Some other formulations of the energy equation

For practical calculations it is often advantageous to use other dependent variables instead of the internal energy in the energy equation. Especially useful are the enthalpy and the temperature form of the energy equation. 

The enthalpy form is obtained, due to h = u+pv, by the addition of gd(pv)/dt to both sides of the energy equation (3.80), giving 

The temperature form of the energy equation is especially important, as its solution describes the temperature field in terms of time and space. For pure substances, this equation is obtained, if we make use of the well known relationship from thermodynamics [3.2] 

3 Convective heat and mass transfer. Single phase flow 

The enthalpy of mixtures is dependent on temperature, pressure and composition. Its differential is given by 

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