Investigation of entropy generation in a square inclined cavity using control volume finite element method with aided quadratic Lagrange interpolation functions

One of the most concerned subjective in Mechanical science is natural convection study in a cavity. Furthermore, the investigation of entropy generation can be useful for better designing of the thermal systems. In the present study, natural convection flow and entropy generation are numerically investigated in the presence of a magnetic field in a square inclined cavity which known as the effect of magneto-hydrodynamic (MHD). Firstly, governing equations, including mass, momentum, and energy balance equations are applied to the problem. Then, governing equations are rewritten in dimensionless form using non-dimensional parameters, vorticity, and stream function. Furthermore, the entropy generation equation is written as a non-dimensional equation. Then, the contribution of the heat transfer entropy generation into the total entropy generation rate is determined using the Bejan number. A new measure for evaluation of the thermal performance of the cavity is presented that is the so-called ecological coefficient of performance (ECOP) based on the second law of thermodynamics. Flow and heat transfer characteristics are investigated for different values of the Rayleigh number, inclination angle, and Hartmann number. The new correlations of entropy generation as a function of Rayleigh number are obtained using the two-dimensional version of quadratic Lagrange interpolation functions (QLIFs). The obtained values for the average Nusselt number and the entropy generation number are compared with those of the literature and excellent agreement is observed. The results show that the entropy generation number rises with increasing of Hartmann number and whereas it has a maximum value for a specified inclination angle. Also, ECOP increases with increasing of Hartmann number for low values of Rayleigh number. The results discover that the optimum values of the inclination angle are 20 degrees, 35 degrees and 48 degrees for Hartmann number 0, 25 and 75 at Ra = 10(5), respectively. Also, with increasing Ha from 25 to 75, the contribution of the N-gen due to magnetic field decreases from 23% to 9% for beta = 0 degrees and it decreases from 24% to 6% for beta = 45 degrees.