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So I stumbled upon this equation:

$\frac{\partial h v}{\partial t}= - \nabla(hv \cdot v)- \nabla P$

where $h$ is enthalpy, $v$ is fluid velocity, $t$ time, and $P$ pressure.

It seems to have the form of the momentum conservation equation in hydrodynamics. However I don't understand the use of enthalpy here. It makes sense to me to replace enthalpy in energy density but not in momentum. I can't find anything online about this.

The source of this equation is equations 2 and 3 in http://arxiv.org/pdf/1008.4806v1.pdf

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    $\begingroup$ Can you provide the source for that equation? I've never seen enthalpy used there either. $\endgroup$
    – Kyle Kanos
    Commented Aug 8, 2015 at 17:49
  • $\begingroup$ Hi. I added the source. $\endgroup$
    – mathdummy
    Commented Aug 8, 2015 at 18:34
  • $\begingroup$ It appears they are using it as an energy equation there. I've seen something similar in some relativistic situations (though there are densities & Lorentz-$\gamma$'s included as well in those cases) $\endgroup$
    – Kyle Kanos
    Commented Aug 8, 2015 at 19:02
  • $\begingroup$ Why the conservation of "flux" tho, instead of just h. Like why not $\frac{\partial h}{\partial t}$ instead of $\frac{\partial h v}{\partial t}$, that's what is confusing me. $\endgroup$
    – mathdummy
    Commented Aug 8, 2015 at 19:18
  • $\begingroup$ In the aforementioned relativistic situations, it is $\partial_t\left(\rho\gamma^2hv\right)$. I am unsure how the authors use that, but they cite Landau & Lifshitz for their equation, so you may want to check that book. $\endgroup$
    – Kyle Kanos
    Commented Aug 8, 2015 at 19:23

1 Answer 1

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The enthalpy flux balance equation is in essence a transport equation. Its use over the more familiar enthalpy balance equation has to do with a breakdown of the diffusive approximation for transport phenomena in cases where the mean free-path of the fluid particles becomes comparable to the typical length-scale of fluid. That is, transport phenomena can be well approximated by diffusive processes, to which the usual enthalpy balance equation applies, only as long as the diffusion velocity in the fluid is much lower than the particle velocity in the fluid flow. The problem considered in the paper lies well outside this regime, hence their use of the enthalpy flux equation instead.

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  • $\begingroup$ Thanks! But why is it we only need to transport flux for enthalpy and not for density, or entropy? what's the unique property of enthalpy that calls for this? $\endgroup$
    – mathdummy
    Commented Aug 9, 2015 at 20:13
  • $\begingroup$ That is a very good question, and got me puzzled too. I eventually found the authors' project page, quarknova.ca, and the page of BurnUD software used in the paper, quarknova.ca/BurnUD/index.html. From what I understand, they consider the combustion of hadronic matter in an ultra-high density star by an expanding bubble of SQM (strange quark matter). The combustion at the interface between the SQM bubble and the hadronic matter is described by reactive-diffusive processes that correspond to the conservation equations for densities and entropy. $\endgroup$
    – udrv
    Commented Aug 10, 2015 at 6:21
  • $\begingroup$ But it also produces sizable pressure gradients and fluid flow across and around the interface, which I guess is described through the enthalpy transport equation. The use of enthalpy transport may have to do with huge energies released across the interface. Matter transport, on the other hand is viewed as still suited for diffusive treatment. The buttom of the BurnUD page has a Help&Contact section. Perhaps it's worth dropping the authors a question? $\endgroup$
    – udrv
    Commented Aug 10, 2015 at 6:22

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