User Wall Heat Flux Coefficient Specification

This node allows you to control the heat flux relationship at walls and interfaces.

The wall heat flux $\dot{q} ″$ is linearized as:

Figure 1. EQUATION_DISPLAY

\dot{q} ″ = A + B T_{c} + C T_{w} + D {(T_{w})}^{4}

(202)

where $T_{c}$ and $T_{w}$ are the cell and wall temperatures, respectively. A, B, C, and D are the net wall heat flux coefficients.

In the absence of radiation, the heat flux from the wall into the domain is given by $k \nabla T_{w}$ , where $\nabla T_{w}$ is the temperature gradient at the wall.

This is discretized as described by Eqn. (898):

$D_{f} = Γ_{f} \nabla ϕ_{f} \cdot a = Γ_{f} [(ϕ_{1} - ϕ_{0}) \overset{⇀}{α} \cdot a + \bar{\nabla ϕ} \cdot a - (\bar{\nabla ϕ} \cdot ds) \overset{⇀}{α} \cdot a]$

where:

$Γ_{f} = k$
$\nabla ϕ_{f} = \nabla T_{w}$
$\nabla ϕ_{0} = \nabla T_{c}$ (the temperature gradient in the near-wall cell)
$ϕ_{f} = T_{w}$
$ϕ_{0} = T_{c}$

Prior to taking the dot product with area a, this expression is:

$k \nabla T = k [(T_{w} - T_{c}) \overset{⇀}{α} + \nabla T_{c} - (\nabla T_{c} \cdot ds) \overset{⇀}{α}]$

which can be rearranged to:

$k \nabla T = k [\nabla T_{c} - (\nabla T_{c} \cdot ds) \overset{⇀}{α}] - k \overset{⇀}{α} T_{c} + k \overset{⇀}{α} T_{w} + 0 {T_{w}}^{4}$

so the internal heat flux coefficients are:

$A_{internal}$ = $k [\nabla T_{c} - (\nabla T_{c} \cdot ds) \overset{⇀}{α}]$
$B_{internal}$ = $- k \overset{⇀}{α}$
$C_{internal}$ = $k \overset{⇀}{α}$
$D_{internal}$ = 0

User Wall Heat Flux Coefficient Specification

The User Wall Heat Flux Coefficient Specification is available in both single phase and multiphase simulations. However, there are some differences between the single phase and multiphase implementations. For information on User Wall Heat Flux Coefficient Specification for multiphase simulations, see Phase Coupled Fluid Energy Model Reference.

Single Phase Implementation

For single phase simulations, the net wall heat flux coefficients A, B, C, and D are composed of the sum of internally calculated and user-defined coefficients:

Figure 2. EQUATION_DISPLAY

\begin{matrix} A = A_{internal} + A_{user} \\ B = B_{internal} + B_{user} \\ C = C_{internal} + C_{user} \\ D = D_{internal} + D_{user} \end{matrix}

(203)

The internal wall heat flux coefficients are evaluated first, in the usual manner according to the active physical processes (for example conduction, radiation and/or boiling). Then the net coefficients are evaluated by summing the internal and user-defined values.

Multiphase Implementation

In Multiphase Segregated Flow simulations, the net wall heat flux coefficients A, B, C, and D are simply the user-defined coefficients:

Figure 3. EQUATION_DISPLAY

\begin{matrix} A = A_{user} \\ B = B_{user} \\ C = C_{user} \\ D = D_{user} \end{matrix}

(204)

The internal coefficients can be included as necessary in the user-defined coefficients using the field functions:

$A_{internal}$ = $InternalWallHeatFluxCoefficientA ("Internal Wall Heat Flux Coefficient, A")

$B_{internal}$ = $InternalWallHeatFluxCoefficientB ("Internal Wall Heat Flux Coefficient, B")

$C_{internal}$ = $InternalWallHeatFluxCoefficientC ("Internal Wall Heat Flux Coefficient, C")

$D_{internal}$ = $InternalWallHeatFluxCoefficientD ("Internal Wall Heat Flux Coefficient, D")

So, for example, you can completely replace net coefficient A with some function f by defining:

Figure 4. EQUATION_DISPLAY

\begin{matrix} A_{user} = f - A_{internal} \end{matrix}

(205)

such that the net coefficient becomes:

Figure 5. EQUATION_DISPLAY

\begin{matrix} A = A_{internal} + (f - A_{internal}) = f \end{matrix}

(206)

The resultant net wall heat flux coefficients are available using the field functions:

A = $NetWallHeatFluxCoefficientA ("Net Wall Heat Flux Coefficient, A")

B = $NetWallHeatFluxCoefficientB ("Net Wall Heat Flux Coefficient, B")

C = $NetWallHeatFluxCoefficientC ("Net Wall Heat Flux Coefficient, C")

D = $NetWallHeatFluxCoefficientD ("Net Wall Heat Flux Coefficient, D")

The user-defined heat flux coefficients do not affect the amount of heat that enters the domain. These coefficients determine how much of the heat flux goes towards increasing the wall temperature, and how much goes towards increasing the cell temperature.

User-defined wall heat flux coefficients can be enabled on Wall or Contact Interface boundaries by setting the Method property of this node.

User Wall Heat Flux Coefficient Specification Properties


Method	Controls whether to specify the heat flux relationship.
	None	Leaves off this feature. The User Wall Heat Flux Coefficient is not specified.
	Specified	Activates this feature. This option adds the following nodes to the Physics Values node, which must be entered as scalar profiles: User Wall Heat Flux Coefficient, A User Wall Heat Flux Coefficient, B User Wall Heat Flux Coefficient, C User Wall Heat Flux Coefficient, D The user specified coefficients are added to the internally calculated net coefficients as given by Eqn. (203).
	Specified Net	Sets the net boundary heat flux coefficients equal to the user specified heat flux coefficients as given by Eqn. (204). This method is available in Multiphase Segregated Flow simulations only.