Theory for Heat Transfer

Theory for Heat Transfer in Solids

The Heat Transfer in Solids Interface solves for the following equation:

(14-1)

The different quantities involved here are recalled below:

•	ρ is the density (SI unit: kg/m3)

•	Cp is the specific heat capacity at constant stress (SI unit: J/(kg·K))

•	T is the absolute temperature (SI unit: K)

•	utrans is the velocity vector of translational motion (SI unit: m/s)

•	q is the heat flux by conduction (SI unit: W/m2)

•	qr is the heat flux by radiation (SI unit: W/m2)

•	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/m3)

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 14-1 is the thermoelastic damping and accounts for thermoelastic effects in solids:

(14-2)

It should be noted that the d ⁄ dt operator is the material derivative.