1. Chapter 10 Heat Transfer
Introduction to CFX

2. Conservation Equations
Governing Equations
Conservation Equations
Continuity
Momentum
Energy
These are the basic equations that are solved for fluid flow problems.
More equations must be solved for more complex flows involving combustion, radiation, etc.
where

3. Governing Equations
Heat transfer in a fluid domain is governed by the Energy Transport Equation:
The Heat Transfer Model relates to the above equation as follows
None: Energy Transport Equation not solved
Isothermal: The Energy Transport Equation is not solved but a temperature is required to evaluated fluid properties (e.g. when using an Ideal Gas)
Thermal Energy: An Energy Transport Equation is solved which neglects variable density effects. It is suitable for low speed liquid flow with constant specific heats. An optional viscous dissipation term can be included if viscous heating is significant.
Total Energy: This models the transport of enthalpy and includes kinetic energy effects. It should be used for gas flows where the Mach number exceeds 0.2, and high speed liquid flows where viscous heating effects arise in the boundary layer, where kinetic energy effects become significant.
Transient
Convection
Conduction
Viscous work
Sources

4. Governing Equations
For multicomponent flows, reacting flows and radiation modeling additional terms are included in the energy equation
Heat transfer in a solid domain is modeled using the following conduction equation
Transient
Conduction
Source

5. Selecting a Heat Transfer Model
The Heat Transfer model is selected on the Domain > Fluid Models panel
Enable the Viscous Work term (Total Energy), or Viscous Dissipation term (Thermal Energy), if viscous shear in the fluid is large (e.g. lubrication or high speed compressible flows)
Enable radiation model / submodels if radiative heat transfer is significant

6. Radiation Radiation intensity is directionally and spatially dependent
Radiation effects should be accounted for when is significant compared to convective and conductive heat transfer rates
To account for radiation, Radiative Intensity Transport Equations (RTEs) are solved
Local absorption by fluid and at boundaries couples these RTEs with the energy equation
Radiation intensity is directionally and spatially dependent
Transport mechanisms for radiation intensity:
Local absorption
Out-scattering (scattering away from the direction)
Local emission
In-scattering (scattering into the direction)

7. Radiation Models
Several radiation models are available which provide approximate solutions to the RTE
Each radiation model has its assumptions, limitations, and benefits
1) Rosseland Model (Diffusion Approximation Model)
2) P-1 Model (Gibb’s Model/Spherical Harmonics Model)
3) Discrete Transfer Model (DTM) (Shah Model)
4) Monte Carlo Model (not available in the ANSYS CFD-Flo product)

8. Choosing a Radiation Model
The optical thickness should be determined before choosing a radiation model
Optically thin means that the fluid is transparent to the radiation at wavelengths where the heat transfer occurs
The radiation only interacts with the boundaries of the domain
Optically thick/dense means that the fluid absorbs and re-emits the radiation
For optically thick media the P1 model is a good choice
Many combustion simulations fall into this category since combustion gases tend to absorb radiation
The P1 models gives reasonable accuracy without too much computational effort

9. Choosing a Radiation Model
For optically thin media the Monte Carlo or Discrete Transfer models may be used
DTM can be less accurate in models with long/thin geometries
Monte Carlo uses the most computational resources, followed by DTM
Both models can be used in optically thick media, but the P1 model uses far less computational resources
Surface to Surface Model
Available for Monte Carlo and DTM
Neglects the influence of the fluid on the radiation field (only boundaries participate)
Can significantly reduce the solution time
Radiation in Solid Domains
In transparent or semi-transparent solid domains (e.g. glass) only the Monte Carlo model can be used
There is no radiation in opaque solid domains

10. Heat Transfer Boundary Conditions
Inlet
Static Temperature
Total Temperature
Total Enthalpy
Outlet
No details (except Radiation, see below)
Opening
Opening Temperature
Opening Static Temperature
Wall
Adiabatic
Fixed Temperature
Heat Flux
Heat Transfer Coefficient
Radiation Quantities
Local Temperature (Inlet/Outlet/Opening)
External Blackbody Temperature (Inlet/Outlet/Opening)
Opaque
Specify Emissivity and Diffuse Fraction

11. Domain Interfaces
GGI connections are recommended for Fluid-Solid and Solid-Solid interfaces
If radiation is modelled in one domain and not the other, set Emissivity and Diffuse Fraction values on the side which includes radiation
Set these on the boundary condition associated with the domain interface

12. Thin Wall Modeling
Using solid domains to model heat transfer through thin solids can present meshing problems
The thickness of the material must be resolved by the mesh
Domain interfaces can be used to model a thin material
Normal conduction only; neglects any in-plane conduction
Example: to model a baffle with heat transfer through the thickness
Create a Fluid-Fluid Domain Interface
On the Additional Interface Models tab set Mass and Momentum to No Slip Wall
This makes the interface a wall rather than an interface that fluid can pass through
Enable the Heat Transfer toggle and pick the Thin Material option
Specify a Material and Thickness
Other domain interface types (Fluid-Solid etc) can use the Thin Material option to represent coatings etc.

13. Thermal Contact Resistance
A Thermal Contact Resistance can be specified using the same approach as Thin Wall modeling
Just select the Thermal Contact Resistance option instead of the Thin Material option

14. Natural Convection
Natural convection occurs when temperature differences in the fluid result in density variations
This is one-type of buoyancy driven flow
Flow is induced by the force of gravity acting on the density variations
As discussed in the Domains lecture, a source term SM,buoy = (r – rref) g is added to the momentum equations
The density difference (r – rref) is evaluated using either the Full Buoyancy model or the Boussinesq model
Depending on the physics the model is automatically chosen

15. Solution Notes
When solving heat transfer problems, make sure that you have allowed sufficient solution time for heat imbalances in all domains to become very small, particularly when Solid domains are included
Sometimes residuals reach the convergence criteria before global imbalances trend towards zero
Create Solver Monitors showing IMBALANCE levels for fluid and solid domains
View the imbalance information printed at the end of the solver output file
Use a Conservation Target when defining Solver Control in CFX-Pre

16. Heat Transfer Variables
The results file contains several variables related to heat transfer
Variables starting with “Wall” are only defined on walls
Temperature
This is the local fluid temperature
When plotted on a wall it is the temperature on the wall, Twall
Wall Adjacent Temperature
This is the average temperature in the control volume next to the wall
Wall Heat Transfer Coefficient, hc
By default this is based on Twall and the Wall Adjacent Temperature, not the far-field fluid temperature
Set the expert parameter “tbulk for htc” to define a far-field fluid temperature to use instead of the Wall Adjacent Temperature
Wall Heat Flux, qw
This is the total heat flux into the domain by all modes – convective and radiative (when modeled)
Mesh
Control Volumes qw
Twall
Where Tref is the Wall Adjacent Temperature or the tbulk for htc temperature if specified

17. Heat Transfer Variables
Heat Flux
This is the total convective heat flux into the domain
Does not include radiative heat transfer when a radiation model is used
Convective heat flux contains heat transfer due to both advection and diffusion
It can be plotted on all boundaries (inlets, outlets, walls etc)
At an inlet it would represent the energy carried with the incoming fluid relative to the fluid Reference Temperature (which is a material property, usually 25 C)
Wall Radiative Heat Flux
The net radiative energy leaving the boundary (emission minus incoming)
Heat Flux + Wall Radiative Heat Flux = Wall Heat Flux
Only applicable when radiation is modeled
Wall Irradiation Flux
The incoming radiative flux