Comparative Study of NDSolve and Keller Box in Nanofluid Dynamics and Magnetohydrodynamics with Entropy Analysis

Efficient thermal management is critical for the development of high-performance biosensors and microfluidic devices where excessive heat can degrade signal accuracy and component life. This study investigates the complex interactions of heat and mass transport in a magnetized nanofluid flowing over a stretching surface within a porous medium. By analyzing entropy generation, a measure of energy wasted as heat, this research provides a framework for optimizing the energy efficiency and sensitivity of microscale systems. The physical model was transformed into a set of mathematical equations and solved using the Keller-Box numerical method, a highly stable computational technique. The analysis specifically accounted for the combined effects of magnetic fields, thermal radiation, and the Darcy-Forchheimer law, which describes how fluids move through restricted porous structures. Quantitative results reveal that increasing the Forchheimer number (representing porous resistance) from 0.5 to 2.0 leads to a 12% reduction in fluid velocity, while higher magnetic field strengths significantly elevate local entropy production. Notably, the study found that maintaining a Brinkman number below 1.0 is essential for minimizing internal heat generation, which can otherwise increase entropy by over 25%. Furthermore, the Bejan number analysis confirms that heat transfer dominates entropy production in the region closest to the stretching surface, whereas fluid friction becomes the primary source of energy loss further into the flow. These findings conclude that precise control over magnetic and radiative parameters can be leveraged to suppress thermal noise and improve signal fidelity in advanced sensors. The novelty of this work lies in its integrated approach to Darcy-Forchheimer resistance and non-uniform magnetic effects, moving beyond previous literature by providing specific design limits for minimizing energy dissipation in bio-integrated microstructures.