Unsteady MHD transport of a tangent-hyperbolic ternary hybrid nanofluid over a permeable stretching surface with variable thermal conductivity and nonlinear radiation.

This work is a numerical exploration of the unsteady MHD transport of a ternary hybrid nanofluid of tangent-hyperbolic flow over a permeable stretching surface. The working fluid consists of [Formula: see text] Cu, and [Formula: see text] nanoparticles dispersed in ethylene glycol. The model includes nonlinear radiation, variable thermal conductivity, Joule heating, and Darcy-Forchheimer porous effects. The governing equations of partial differential equations are reduced to similarity equations of ordinary differential equations and solved by MATLAB BVP5C. Simulations show that an increase in the Weissenberg number and Forchheimer parameter decreases the velocity field because of the increase in elastic and inertial resistance and the energy dissipation elevates the fluid temperature. The variable thermal conductivity will greatly enhance thermal gradients near the wall and increase the performance of heat transfer. Moreover, increased concentrations of nanoparticles enhance skin-friction coefficients, Nusselt and Sherwood numbers. The ternary hybrid nanofluid is better than mono and binary systems due to synergistic interactions of the nanoparticles that promotes thermal conductivity and mass diffusion. The findings indicate that the Nusselt number decreases up to 92.14% with increasing magnetic parameter and decreases to about 95.93% with increasing thermal radiation, which shows a high level of suppression of heat transfer. Conversely, the stretching parameter augments the skin friction and mass transfer by approximately 42.48 and 11.47% respectively, whereas thermophysical parameters augment the Nusselt number by up to 286.9%. Comprehensively, the numerical analysis shows, quantitatively, the competing interplay of electromagnetic, thermal and diffusive processes in dictating transport behaviour in ternary hybrid nanofluid flow. These results demonstrate the possibilities of tangent-hyperbolic ternary hybrid nanofluids in the advanced cooling and thermal management processes with intricate rheological and electromagnetic interactions. The soundness and correctness of the numerical framework is validated against existing literature.