Optimization of MHD Jeffrey-Hamel flow in convergent–divergent channels with slip and viscous-dissipation: vorticity–stream-function analysis of flow reversal and heat transfer

This work explores the thermal-fluidic optimization in divergent and convergent channel flows, addressing important issues in heat transfer, flow separation and energy consumption in nozzle systems and biomedical devices. Prior researchers focused on the similarity solutions of the Navier-Stokes equations in a Jeffrey-Hamel flow problem. This work extends the classical problem beyond conventional similarity solutions by employing the vorticity-stream function technique to analyse flow and convective heat transfer in a convergent-divergent channel, provides novel insight into this problem. The governing equations, including heat radiation, velocity slip, viscosity dissipation and magnetohydrodynamic effects, are modelled using the vorticity-stream function technique. The energy equation is modelled under convective boundary conditions, assuming small mean temperature fluctuations. The Navier-Stokes equations for viscous fluid flow are numerically solved with the Keller-Box method. The findings reveal that high inertial forces dominate in the converging section while flow reversal appears in the divergent section. The magnetic parameters decline the flow profile in both conduits. Slip parameters uplift velocity gradients in converging regions and encourage plug-like flow by decreasing wall adherence. The radiation parameters reduce the heat transfer, assisting cooling in the divergent zone.