Heat transfer enhancement in Darcy–Forchheimer Jeffrey–Hamel flow of a partially ionized power-law nanofluid under Hall and ion-slip effects

Partially ionized fluids subjected to magnetic fields exhibit distinctive transport characteristics that are highly relevant to advanced thermal fluid systems. This study examines a modified Jeffrey Hamel configuration by analyzing Darcy Forchheimer flow of a partially ionized Power-law nanofluid, with emphasis on Hall and ion-slip effects. To overcome the limitations of classical Jeffrey Hamel models, an improved heat transport formulation is employed. Copper nanoparticles dispersed in ethylene glycol are considered to enhance thermal conductivity within non-parallel walls, while a constant pressure gradient drives the flow through both diverging and converging channels. The governing equations, based on modified Navier Stokes momentum balance, Fourier heat conduction, and generalized Ohm’s law, are solved to quantify the effects of key physical parameters. The results reveal that increasing the Hall current and ion-slip parameters significantly accelerates the fluid motion, with peak velocity rising by approximately 15–20% as their combined strength increases, while simultaneously weakening the resistive Lorentz force. Higher Reynolds and Weissenberg numbers reduce frictional drag, whereas inertia effects, porous resistance, and viscoelasticity suppress velocity in the diverging channel. Moreover, the diverging flow regime exhibits up to 25% higher wall shear stress and noticeably enhanced heat-transfer rates compared with the converging case. The combined influence of partial ionization, nanofluid suspension, and non-Newtonian behavior provides a viable mechanism for improving flow control and thermal performance in magneto-nanofluid systems used for thermal management and energy-conversion applications.