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Energy transport equation

The energy transport equation based on enthalpy is given as follows:

∂ρh∂t+∇ ∙ (ρuh)+∂ρK∂t+∇ ∙ (ρuK)−∂p∂t−∇ ∙ (αeff∇h)=ρu⋅g+frad(h)+Sρ,h \frac{\partial \rho h}{\partial t} + \div (\rho \u h) + \frac{\partial \rho K}{\partial t} + \div (\rho \u K) - \frac{\partial p}{\partial t} - \div (\alpha_{eff} \grad h) = \rho \u \cdot \vec{g} + f_{rad}(h) + \vec{S}_{\rho, h}

The energy transport equation based on internal energy is given as follows:

∂ρe∂t+∇ ∙ (ρue)+∂ρK∂t+∇ ∙ (ρuK)+∇ ∙ (pu)−∇ ∙ (αeff∇e)=ρu⋅g+frad(e)+Sρ,e \frac{\partial \rho e}{\partial t} + \div (\rho \u e) + \frac{\partial \rho K}{\partial t} + \div (\rho \u K) + \div (p \u) - \div (\alpha_{eff} \grad e) = \rho \u \cdot \vec{g} + f_{rad}(e) + \vec{S}_{\rho, e}

where:

PropertyDescription
ttTime
ρ\rhoDensity
hhEnthalpy
eeInternal energy
u\uVelocity
KKKinetic energy
ppPressure
αeff\alpha_{eff}Effective thermal diffusivity
g\vec{g}Gravitational acceleration
fradf_{rad}Radiation function
S\vec{S}Source term through fvOption