= Energy fluxes of a strong adiabatic shock
{title2=$F_{\rm int}=2\rho_1u_1^3/(\gamma+1)^2,\quad\Delta F_{\rm kin}=2\gamma\rho_1u_1^3/(\gamma+1)^2$}
In the rest frame of a strong planar <shock wave>, a perfect gas has $\rho_2/\rho_1=(\gamma+1)/(\gamma-1)$, $u_2/u_1=(\gamma-1)/(\gamma+1)$ and $p_2=2\rho_1u_1^2/(\gamma+1)$. Its downstream <specific internal energy> is $\epsilon_2=p_2/[(\gamma-1)\rho_2]=2u_1^2/(\gamma+1)^2$. Multiplying by mass flux $j=\rho_1u_1$ gives the internal-energy flux in the title. The lost bulk <kinetic energy> flux instead equals $j(u_1^2-u_2^2)/2=\gamma F_{\rm int}$: this includes downstream pressure work and is the increase of <specific enthalpy> flux in the cold-upstream limit. Neither quantity is a temperature change per unit time of a fixed target mass without further information about that target.
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