The energy balance equations for the thermal hydraulic reactor model are.
$$\frac{M_f}{n}C_p\frac{dT_f(n)}{dt}=P_f(n)-P_g(n)$$
$$\frac{M_c}{n}C_p\frac{dT_c(n)}{dt}=P_g(n)-P_c(n)$$
$$[M_m(n)C_p+\frac{\sum M_sC_p}{n}]\frac{dT_b(n)}{dt}=P_c(n)+P_m(n)-P_{cool}(n)-\frac{1}{n}P_{loss}$$
Where \(M_f\) is the mass of fuel in the reactor, \(T_f(n)\) is the mean fuel temperature in the \(n^{th}\) axial segment. \(P_g\) is the rate of heat transfer from the fuel to the cladding. \(M_c\) is the cladding mass, \(P_c\) is the heat transfer from the cladding to the coolant, \(M_m(n)\) is the coolant/moderator volume in the \(n^{th}\) axial segment, \(T_b(n)\) is the bulk coolant temperature in the core, \(P_{cool}(n)\) is the heat removed by the cooling system of the \(n^{th}\) axial segment, and \(P_{loss}\) is the heat lost through the thermal insulation.
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