Effects of Alumina–Tantalum Hybrid Nanofragment on Engine Oil Flow Using a New Local Thermal Nonequilibrium Formulation

The aim of this work is to study the alumina–tantalum/motor oil hybrid nanoliquid flow in a porous cavity subjected to a uniform magnetic field. We have used the Darcy–Bénard convection model for the momentum equation and a new local thermal nonequilibrium formulation for heat transport. Linear stability theory and nonlinear stability theory based on the double Fourier series representation are used to study the onset of stationary and chaotic convection in the hybrid nanofluid. The analytical expression of the stationary thermal Rayleigh–Darcy number has been found as a function of dimensionless parameters and physicochemical properties of the hybrid nanoliquid. Tools such as bifurcation diagrams, Lyapunov exponent, phase spaces, and time histories were used to analyze the chaotic and regular behaviors of the resulting five-dimensional system of nonlinear equations. The added value of this work lies in the stabilization and control of chaotic convection in motor oil flow using hybrid alumina and tantalum nanoparticles and a uniform magnetic field.