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03fluid_eqns07part2 - FLUID MODELS Part 2 Reduced Equations...

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FLUID MODELS: Part 2 Reduced Equations Splitting the energy equation : We can use the momentum equation and the continuity equation to write the energy equation in a shorter form. First take the dot product of u with the differential form of the momentum equation. or Subtract this from the energy equation to give Using the continuity equation we can write Using this the species energy equation can be rewritten Adiabatic equations : Neglecting the thermal conduction term makes the situation adiabatic . The caloric equation of state can be written For a calorically perfect gas this is ( 29 T e e = where is the specific heat at constant volume. For the case of constant specific heats we get Substituting into the energy equation above Dividing by and rearranging For a thermally and calorically perfect gas where p c is the specific heat a constant pressure. The enthalpy is given by ( 29 dT T c dh p = . We also define the ration of specific heats k as Using these and we can write Integrating Using we can write or This equation represent an energy equation for a ideal gas with no external work interactions other than the pressure work and for adiabatic , no heat interaction, processes.
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