Numerical analysis of entropy generation in nanofluid flow over a transparent plate in porous medium in presence of solar radiation, viscous dissipation and variable magnetic field

The entropy generation of magneto-hydrodynamic mixed convection flow of nanofluid over a nonlinear stretching inclined transparent plate embedded in a porous medium due to solar radiation is investigated numerically. The nanofluid is made of Cu nanoparticles with water as the base fluid. The two-dimensional governing equations, in presence of the effects of viscous dissipation, variable magnetic field and solar radiation are transformed by similarity method to two coupled nonlinear ODEs and then solved using the numerical implicit Keller-Box method. The effects of various parameters such as nanoparticle volume fraction, magnetic parameter, porosity, effective extinction coefficient of porous medium, diameter of porous medium solid particles and Eckert, Brinkman and Hartman numbers is investigated on velocity, temperature and entropy generation number profiles. The results reveal that near to the plate surface the increase of nanoparticle volume fraction, porosity and porous medium geometric parameter cause the entropy generation number to increase, but far enough from the plate surface the increase of nanoparticle volume fraction, porosity and porous medium geometric parameter cause the entropy generation number to decrease. Also the entropy generation number increases with the increase of Brinkman number and Hartman number, and this increase is dominant near the plate surface. Closer to the plate surface the reduction of Eckert number causes the increase of entropy generation number, but the entropy generation number increases with the increase of Reynolds number.