Page 418 - Introduction to Continuum Mechanics
P. 418
402 Energy Equation in Terms of Enthalpy
Equations (6.25.1) and (6.25.6) are four equations for six unknowns v 1? v^, v^, p, p, 0; the fifth
equation is given by the equation of continuity
and the sixth equation is supplied by the energy equation
where Ty is given by Eq. (6.25.5) and the dependence of the internal energy u onp and @ is
assumed to be the same as when the fluid is in the equilibrium state, for example, for ideal gas
where c v is the specific heat at constant volume.
In general, we have
Equations (6.25.1),(6.25.6),(6.25.7),(6.25.8), and (6.25.10) form a system of seven scalar equa-
V
^ >
tions for the seven unknowns vj, V2> 3»P» A ®> an u
6.26 Energy Equation in Terms of Enthalpy
Enthalpy per unit mass is defined as
where u is the internal energy per unit mass,/? the pressure,p the density.
Let h 0 = h+v /2, (h 0 is known as the stagnation enthalpy). We shall show that in terms of
h 0, the energy equation becomes (neglecting body forces)
where 7^' is the viscous stress tensor, q f the heat flux vector. First, by definition,
From the energy equation [Eq. (6.18.1)], with q s = 0, we have
