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I have dynamically modelled a drum boiler, but when i am solving the equation i am getting an negative rate of change of enthalpythe reason i find is the enthalpy of the steam is very higher than the enthalpy of water. can someone please verify the model and help me with this.

$$\rho_w\cdot V_w\cdot \frac{\mathrm{d} h_w}{\mathrm{d} t} = Q+\dot{m}\cdot (h_w-h_s)-M\cdot C_p\cdot \frac{\mathrm{d} T_m}{\mathrm{d} t}$$

where $$M\cdot C_p\cdot \frac{\mathrm{d} T_m}{\mathrm{d} t} = Q-(n\cdot \pi \cdot D\cdot L\cdot \alpha \cdot (T_m-T_s))$$

ρ

_{w}= density of water

V

_{w}= volume of water

m

^{.}= massflow rate of water

h

_{s}= enthalpy of steam

M = mass of metal

C

_{p}= specific heat of metal

T

_{m}= temperature of metal

n = number of tubes

D = Dia of tube

L = length of tube

∝ = heat transfer coefficient