Optimizing power and cooling: SOR-based computational analysis of hybrid nanoliquid flow in Darcy porous medium

• Two dimensional unsteady flow of a hydromagnetic hybrid nanofluid is addressed. • A variable pressure gradient is utilized to control flow resistance and enhance fluid motion in porous media. • Nonlinear thermal radiation and viscous dissipation are incorporated to analyze thermal transport characteristics. • Joule heating driven by buoyancy forces is also considered. • Transformed equations are numerically solved using the successive over-relaxation (SOR) algorithm. Hybrid nanofluids in porous media offer groundbreaking potential for engineering advancements in sustainability, energy efficiency, cooling systems, and fluid management solutions for power generation. Thus, the major objective of this study is to investigate the influence of nonlinear thermal radiation on a hybrid nanofluid containing of T i O 2 and A g nanoparticles over a flat plate under the influence of an inclined magnetic field and viscous dissipation. Metallic nanoparticles like argentum exhibit high thermal conductivity, while non-metallic nanoparticles such as titanium oxide offer durability and excellent thermal resistance. This combination T i O 2 − A g is expected to achieve more effective heat transfer performance compared to individual nanofluids. The governing equations are solved numerically using the finite difference method, incorporating the SOR technique as the computational approach. A detailed analysis of velocity, temperature, and streamlines is conducted. The results are presented through visual plots and analyzed for various governing parameter values. Findings indicate that an increased magnetic field reduces velocity by 17.5 %, while a higher Darcy parameter enhances velocity by 12 %. Additionally, an increase in thermal radiation leads to a 28 % rise in temperature distribution and greater viscous dissipation results in a 35 % temperature increase. A higher Prandtl number decreases the thermal boundary layer thickness by 45 %. Silver's thermal conductivity is 7.5 % higher than copper's, whereas titanium dioxide is 97–98 % lower. These insights are valuable for applications in industries such as glass and polymer manufacturing, heat exchanger design, metallic plate cooling, and thermal management systems.