Temperature Boundary Conditions
When a fixed temperature condition is applied at the wall, the heat flux to the wall from a fluid cell is computed as
|=||fluid-side local heat transfer coefficient|
|=||wall surface temperature|
|=||local fluid temperature|
|=||radiative heat flux|
Note that the fluid-side heat transfer coefficient is computed based on the local flow-field conditions (e.g., turbulence level, temperature, and velocity profiles), as described by Equations 7.13-15 and 12.10-5.
Heat transfer to the wall boundary from a solid cell is computed as
|=||thermal conductivity of the solid|
|=||local solid temperature|
|=||distance between wall surface and the solid cell center|
Heat Flux Boundary Conditions
When you define a heat flux boundary condition at a wall, you specify the heat flux at the wall surface. FLUENT uses Equation 7.13-8 and your input of heat flux to determine the wall surface temperature adjacent to a fluid cell as
where, as noted above, the fluid-side heat transfer coefficient is computed based on the local flow-field conditions. When the wall borders a solid region, the wall surface temperature is computed as
Convective Heat Transfer Boundary Conditions
When you specify a convective heat transfer coefficient boundary condition at a wall, FLUENT uses your inputs of the external heat transfer coefficient and external heat sink temperature to compute the heat flux to the wall as
|=||external heat transfer coefficient defined by you|
|=||external heat-sink temperature defined by you|
|=||radiative heat flux|
Equation 7.13-12 assumes a wall of zero thickness.
External Radiation Boundary Conditions
When the external radiation boundary condition is used in FLUENT, the heat flux to the wall is computed as
|=||emissivity of the external wall surface defined by you|
|=||surface temperature of the wall|
|=||temperature of the radiation source or sink on the exterior|
|of the domain, defined by you|
|=||radiative heat flux to the wall from within the domain|
Equation 7.13-13 assumes a wall of zero thickness.
Combined External Convection and Radiation Boundary Conditions
When you choose the combined external heat transfer condition , the heat flux to the wall is computed as
where the variables are as defined above. Equation 7.13-14 assumes a wall of zero thickness.
Calculation of the Fluid-Side Heat Transfer Coefficient
In laminar flows, the fluid side heat transfer at walls is computed using Fourier's law applied at the walls. FLUENT uses its discrete form:
where is the local coordinate normal to the wall.
For turbulent flows, FLUENT uses the law-of-the-wall for temperature derived using the analogy between heat and momentum transfer [ 197]. See Section 12.10.2 for details.