Temperature Evolution Equation of a Compressible Turbulent Ferrofluid

A temperature evolution equation for compressible ferrofluids is derived using basic laws of thermodynamics of moving electromagnetic media. Along with the compressibility the change in kinetic energy is also included in the laws of thermodynamics to make the equation suitable for studying convective instabilities and fully developed turbulence in compressible ferrofluids as is shown by an order of magnitude analysis. The derived equation is found to be consistent with the total energy conservation when the forcing and dissipative effects are neglected. One can indeed recover the previously derived temperature evolution equations under suitable limits. In hydrodynamic limit, the equation is reduced to the temperature evolution of a neutral compressible fluid and can be potentially important for studying astrophysical turbulence.