Theory for Heat Transfer in Fluids

The Heat Transfer in Fluids Interface solves for the following equation (11.2-5 in Ref. 5):

(14-3)

considering that:

•	the Cauchy stress tensor, σ, is split into static and deviatoric parts as in:

•	the dependent variables are the temperature, T, and pressure, p.

The different quantities involved here are recalled below:

•	ρ is the density (SI unit: kg/m3)

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

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

•	u is the velocity vector (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)

•	αp is the coefficient of thermal expansion (SI unit: 1/K):

for ideal gases, the thermal expansion coefficient takes the simpler form αp = 1 ⁄ T

•	p is the pressure (SI unit: Pa)

•	τ is the viscous stress tensor (SI unit: Pa)

•	Q contains heat sources other than viscous dissipation (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 of the right-hand side of Equation 14-3 is the work done by pressure changes and is the result of heating under adiabatic compression as well as some thermoacoustic effects. It is generally small for low Mach number flows.

(14-4)

The second term represents viscous dissipation in the fluid:

(14-5)