ABSTRACT
This chapter considers the partial differential equations for instability in a nanofluid layer, which are solved for two different models. Model 1 considers the initial particle volume fraction to be varying in the vertical direction, whereas the constant value of nanoparticles at the initial state is considered under Model 2. The expressions for the thermal Rayleigh number are derived analytically and numerical computations are performed with the help of the software Mathematica. The instability of the system also depends on differences in nanoparticle volume fraction at the boundaries of the layer, in addition to other parameters, if the initial nanoparticle varies in the vertical direction, whereas this is not the case if nanoparticles are considered to be constant at the basis state. Differences in volume fractions at the boundaries make the system more unstable for top-heavy distributions than for bottom-heavy arrangements under Model 1, whereas it has no impact on stability in Model 2. The density of nanoparticles destabilizes the system while conductivity stabilizes it. The stability order for metals is established as aluminum > silver > gold > iron, whereas, for non-metals, the order is alumina > silicon oxide > copper oxide > titanium oxide.
