This work analyzes an unsteady triple-diffusive nanofluid flow on a spinning sphere under the influence of a time-dependent magnetic field and Hall current. Liquid hydrogen (H 2 (l)) and ammonia (NH 3 ) are considered as diffusive species to model practical cryogenic and chemical applications. The classical Fourier and Fick laws are generalized through the Cattaneo–Christov model, and the resulting nonlinear equations are solved using a similarity transformation and the bvp4c method in MATLAB. The Taguchi method is applied to optimize heat transfer performance. Results demonstrate that raising the magnetic parameter accelerates velocity in the x -direction but decelerates it in the z -direction, with the Hall current compounding these effects. The rotation parameter promotes thermal diffusion, causing faster cooling of the fluid. The ANOVA results show that the magnetic parameter M has a dominant impact (92.43%) to heat transmission whereas the thermal relaxation parameter β T has a minimal effect (0.04%). These findings highlight crucial control factors for optimizing magnetohydrodynamic nanofluid systems used in cryogenic, reactor and biomedical cooling applications. 2000 Mathematics Subject Classification: 76W05, 76V05
Majumder et al. (Mon,) studied this question.