MHD conjugate natural convection and entropy generation of a nanofluid filled square enclosure with multiple heat-generating elements in the presence of Joule heating

Abstract

MHD conjugate natural convective flow and heat transfer of TiO2-water nanofluid confined in a tilted square enclosure with multiple heat-generating and conducting solid elements have been investigated numerically in the present study. A constant magnetic field is applied in a parallel direction to the vertical side of the enclosure. Two heat-generating solid elements are attached to the adiabatic bottom wall, whereas the vertical walls are kept at comparatively low temperatures, and the top wall is kept thermally insulated. The system of mass, momentum and energy equations controlled by the governing parameters (Rayleigh, Prandtl, Hartmann numbers, and Joule heating parameter) is solved using the finite element approach. Two configurations of the enclosure based on the position of heat-generating and conducting elements are considered. By changing the Hartmann number from 0 to 20, the tilt angle of the enclosure from 0° to 45°, the Rayleigh number from 103 to 106, and the volume fraction of nanoparticles from 0 to 0.06, changes in flow and thermal patterns in terms of streamline and isotherms are observed. To investigate how the governing parameters affect conjugate heat transfer mechanism within each configuration, average Nusselt number along the heated element, average fluid temperature, total entropy generation, and thermal performance criteria are evaluated. It is observed that pure water manifests better heat transfer characteristics than nanofluid, with a higher Nusselt number and lower thermal performance criteria. Moreover, it reveals that the position of the heat-generating elements and the inclination angle of the enclosure profoundly influence thermal performance.