A multivariate spectral quasilinearisation method for entropy generation in a square cavity filled with porous medium saturated by nanofluid

We investigate flow in a square cavity filled with a porous medium saturated with a nanofluid and subjected to an applied magnetic field. The cavity walls, except the top, are at rest. The vertical walls of the cavity are adiabatic and bottom wall is kept at a fixed temperature. Flow is generated by the motion of the top wall. The entropy generated through fluid friction, heat and mass transfer is investigated. The equations in non-dimensional form are solved using a multi-variate spectral quasilinearisation method. The applicability and accuracy of this is new method is confirmed by solving the cavity flow model equations. We show that this method may be used to solve nonlinear partial differential equations over a large time domain and in two space variables. The numerical results are given in terms of streamlines, isotherms, isoconcentration and entropy generation. The results show that flow behavior, heat and mass transfer are strongly affected by the Rayleigh, Eckert and Lewis numbers. The entropy generation, which increases with increasing Rayleigh number, is shown to depend primarily on the Brownian motion parameter.