Analysis of power-law natural conjugate heat transfer under the effect of magnetic field and heat absorption/production based on the first and second laws of thermodynamics for the entropy via lattice Boltzmann method

Abstract

The amount of entropy generated during the conjugate heat transfer of a non-Newtonian fluid regarding to natural convection within a two-dimensional cavity under the influence of a magnetic field and heat absorption/production has been appraised. The lattice Boltzmann method (LBM) method is developed to perform numerical simulations. Moreover, the first and second laws of thermodynamics are simulated via LBM for the entropy investigation. The influence of variables such as wall shape and aspect ratio of chamber, thermal conductivity ratio, fluid type, Hartmann number, heat absorption/production coefficient and type of magnetic field are analyzed. The lower the power-law index, the more effective the magnetic field applied. The mean Nusselt number for pseudoplastic fluid is about 52% and for dilatant fluid about 18% decreases to the highest value with enhancement of the Hartmann number. By changing the shape of the wall, the amount of current vigor, heat transfer and entropy produced can be significantly affected. In such a way that by designing the wall diagonally, the amount of heat transfer up to about 11% and the power of flow up to about 32% more than other cases. The effect of increasing the strength of the magnetic field decreases with increasing the chamber aspect ratio, and in this case the lowest heat transfer rate is seen, however the Bejan number increases.