On the spectral numerical study of magneto – convective flow of Jeffery fluid through Poro-elastic media with thermal radiation and buoyancy effects

Many physiological systems involving soft tissues depend on flow through a deformable porous media; coronary blood, for example, flows through arteries containing arteriosclerosis. Systems that permit highly viscous pressure force flows through elastic porous materials are said to be deformable. A novel mathematical model for the nonlinear convective flow for large temperature differences is developed based on this supposition. The constant magneto-convective flow of Jeffery fluid through a deformable porous material with nonlinear convection and heat radiation is the subject of this inquiry. The solid displacement, flow velocity, and energy equations' governing equations are built using well-established flow assumptions and one-way flow inside the impermeable vertical walls. The governing equations' dimensionless form is solved using the Spectral Chebyshev Collocation methods, and the fourth-order Shooting-Runge-Kutta Scheme is used to validate the solution. The Spectral Quasilinearization method is utilized in the limiting situation and validated against the body of existing research. The impacts of each flow parameter are explained through the display of graphic data. Tabular representation is also provided for results convergence and comparison. Understanding heat transport to soft tissues, particularly during hyperthermia for cancer treatment, is important, and this study contributes to that understanding.