Interphase heat transfer occurs due to thermal non-equilibrium
across phase interfaces. The total heat per unit volume transferred
to phase 
due to interaction with other
phases is denoted 
, and is given
by:
 | (5–122) |
where:
 | (5–123) |
Heat transfer across a phase boundary is usually described in
terms of an overall
heat transfer
coefficient 
, which is the amount of heat energy crossing
a unit area per unit time per unit temperature difference between
the phases. Thus, the rate of heat transfer, 
, per unit time across
a phase boundary of interfacial area per unit volume 
, from phase 
to
phase 
, is:
 | (5–124) |
This may be written in a form analogous to momentum transfer:
 | (5–125) |
where the volumetric heat transfer coefficient, 
, is modeled using the correlations described below.
For particle model, the volumetric heat transfer coefficient is modeled as:
 | (5–126) |
Hence, the interfacial area per unit volume and the heat transfer
coefficient 
are required.
More information on interfacial area density calculation is available.
It is often convenient to express the heat transfer coefficient in terms of a dimensionless Nusselt number:
 | (5–127) |
In the particle model, the thermal conductivity scale 
is
taken to be the thermal conductivity of the continuous phase, and
the length scale 
is taken to be the mean diameter
of the dispersed phase:
 | (5–128) |
For laminar forced convection around a spherical particle, theoretical
analysis shows that 
. For a particle in a moving incompressible
Newtonian fluid, the Nusselt number is a function of the particle
Reynolds number 
and the surrounding fluid Prandtl
number 
.
Additional information on models in Ansys CFX is available in Particle Model Correlations for Overall Heat Transfer Coefficient in the CFX-Solver Modeling Guide. Some additional details for the Interface Flux model are provided below.
Interface Flux
The heat flux coefficients for both fluids and the interfacial heat flux value, F 12, from Fluid 1 to Fluid 2 (Fluid 1 is the fluid to appear on the left of the Fluid Pairs list) are specified. F 12 is the rate of heat transfer per unit time per unit interfacial area from phase 1 to phase 2. Hence, the heat transferred to fluid 2 from fluid 1 per unit volume is given by:
(5–129)
may be given
as a constant or an expression.Typically,
will be a function of the fluid 1 and fluid 2 temperature
fields, and possibly other variables. In this case, you may accelerate
convergence of the coupled solver by also specifying optional fluid
1 and fluid 2 heat flux coefficients. 
(5–130)
The solver takes the absolute value of these flux coefficients to ensure that they are positive. This is required for numerical stability. The partial derivatives need not be computed exactly; it is sufficient for the specified coefficients to simply approximate the partial derivatives. Specification of heat flux coefficients only affects the convergence rate to the solution of the coupled heat transfer equations, it does not affect the accuracy of the converged solution.
For example, the simple model using a heat transfer coefficient multiplied by a bulk temperature difference my be recovered using:
When using the mixture model, the Nusselt number is defined in terms of a mixture conductivity scale and the mixture length scale:
 | (5–131) |
For details, see Mixture Model Correlations for Overall Heat Transfer Coefficient in the CFX-Solver Modeling Guide.
There are special situations where the use of an overall heat transfer coefficient is not sufficient to model the interphase heat transfer process. A more general class of models considers separate heat transfer processes either side of the phase interface. This is achieved by using two heat transfer coefficients defined on each side of the phase interface.
Defining the sensible heat flux to phase 
from the interface
as:
 | (5–132) |
and the sensible heat flux to phase 
from the interface
as:
 | (5–133) |
where 
and 
are the phase 
and phase 
heat transfer
coefficients respectively. 
is interfacial temperature,
and it is assumed to be the same for both phases.
The fluid-specific Nusselt number is defined as:
 | (5–134) |
where 
is
the thermal conductivity of fluid 
, and 
is the interfacial
length scale (the mean particle diameter for the Particle Model, and
the mixture length scale for the Mixture Model).
In the absence of interphase mass transfer, you must have overall
heat balance 
. This condition determines the interfacial temperature:
 | (5–135) |
It also determines the interphase heat fluxes in terns of an overall heat transfer coefficient:
 | (5–136) |
Hence, in the absence of interphase mass transfer, the two resistance model is somewhat superfluous, as it may be implemented using a user-specified overall heat transfer coefficient.
It is possible to specify a zero resistance condition on one
side of the phase interface. This is equivalent to an infinite fluid
specific heat transfer coefficient 
. Its effect is to force the interfacial
temperature to be the same as the phase temperature, 
.
Modeling advice is available in Two Resistance Model for Fluid Specific Heat Transfer Coefficients in the CFX-Solver Modeling Guide.