Hydrothermal optimisation of hybrid nanoparticle mixture fluid flow in a porous enclosure under a magnetic field and thermal radiation

Fluid cavities have important integral roles in different engineering systems. However, a significant challenge is created by the natural convection (NC) within these cavities. Hence, the present work aimed to assess the heat transfer (HT) and fluid flow within a porous medium. For this purpose, a base fluid (f) was chosen comprising a 50–50 mixture of water–ethylene glycol. Moreover, by incorporating TiO₂–Al₂O₃ hybrid nanoparticles (HNP) into the base fluid, their effect on the HT processes and flow was explored. Primarily, the governing equations were derived by considering momentum, continuity and energy equations. Then, similarity solutions were utilised to convert partial differential equations (PDEs) for the flow and energy functions into ordinary differential equations (ODEs). Then, the problem was solved by considering the boundary conditions. To solve the ODEs, the non-commercial software Flex PDE was used through the numerical solution and finite element discretisation methods. Moreover, in the present work, optimal values were used to determine the response surface method (RSM). According to the results, an upward trend was presented by the temperature (T) profile with a decrementation in the electromagnetic intensity and porosity level. Moreover, the temperature profile was not significantly affected by increasing the radiation parameter (Rd).