Ferrofluid non-Darcy heat transfer involving second law analysis: an application of CVFEM

The non-Darcy heat transportation of the ferrofluid together with the entropy generation has been studied in a permeable zone under the role of magnetic force. To incorporate the permeable impact, the non-Darcy approach was utilized. CVFEM-based code is implemented to explore the entropy generation and heat transportation for the parametric ranges of Rayleigh (Ra), Darcy (Da) and Hartmann (Ha) numbers. The results demonstrate that here the conduction is the significant mode of transportation of heat at higher Ha; however, the increment in Ra and Da promotes the convection. The Bejan number increases at higher Ha and it decreases with the augmentation of Ra and Da. The enhancement of Ra and Da results in the declination of X_d, and it escalates under the impact of stronger Ha.