Based on the First Law of Thermodynamics, the change of internal energy has to be balanced by the pressure work and heat transfer. For the flow problems relevant to internal combustion engines, the effects of convection, turbulent transport, turbulent dissipation, sprays, chemical reactions, and enthalpy diffusion of a multi-component flow should also be considered. The internal energy transport equation is:

(2–5)

where I is the specific internal energy, J is the heat flux vector accounting for contributions due to heat conduction and enthalpy diffusion:

(2–6)

λ is the thermal conductivity, which is related to the thermal diffusivity α and heat capacity by , T is the fluid temperature, and h _k is the specific enthalpy of species k. is the dissipation rate of the turbulent kinetic energy, which will be defined in Turbulence Models . and are source terms due to chemical heat release and spray interactions, respectively. The term accounts for the effects of ensemble-averaging or filtering of the convection term, that is, . Again, it needs to be properly modeled from the turbulence approach. is the radiative heat loss, whose modeling is introduced in Radiation Heat Transfer Model .