Numerical simulation for radiative hybrid nanofluid (<mml:mstyle>TiO</mml:mstyle>2+<mml:mstyle>Fe</mml:mstyle>3<mml:mstyle>O</mml:mstyle>4/<mml:mstyle>H</mml:mstyle>2<mml:mstyle>O</mml:mstyle>) flow due to a non-uniform stretching sheet with variable permeability

Variable permeability plays a crucial role in various manufacturing and technical applications such as fixed-bed catalytic reactors, heat exchangers, and dying, among others. The primary focus of this paper is to investigate the impacts of variable permeability on hybrid nanofluid (HNF) flow due to nonlinear sheet stretching with thermal heat flux. The HNF is made up of a mixer of TiO(2 )and Fe3O4 nanoparticles and water serving as the base fluid. Using efficient similarity transformations, the flow-governing equations are converted into a set of ordinary differential equations, and the resulting system is computationally solved by using the MATLAB program (bvp4c). The impact of various physical variables on the fluid velocity and heat transfer characteristics is analyzed via graphs. It is found that as the permeability parameter rises, the velocity of the HNF diminishes while the temperature amplifies. The drag force coefficient declines with an intensification of the volume fraction of the Fe3O4 nanoparticles. The HNF (TiO2+Fe3O4/H2O) exhibits 0.45-0.75% increase in heat transfer rate when compared to a nanofluid (Fe3O4/H2O) for different values of heat source parameter. The current investigation is compared to the existing literature, revealing a good level of agreement.