Steady Finite Amplitude Convection in Type 2 Hybrid Nanofluids With Rough Boundaries and Robin Boundary Condition on Temperature

The study concerns linear and weakly non-linear analysis of a Rayleigh-Bénard convection problem subjected to a most general boundary condition. This general boundary condition consists of rough boundaries on velocity and Robin boundary condition on temperature. With the help of specific non-dimensional parameters, i.e., the slip-Darcy number and the Biot number that arise at lower and horizontal boundaries, we have been able to integrate 16 Rayleigh-Bénard convection problems into one. Both parameters display a stabilising effect on the onset of convection. Utilising a minimal Fourier series representation a generalised Lorenz model is derived. The solution of this Lorenz model is used to obtain the Nusselt number expression. The study also involves the usage of mono nanofluid and hybrid nanofluid of the type where spherical-shaped nanoparticles (alumina/copper) are dispersed into a binary base fluid mixture (water -EG). The thermophysical properties of the binary base fluid mixture and the corresponding nanofluids are calculated using mixture theory. Also, the thermophysical properties of mono nanofluid are derived and calculated from the mixture theory defined for the hybrid nanofluid type, which accounts for the correctness of the mixture theory used (verified using phenomenological laws and mixture theory for mono nanofluid). The paper’s main aim is to throw light on the ease rendered by the usage of general boundary condition, along with presenting a theoretical base for choosing the most suitable nanofluid concerning convection problems. An increase of 96.2984% in critical Rayleigh number is observed in the case of water-EG-alumina nanofluid when Biot number is increased from 〖10〗^(-3) to 〖10〗^6. Likewise, an increase of 107.223% in critical Rayleigh number for water-EG-alumina nanofluid is observed when slip-Darcy number is increased from 〖10〗^(-3) to 〖10〗^6. Limiting cases of the Rayleigh-Bénard problem for 16 boundary conditions including free/rigid isothermal/adiabatic combinations at lower and upper boundaries are obtained, thereby presenting a strong validation for the study. Plots of stream function for different boundary conditions are included for a better physical understanding of the problem.