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Energy Equation for Compressible Viscous Flows
There are six types of energy important in our analysis (we exclude, chemical, electromagnetic and nuclear energies):
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Mechanical energy |
Thermodynamic energy |
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Kinetic energy |
Internal energy |
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Potential energy |
Heat |
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—- Work done by pressure ^ |
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—- Work done by friction ^ |
For inviscid flow, the Euler equations have the following energy balance:
dpuH dpv H
dx + dy
where H = h + 2 (u2 + v2) + potential energy, and h = e + p. Here we have ignored heat and viscous dissipation.
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For the Navier-Stokes equations, the energy equation is
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where k is the heat conductivity coefficient, and the viscous dissipation term is given by:
corresponding to the rate of work done by viscous forces.
