Joule Heating and Viscosity-Ratio Effects on Dissipative Ternary Nanofluid Flow over a Permeable Surface

This study examines the effects of viscous dissipation, Joule heating, and coupled heat transfer on dissipative ternary nanofluid flow over a permeable surface. The ternary nanofluid is composed of Al₂O₃, SiO₂, and TiO₂ nanoparticles dispersed in water as the base fluid. By introducing suitable similarity transformations, the governing partial differential equations are reduced to a coupled system of ordinary differential equations. The thermal field is analyzed for both prescribed surface temperature (PST) and prescribed heat flux (PHF) conditions, while a temperature-dependent heat source/sink term is incorporated to maintain energy balance within the fluid domain. The resulting energy equation is treated analytically with the aid of Kummer’s function and Laguerre polynomial techniques. The effects of the main controlling parameters, including the inverse Darcy number, magnetic parameter, viscosity-ratio parameter, and radiation parameter, are discussed with the support of graphical results. It is found that an increase in the magnetic parameter reduces the velocity by about 12% and raises the temperature by nearly 18%. These findings provide useful guidance for the design and thermal optimization of engineering systems involving complex nanofluids in porous media, including polymer extrusion and automotive cooling applications.