LTNE magneto-thermal stability analysis on rough surfaces utilizing hybrid nanoparticles and heat source with artificial neural network prediction

The present study introduces the simultaneous effects of local thermal non-equilibrium (LTNE), heat source and magnetic field on thermal instability to the onset of convection in electrically conducting Al $$_2$$ O $$_3$$ –Cu/water hybrid nanoliquid flowing through parallel plates with rough boundaries. The Saffman-interface condition is incorporated for non-neglecting surface roughness. Linear stability analysis in longitudinal mode is performed by constructing eigenvalue problem, which is solved numerically using finite difference code with three-stage Lobatto IIIa formula and compared with Runge Kutta shooting method. The present numerical code for limiting cases, i.e. free–free, rigid–rigid, rigid–free boundaries, is also compared with Galerkin method (number of terms, $$N_{\max }= 15$$ ). Increasing the values of roughness parameters ( $$\lambda _1$$ , $$\lambda _2$$ ), LTNE parameter ( $$N_{\text {H}}$$ ), Heat source/sink ( $$S_{\text {bl}}, S_{\text {np}}$$ ) and Chandrashekar number (Q) favours the convection, thus destablizes the system whereas Lewis number (Le) follows the opposite trend. The artificial neural network with four input variables for predicting the critical Rayleigh number using Levenberg–Marquardt back propagation algorithm, is also presented. The optimal number of neurons in the hidden layer is selected on the basis of coefficient of determination ( $$R^2$$ ), root mean square error and root mean relative error. Finally, the simulated and predicted results are compared and in good agreement.