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The enthalpy increase is


        DH       DT  c    dT+v     VT)              (8.7)
        Dt   tl-p 5t ! pat+v       VT(87

where

        p = density of the medium

        Cp = specific heat

        T = absolute temperature

For steady state conditions with uranium and hydrogen flowing in the axial direction only, the heat balance equation becomes


                   dT
             PC p'z dz =S - 7  • q                  (8.8)


In the present case, in which only the radial profiles of uranium, hydrogen, and temperature are considered, the application of the diffusion approximation (8.4) to the energy balance equation yields


               v • (KRVT) + S = 0                   (8.9)

The solution to equation (8.9) represents the radial temperature distribution in the plasma core reactor, based on the Rosseland diffusion approximation for photons. The temperature distribution will be determined by the opacity, KR, and the heat generation rate,.S, which is proportional to the spatially dependent fission rate.