Entropy generation in Joule-heated radiative hybrid nanofluid flow over a permeable radially stretching disk with Cattaneo–Christov heat flux

This study aims to examine unsteady axisymmetric magnetohydrodynamic flow and heat transfer above a permeable disk stretching radially.

The accounted model incorporates nonlinear thermal radiation, viscous dissipation, Joule heating and the Cattaneo–Christov heat-flux relation. A TiO₂–CoFe₂O₄/H₂O hybrid nanofluid is represented through commonly used effective-property formulas. By means of a similarity transformation, the governing boundary-layer equations are reduced to a coupled nonlinear ordinary differential system, which is then solved with MATLABbvp4c.

The calculations indicate that thermal relaxation changes the near-wall temperature response and, for the parameter range studied here, produces a slight increase in the reduced Nusselt measure $Nu<private-char specific-use="loader-generated">&#xef07;</private-char>Re−1/2$⁠. The Fourier result is recovered smoothly as $Λ→0$⁠. Radiation and viscous heating raise the temperature field and modify entropy production, whereas magnetic forcing slows the flow and changes the irreversible behavior through Joule dissipation. Suction narrows the boundary layer and improves wall heat removal. The results also show that increasing hybrid nanoparticle loading does not translate into a proportionally larger heat-transfer gain, because the rise in conductivity is accompanied by changes in effective heat capacity and momentum resistance.

This study clarifies how thermal relaxation, radiation, magnetic forcing, wall mass transfer and hybrid loading act together in heat transfer and entropy generation over a stretching disk.