The convervation of energy amounts to (Equation (1.551) in [19]):
![]() |
(692) |
where
is the deformation rate tensor,
is the heat
conduction coefficient and
is the heat production per unit of volume. The
total time derivative of the energy density
can also be written
as:
![]() |
(693) |
is the specific heat at constant volume. Since (conservation of mass)
![]() |
(694) |
this also amounts to:
![]() |
(695) |
leading to
![]() |
(696) |
In some other books one may find the completely equivalent expression:
![]() |
(697) |
where is the specific heat at constant pressure. Integrating across a
volume V one obtains:
![]() |
![]() |
|
![]() |
(698) |
The following terms can be distinguished: