MHD natural convection nanofluid flows in a wavy trapezoidal porous enclosure with differentially heated side walls

Flow analysis of the Al2O3- water nanofluid in a porous trapezoidal enclosure is deliberated in this research work. The enclosure is bounded by four differentially heated walls with the bottom wall considered as wavy. The viscous and Joule dissipation effects are taken into account. The governing equations of the flow are non-dimensionalised, and the Galerkin finite element method is employed to solve the resulting unsteady initial and boundary value problem using Taylor-Hood elements to avoid instabilities. The numerical scheme is validated with available literature for a simplified case of a problem, and the results are found to be in good agreement. The influence of Darcy number and nanoparticle volume fraction on the dimensionless streamlines and isotherms are plotted and illustrated in detail. The rate of heat transfers near the bottom wall in a porous medium is analysed through simulated data. It is found that the heat transfer rate increases in the presence of a porous domain. Further, a sensitivity analysis has been performed using Response Surface Methodology (RSM) to identify the pertinent parameters of the problem such as Hartmann number, Darcy number, and nanoparticles whose variation have an important influence on the average Nusselt number. The analysis reveals that the Darcy number, Hartmann number and the nanoparticle volume fraction are related to the average Nusselt number. Thus, the finding suggests that the porous medium has a significant role in enhancing the heat transfer in a flow of MHD nanofluid within a wavy trapezoidal enclosure.