Second law analysis of thermo-magneto-hydrodynamic couple-stress fluid flow in a cavity with heated fin

Abstract

The objective of current study is to analyze the magnetohydrodynamic (MHD) natural convection flow of couple-stress fluid and entropy generation (second law analysis) inside the cavity with heated fin by using the Galerkin finite element method. The heated fin has been placed in middle of the heated bottom wall, the temperature $T_c$ is fixed on the vertical walls and an insulated situation is considered at the top wall. The irreversibility ratio and heat flux inside the enclosure are examined through entropy generation and Bejan heatlines, respectively. The obtained results show that the intensity of circulations of streamlines decrease from $3.9744$ to $0.03148$ and heatlines from $7$ to $4.5$ due to increasing couple-stress parameter $(K)$ from $0$ to $1.5.$ It is noted that the heatlines bowls appear due to enhanced buoyancy-driven flow against high Rayleigh number. The reverse relation is noted between the entropy generation and the Hartmann number. The overall heat transfer rate along with the bottom and vertical side walls increase $111.65\mathrm{\%}\mathrm{ }$ and $75.8297\mathrm{\%},$ respectively, with increasing the fin height from $0$ to $0.25.$ Obtained results could help to optimize heat transfer in engineering systems like heat exchangers, cooling processes of devices, chemical reactors, and solar collectors.

Keywords:

• Couple stress fluid
• finite element method
• heated fin
• magnetohydrodynamic (MHD)
• second-law analysis