems, like, heat exchangers, chemical action reactors, geothermic systems, geological setups, and many others, involve convective heat transfer through a porous medium. The diffusion rate, drag force, and mechanical phenomenon are dealt with in the Darcy–Forchheimer model, and hence this model is vital to study the fluid flow and heat transport analysis. Therefore, numerical simulation of the Darcy–Forchheimer dynamics of a Casson material in a circular tube subjected to the energy losses due to the viscous heating and Joule dissipation mechanisms is performed. The novelty of the present investigation is to scrutinize the convective heat transport characteristics in a circular tube saturated with Darcy–Forchheimer porous matrix by utilizing the non-Newtonian Casson fluid. The flow occurs due to the elongation of the surface of a tube with a uniform heat-based source/sink. The similarity solution of the nonlinear problem was obtained using dimensionless similarity variables. The effects of operating parameters related to the flow phenomena are analyzed. Further, the friction factor and Nusselt number are also analyzed in detail. The present flow model ensures no flow reversal and acts as a coolant of the heated cylindrical surface; the existence of the magnetic field, as well as an inertial coefficient, acts as the momentum-breaking forces, whereas Casson fluidity builds it. The Joule heating phenomenon enhances the magnitude of temperature. The thermal field of the Casson fluid is higher at the surface of the circular pipe due to convective thermal conditions.