Dynamics of unsteady MHD pressure-driven non-isothermal radiative flow of Maxwell fluid with joule heating and viscous dissipation

A viscoelastic (Maxwell) fluid exhibits both elastic and viscous behavior, characterized by a relaxation time that indicates how long the fluid takes to return to its original state after deformation, and plays a crucial role in various industrial and engineering processes. The present analysis consists of unsteady magnetohydrodynamic (MHD) Maxwell fluid flow due to pressure-and buoyancy-driven flow. Additionally, we incorporated the effects of thermal radiation, Joule heating, and viscous dissipation during heat transfer. The unsteady coupled partial differential equations (PDEs) governing the flow and heat transfer, after non-dimensionalization, are solved using MATLAB code based on the implicit finite difference technique. The results are performed against the wide range of key dimensionless parameters ( α ) and ( λ ) are the mixed convection (representing the combined influence of buoyancy and forced convection) and Maxwell parameters (characterizing the fluid’s relaxation behavior and elastic effects). At a small value of ( α ), only a single peak/circulation of the velocity field is formed, but at a large ( α ) , another peak with intensity 1.1515 is also formed near the z-axis, due to the dominant convective flow. The intensity of the velocity-field circulation is reduced to 0.3132 to 0.23732 as the viscoelastic parameter ( λ ) increases from 0.1 to 1.3 .