Optimization and nonlinear thermal sensitivity analysis of Jeffrey fluid flow between permeable disks with modified Darcy law: Implications for energy and cooling systems

The present study aims to investigate the magnetohydrodynamic flow and heat transfer characteristics of a Jeffrey fluid between two permeable flat disks under the combined effects of Hall current and a modified Darcy law. The primary objective is to obtain exact analytical solutions for both accelerating and decelerating radial flow configurations and to analyze the influence of key physical parameters on velocity and temperature fields. Thermal effects arising from radiation and internal heat generation or absorption are also incorporated to enhance the physical realism of the model. Closed-form solutions of the nonlinear governing equations are derived using Jacobi elliptic functions, enabling an accurate description of the flow behavior. The results reveal that the Hall parameter significantly enhances both accelerating and decelerating velocities, whereas magnetic and porous medium resistances suppress the flow. The temperature distribution is found to increase with heat generation and decrease with stronger thermal radiation. Streamline patterns and sensitivity analysis further validate the robustness of the obtained solutions. The findings of this study provide valuable insights into non-Newtonian transport phenomena and are relevant to applications in energy systems, cooling technologies, rotating machinery, and porous media engineering.