5.5.1.2 Energy equation

ρ¯h˜+v˜22p¯t+ρ¯vJ˜h˜+v˜22xjρ¯givι˜τιJ¯+Rijvι˜xj+qJ¯+qjtxj=qext¯

si223_e

ρ¯h˜+v˜22p¯t=ρ¯h˜St+ρ¯v˜22Stp¯St

si224_e

Let us define the mass-weighted space-time average enthalpy H and the space-time average pressure P

Hρ¯h˜Sρ¯S;

si225_e

Pp¯S=pˆ

si226_e

An approximation is necessary for the second term

ρ¯v˜22ρ¯SV22

ρ¯h˜+v˜22

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