Governing Equations
Conjugate Heat Transfer
Conjugate Heat Transfer
Flow Simulation allows to predict simultaneous heat transfer in solid and fluid media with
energy exchange between them.
Heat transfer in fluids is described by the energy conservation equation 2-3 (see “The NavierStokes Equations for Laminar and Turbulent Fluid Flows” on page 14), where the heat flux is
defined by equation 2-16. The phenomenon of anisotropic heat conductivity in solid media is
described by the following equation:
(2-50)
where e is the specific internal energy, e = C·T, C is specific heat, QH is specific heat release (or
absorption) per unit volume, and Ȝi are the eigenvalues of the thermal conductivity tensor. It is
supposed that the heat conductivity tensor is diagonal in the considered coordinate system. For
isotropic medium Ȝ1 = Ȝ2 = Ȝ3 = Ȝ.
If a solid consists of several solids attached to each other, then the thermal contact resistances
between them (on their contact surfaces), specified in the Engineering database in the form of
contact conductance (as m2·K/W), can be taken into account when calculating the heat
conduction in solids. As a result, a solid temperature step appears on the contact surfaces. In the
same manner, i.e. as a thermal contact resistance, a very thin layer of another material between
solids or on a solid in contact with fluid can be taken into account when calculating the heat
conduction in solids, but it is specified by the material of this layer (its thermal conductivity
taken from the Engineering database) and thickness.
The surface heat source (sink) due to Peltier effect may also be considered (see “Thermoelectric
Coolers” on page 92).
The energy exchange between the fluid and solid media is calculated via the heat flux in the
direction normal to the solid/fluid interface taking into account the solid surface temperature
and the fluid boundary layer characteristics, if necessary.
If a solid medium is porous with a fluid flowing through it, then a conjugate heat transfer
problem in this porous-solid/fluid medium can be solved also in the manner described below
(see “Flows in Porous Media” on page 66).
Joule Heating by Electric Current in Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Flow Simulation, v2021
July 2020
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