Electromagnetic high-temperature therapy is popular in medical engineering treatments for various diseases include tissue damage ablation repair, hyperthermia and oncological illness diagnosis. The simulation of transport phenomena in such applications requires multi-physical models featuring magnetohydrodynamics, biorheology, heat transfer and deformable porous media. Motivated by investigating the fluid dynamics and thermodynamic optimization of such processes, in the present article a mathematical model is developed to study the combined influence of thermal buoyancy, magnetic field and thermal radiation on the fluid and heat characteristics in electrically-conducting viscoelastic biofluid flow through a vertical deformable porous medium. Jefferys elastic-viscous model is deployed to simulate non-Newtonian characteristics of the biofluid. It is assumed that heat is generated within the fluid by both viscous and Darcy (porous matrix) dissipations. The boundary value problem is normalized with appropriate transformations. The non-dimensional biofluid velocity, solid displacement and temperature equations with appropriate boundary conditions are solved computationally using a spectral method. Verification of accuracy is conducted via monitoring residuals of the solutions and Validated with shooting technique is included. The effects of Jeffrey viscoelastic parameter, viscous drag parameter, magnetic field parameter, radiation parameter and buoyancy parameter on flow velocity, solid displacement, temperature and entropy generation are depicted graphically and interpreted at length. Increasing magnetic field and drag parameters are found to reduce the field velocity, solid displacement, temperature and entropy production. Higher magnitudes of thermal radiation parameter retard the flow and decrease Nusselt number whereas they elevate solid displacement.

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