Theory for Heat Transfer in Solids
The Heat Transfer in Solids Interface
solves for the following equation derived from
Equation 4-13
:
(4-14)
The different quantities involved here are recalled below:
•
ρ
is the density (SI unit: kg/m
3
)
•
C
p
is the specific heat capacity at constant stress (SI unit: J/(kg·K))
•
T
is the absolute temperature (SI unit: K)
•
u
trans
is the velocity vector of translational motion (SI unit: m/s)
•
q
is the heat flux by conduction (SI unit: W/m
2
)
•
q
r
is the heat flux by radiation (SI unit: W/m
2
)
•
α
is the coefficient of thermal expansion (SI unit: 1/K)
•
S
is the second Piola-Kirchhoff stress tensor (SI unit: Pa)
•
Q
contains additional heat sources (SI unit: W/m
3
)
For a steady-state problem the temperature does not change with time and the terms
with time derivatives disappear.
The first term on the right-hand side of
Equation 4-14
is the
thermoelastic damping
and accounts for thermoelastic effects in solids:
(4-15)
It should be noted that the
d
⁄
dt
operator is the material derivative, as described in the
Time Derivative
subsection of
Material and Spatial Frames
.
