Engine oil is a liquid used in a wide range of applications, as it is an essential lubricant, but it also cools, washes and helps prolong the performance of industrial machinery, vehicle engines and aircraft combustion treatment. This paper deals with the (alumina-tantalum)/engine oil hybrid nano-liquid flow in a porous medium subjected to rotational and Lorenz forces. We have used the Darcy-Bénard convection model for the momentum equation and a new local thermal non-equilibrium formulation for heat transport. Linear stability theory and non-linear stability theory based on the minimal double Fourier series representation are used to study the appearance of stationary and chaotic convection in the hybrid nano-liquid. The analytical expression of the stationary thermal Rayleigh-Darcy number has been found to be a function of the parameters and physicochemical properties of the nano-liquid. In addition, a robust 6-dimensional nonlinear system was determined for the study of chaotic convection. The effects of dimensionless parameters and nanofragments were analyzed graphically. The added value of this work lies in stabilizing and controlling the onset of thermal instability and chaotic convection in engine oil by adding alumina-tantalum nanofragments and applying a magnetic field and/or a rotational force.
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