### 2.7.5. Heat Transfer

#### 2.7.5.1. Adiabatic

The heat flux across the wall boundary is zero (that is, insulated). When radiation is included, the total heat flux is zero:

| (2–7)

For details, see CFX-Solver Output File (Radiation Runs) in the CFX-Solver Manager User's Guide.

#### 2.7.5.2. Fixed Temperature

The wall boundary is fixed at a specified temperature . The heat flux into the domain is calculated for laminar flows from the temperature gradient at the wall, and for turbulent flows by:

| (2–8)

where is the near-wall temperature and involves the use of turbulent wall functions. For details, see Heat Flux in the Near-Wall Region in the CFX-Solver Theory Guide.

#### 2.7.5.3. Heat Flux and Wall Heat Flux

A heat flux is specified across the wall boundary. A positive value indicates heat flux into the domain. For multiphase cases, when the bulk heat flux into both phases is set this option is labeled Wall Heat Flux instead of Heat Flux. When set on a per fluid basis, this option is labeled Heat Flux.

#### 2.7.5.4. Heat Transfer Coefficient and Wall Heat Transfer Coefficient

In this case, the heat flux at a wall boundary is implicitly specified using an external heat transfer coefficient, h c, and an outside or external boundary temperature, T o. This boundary condition can be used to model thermal resistance outside the computational domain, as in the diagram below:

Figure 2.4: Heat Transfer

The heat flux at the Heat Transfer Coefficient wall is calculated using:

| (2–9)

where T o is the specified outside or external boundary temperature. is the temperature at the wall (edge of the domain), which for turbulent flows is calculated from a surface energy balance and for laminar flows is the boundary temperature field calculated by the solver. The heat flux q w is the total heat flux from conduction and radiation when radiation is modeled. For details, see CFX-Solver Output File (Radiation Runs) in the CFX-Solver Manager User's Guide.

#### 2.7.5.5. ANSYS Multi-field

The wall temperature distribution or wall heat flow distribution is fixed according to the data received from the ANSYS Multi-field solver in regions that match ANSYS side, whereas adiabatic condition is imposed in regions that do not match ANSYS side. For more information about simulations involving Fluid Structure Interaction (FSI) and the ANSYS Multi-field, refer to Coupling CFX to an External Solver: ANSYS Multi-field Simulations and the Mechanical APDL Coupled-Field Analysis Guide.

#### 2.7.5.6. Results File Variables for Postprocessing

The results file contains several wall-only variables when the Thermal or Total Energy heat transfer models are active. Figure 2.5: Variables at a Wall Boundary depicts the variables that can be written at a wall boundary condition.

Figure 2.5: Variables at a Wall Boundary

#### 2.7.5.7. Wall Temperature (Tw )

This is the hybrid temperature field at a wall boundary condition. For Fixed Temperature walls, the wall temperature is the specified value . For all other heat transfer boundary conditions, the wall temperature is backed out from turbulent wall functions when running a turbulent flow model. For laminar flow modeling the wall temperature is just the local fluid temperature at the vertex adjacent to the wall.

When running the inhomogeneous heat transfer model, this variable is written per fluid. Similarly, for a porous solid, this variable is written for the solid phase as well.

#### 2.7.5.8. Wall Heat Flux and Heat Flux (qw )

`Wall Heat Flux` is the total heat flux into the domain, including convective and radiative contributions. There are also variables called `Wall Convective Heat Flux` and `Wall Radiative Heat Flux` for the separate convective and radiative contributions.

When running the inhomogeneous heat transfer model, this variable is written per fluid. Similarly, for a porous solid, this variable is written for the solid phase as well.

`Heat Flux` is also the total heat flux into the domain, including convective and radiative contributions. This variable is different from the `Wall Heat Flux` in several ways:

- There are no equivalent separate variables for the convective and radiative components.

- It can be plotted local to a specific boundary condition. `Wall Heat Flux` contains contributions from adjacent boundary conditions. For example, edge values of `Heat Flux` on a heat-transfer coefficient boundary are not affected by being adjacent to an adiabatic wall.

- It is computed on boundary vertices by the post processor directly from the energy flows written to the results file by the CFX-Solver, and the geometric area of the control volume face at the boundary vertex. This is sometimes advantageous over the `Wall Heat Flux` variable in that it eliminates the arithmetic averaging procedure used by the CFX-Solver to compute `Wall Heat Flux` at each boundary vertex from the faces adjacent to each vertex. For porous domains, the use of the geometric area introduces another difference to the `Wall Heat Flux` variable since the CFX-Solver uses the phasic area (geometric area * fluid/solid volume porosity) instead of the geometric area at the boundary face. `Heat Flux` should be used in preference to `Wall Heat Flux` when this is possible.

In the CFX-Solver the heat flux variables available for use in expressions are just `Wall Heat Flux` and `Wall Convective Heat Flux`. These variables are based on energy flows and so are equivalent to the variable `Heat Flux` and its convective component in the post-processor.

#### 2.7.5.9. Wall Heat Transfer Coefficient (hc ) and Wall Adjacent Temperature (Tnw )

These two variables are calculated as part of the convective heat transfer at a wall.

Laminar flow model:

- Wall Heat Transfer Coefficient, , is calculated by rearranging the expression for the convective heat flux in Equation 2–8 and setting the wall temperature as described above.

- Wall Adjacent Temperature, , is the average temperature in the element adjacent to the wall.

Turbulent flow model:

- Wall Heat Transfer Coefficient is given by the thermal wall functions. The theory of thermal wall functions can be found at Heat Flux in the Near-Wall Region in the CFX-Solver Theory Guide.

- For turbulent flow without viscous work active, the Wall Adjacent Temperature is the conservative (solved for) temperature in the control volume adjacent to the wall. On the other hand, if viscous work is active, Equation 2–267 in the CFX-Solver Theory Guide, can be rearranged as:

  | (2–10)

  Therefore, with viscous work active, the Wall Adjacent Temperature becomes:

  | (2–11)

For details of the treatment of heat transfer at a wall for turbulent flows, refer to the discussion of Heat Flux in the Near-Wall Region in the CFX-Solver Theory Guide.

#### 2.7.5.10. Wall External Heat Transfer Coefficient and Wall External Temperature

These are the specified values when running a heat transfer coefficient and external temperature boundary condition.

Additional information for multiphase cases is available. For details, see Wall Boundaries in Multiphase.

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