Study of Brinkman–Bènard nanofluid convection with idealistic and realistic boundary conditions and by considering the effects of shape of nanoparticles

This study deals with linear and weakly non-linear stability analyses of Brinkman–Bènard convection in nanoliquid-saturated porous enclosures. Water with a dilute concentration of molybdenum disulfide nanoparticles with 0.06 volume fraction and 30% glass fiber-reinforced polycarbonate as a porous medium with porosity 0.88 are considered to be a working medium. The analytical solution is obtained in the present study for idealistic and realistic boundary conditions, and their results are compared. An analytically intractable Lorenz model with quadratic nonlinearities is reduced to a tractable Ginzburg–Landau amplitude equation with cubic nonlinearity using the multiscale method. Nanoparticles with different shapes are considered in the study, and their effects on the onset and heat transfer are discussed in great detail graphically in the presence of other parameters arising in the problem.