[HelloCthulhu]

Greetings!

I'm trying to find an equation to calculate the change in internal energy for water electrolysis within a magnetic field perpendicular to the current; magnetohydrodynamics (MHD). The cross products of current I and magnetic field B generates a force F perpendicular to the magnetic field; Lorentz Force. Considering that the system work equation for water electrolysis is W = PΔV, how would I rewrite this equation to include a magentic field perpedicular to the current?

I've uploaded 12 pages from the research paper "MHD Propulsion" - Sutcliffe & Neiser 2009. It includes an example of the force equation for MHD thrust: F = IL X B. Any help is greatly appreciated.

[Enthalpy]

Your query is a bit surprising. MHD is usually about propulsion or conversion of work to electricity; do you really mean electrolysis, whose goal with water is to split oxygen and hydrogen, or rather consider a current through water for MHD purpose?

Then, thermodynamics is rarely useful with liquids, when their volume changes little. Why thermodynamics? MHD is already complicated enough, it's a matter of electromagnetism that is made much worse by flow instability. If the purpose is to make thrust from a current, study the electromagnetic and flow aspects, not thermodynamic ones.

And why MHD anyway? It's extremely inefficient, because all the voltage is lost in ohmic loss instead of useful flow speed. The biggest known achievements (submarines are rumoured to do better, I doubt) report "efficiencies" like 5%. To obtain thrust from electricity, let an electric motor rotate a propeller.

[HelloCthulhu]

Thank you for the response!

I'm just interested in the effects it has on convection, mass transfer, etc. I find MHD fascinating, especially with the recent leaps in materials science; graphene, aerogel, etc. Who knows what we may learn by studying MHD at the thermodynamic level? Any clue how I would calculate the system work  for water electrolysis while in a magnetic field perpendicular to the current? I've only found 1 paper with equations for the internal energy: "Magnetohydrodynamic Electrochemistry in the Field of Nd−Fe−B Magnets. Theory, Experiment, and Application in Self-Powered Flow Delivery Systems" - Leventis & Gao 2001. I found it very confusing. I'll post the 6 pages including the formulas. Any help is greatly appreciated.