= Solution
The calculation in part (a) leaves the <cross-helicity conservation law> source
$$
\boxed{Q_h=T\,\mathbf B\cdot\nabla s.}
$$
At positive <temperature>, this vanishes exactly when the <magnetic field> is tangent to constant-<specific entropy> surfaces: $\mathbf B\cdot\nabla s=0$. A <homentropic flow> is a sufficient special case; uniform <entropy> throughout space is not necessary. Mere advection of <specific entropy>, $Ds/Dt=0$, constrains its variation along the velocity rather than along the <magnetic field>, so it does not by itself eliminate this source. To conserve total <cross-helicity> in a volume, the net boundary flux must also vanish.
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