## 7.13.4 Heat Transfer Calculations at Wall Boundaries

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

 (7.13-8)

where

 = 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

 (7.13-9)

where

 = 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

 (7.13-10)

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

 (7.13-11)

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

 (7.13-12)

where

 = 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.

When the external radiation boundary condition is used in FLUENT, the heat flux to the wall is computed as

 (7.13-13)

where

 = emissivity of the external wall surface defined by you = Stefan-Boltzmann constant = 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

 (7.13-14)

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:

 (7.13-15)

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.

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