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The fluid flow and heat transfer applications in coaxial double-revolving disks are extensive and encompass multiple engineering and scientific disciplines. This study presents a comprehensive heat transfer analysis in a second-grade hybrid nanofluid. The fluid, influenced by variable thermal conductivity, is confined between two rotating disks in a magnetohydrodynamic Darcy-Forchheimer flow. The hybrid nanofluid combines titanium dioxide (TiO₂) and cobalt ferrite (CoFe₂O₄) nanoparticles with engine oil. These issues have not been addressed in previous research. Similarity transformations make flow equations dimensionless. The resulting equations are solved using a semi-analytical approach called the homotopy analysis method (HAM). This approach provides flexibility in selecting the base function and an initial estimate. The temperature profile improved with higher values of the variable thermal conductivity parameter. Furthermore, the heat transfer rate was enhanced by increasing the variable thermal conductivity, the volume fraction concentration of TiO₂, and the Reynolds number. The sensitivity analysis is performed using response surface methodology (RSM). Both the R-squared and adjusted R-squared values attain 100%. The heat transfer rate is found to have a maximum sensitivity of 0. 50243 towards varying thermal conductivity parameters and a minimum sensitivity of - 0. 00666 towards magnetic field parameters. The research utilizes RSM to elucidate methods for improving heat transfer. This work offers practical solutions for developing more efficient thermal management systems. This research provides practical strategies for improving thermal management systems. These solutions are especially useful in rotating machinery-intensive industries. Designing biochemical and pharmaceutical microfluidic pumps and mixers requires understanding hybrid nanofluid flows between spinning disks.
Enamul et al. (Mon,) studied this question.