The Nonisothermal Flow and Conjugate Heat Transfer Equations
In industrial applications it is common that the density of a process fluid varies. These variations can have a number of different sources, but the most common one is the presence of an inhomogeneous temperature field. This module includes the Nonisothermal Flow predefined multiphysics coupling to simulate systems in which the density varies with temperature.
Other situations where the density might vary includes chemical reactions (for instance, where reactants associate or dissociate).
The Nonisothermal Flow and Conjugate Heat Transfer interfaces contain the fully compressible formulation of the continuity and momentum equations:
(4-1)
where
•
  ρ is the density (SI unit: kg/m3)
•
  u is the velocity vector (SI unit: m/s)
•
  p is the pressure (SI unit: Pa)
•
  μ is the dynamic viscosity (SI unit: Pa·s)
•
  F is the body force vector (SI unit: N/m3)
It also solves the heat equation, which for a fluid is given by
(4-2)
where in addition to the quantities above
•
 Cp is the specific heat capacity at constant pressure (SI unit: J/(kg·K))
•
 T is the absolute temperature (SI unit: K)
•
 q is the heat flux by conduction (SI unit: W/m2)
•
  τ is the viscous stress tensor (SI unit: Pa)
•
S is the strain-rate tensor (SI unit: 1/s)
•
 Q contains heat sources other than viscous heating (SI unit: W/m3)
The work done by pressure changes term
with .
and the viscous heating term
are often negligible. The pressure work term is included by default, while the viscous heating term is optional. The latter can be accounted for by selecting the corresponding check box in the Nonisothermal Flow feature. When, in addition, the Include kinetic energy check box is selected, the conservative form of the total energy equation is solved
(4-3)
where
(4-4)
Observe that the pressure in the pressure work term always is the absolute pressure even if a reduced pressure is used in the momentum equation. For a detailed discussion of the fundamentals of heat transfer in fluids, see Ref. 3.
The physics interface also supports heat transfer in solids:
where Qted is the thermoelastic damping heat source (SI unit: W/(m3)). This term is not included by default but must be added by selecting corresponding check box.
•
Theory for Heat Transfer in Fluids in the Heat Transfer Module User’s Manual.
•
Turbulent Nonisothermal Flow Theory
•
References for the Nonisothermal Flow and Conjugate Heat Transfer Interfaces