Magnetohydrodynamics thermogravitational convective in a novel I-shaped wavy-walled enclosure considering various inner hot pipe locations

The present work numerically examines natural convection within an I-shaped wavy-walled enclosure with multi-pipes of heat exchangers filled with multi-layers of nanofluid and porous medium saturated with the same nanofluid. The finite element scheme is used to solve governing equations of mass, momentum along with the energy in dimensionless form. The influence of various dimensionless parameters such as Rayleigh number (10(4) <= Ra <= 10(6)), Darcy number (10(-5) <= Da <= 0.1), Hartmann number (0 <= Ha <= 60), number of undulations (1 <= N <= 5), nanofluid volume fraction (0.00 <= phi <= 0.06), porous layer thickness 0.6 <= X-P <= 1 and MHD inclination angle (0 degrees <= gamma <= 90 degrees) is studied to explain their effect on fluid flow and heat transfer that presented in terms of streamlines, isotherms and average Nusselt number. Three different thermal cases of the location of the internal hot pipe are treated. Our results are in a good agreement with previous works. The finding of this study proved that for better heat transfer, it was recommended to use number of undulation N = 1 and that the location of the inner pipe is at the bottom of the enclosure ( case 1). Moreover, it was obtained that the increase of Rayleigh number (Ra), Darcy number (Da), inclination angle of MHD and the reduction of the porous layer thickness as well as the reduction of Hartmann number (Ha) leads to an increase in heat transfer. Also, the results indicate that enhancement percentage of Nusselt number is 57.77% for Case 1 in a comparison with Case 3 when the number of undulation is N = 1. Finally, applying the magnetic field in the vertical direction (at gamma = 90 degrees) enhances Nusselt number for Case 1 by 53% in a comparison with Case 3.