On the entropy generation for a porous enclosure subject to a magnetic field: Different orientations of cardioid geometry

Natural or free convection is one mode of convection heat transfer where temperature changes leads to density variation. For example, free convection can happen in an enclosure that has two walls with different temperatures. In the present study, the heat transfer behavior of a cardioid shaped porous cavity is investigated. Regarding the situation of the inner cardioid, four modes can be considered for the problem that is called cases A, B, C and D. The Cu-water nanofluid has been selected as working fluid and the flow is affected by an external magnetic field. Non-dimensional governing equations (stream-vorticity functions) are solved numerically using the control volume finite element method (CVFEM). The ecological coefficient of performance (ECOP) as a criterion of cavity performance is evaluated. The effects of decision variables such as Darcy number, Hartmann number, Rayleigh number, and nanoparticle volume fraction on the entropy generation number, the ECOP and the average Nusselt number are studied. The results show that case C is better rather than other cases from the view point of the second law of thermodynamics.