Entropy Generation Analysis of Magnetohydrodynamic Flow Systems

Abstract

Magnetohydrodynamic (MHD) channel flows are widely used in liquid-metal cooling loops, electromagnetic pumps,
and plasma-facing energy systems, where an imposed transverse magnetic field suppresses velocity fluctuations
but introduces an additional, often dominant, irreversibility channel through Joule dissipation. We report a
volume-averaged entropy generation analysis of steady, incompressible, electrically conducting fluid flow between
parallel plates subject to a transverse magnetic field, solving the coupled momentum and energy equations across
54 combinations of Hartmann number (0 to 40) and wall heat flux (500 to 4000 W/m^2) at a fixed Reynolds number
of 1200. Total dimensionless entropy generation number N_S rose from 0.86 at Ha = 0 to 3.42 at Ha = 40, a 298%
increase, while the Bejan number, the fraction of entropy generation attributable to heat transfer irreversibility, fell
from 0.71 to 0.19 over the same range, indicating a decisive shift toward magnetic-field-driven irreversibility at high
Hartmann number. Joule dissipation accounted for 61% of total entropy generation at Ha = 40 versus 0% at Ha = 0
by construction, and exceeded viscous dissipation as the second-largest contributor once Ha exceeded 14, a
threshold that was consistent within +/-1 Hartmann-number unit across all five wall heat flux levels tested. An
optimum Hartmann number of Ha = 9.4 minimized total entropy generation at the lowest heat flux tested (500
W/m^2), but this optimum vanished at wall heat fluxes above 2200 W/m^2, where N_S increased monotonically with
Ha across the full range, reflecting the growing dominance of Joule heating once conductive wall loading is high
enough that additional flow damping no longer meaningfully reduces thermal irreversibility. A regression of N_S
against Ha^2 and wall heat flux explained 97.3% of the variance in the simulated dataset (R^2 = 0.973,
root-mean-square error 0.081), confirming the expected quadratic scaling of Joule dissipation with magnetic field
strength. These results indicate that entropy generation minimization in MHD channel flow is not achieved by
uniformly maximizing or minimizing the applied magnetic field, but requires a heat-flux-dependent optimum
Hartmann number below which flow damping benefits outweigh Joule losses, a design criterion directly applicable
to liquid-metal blanket and MHD pump engineering.