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8.6.1 Isotropic Diffusion

For isotropic diffusion, $\Gamma$ in Equation  8.6-1 is equal to a scalar $\Gamma$ times the identity matrix and the equation reduces to


 \nabla \cdot (\Gamma \nabla \phi^k ) (8.6-2)

You can specify isotropic diffusivity as a single user-defined function that applies to all UDS transport equations. For this case, choose user-defined from the drop-down list for UDS Diffusivity in the Materials panel (Figure  8.6.1).

Define $\rightarrow$ Materials...

Figure 8.6.1: The Materials Panel
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If you have previously loaded a compiled UDF library or have interpreted the UDF, then the User-Defined Functions panel will open, allowing you to hook the DEFINE_DIFFUSIVITY UDF to FLUENT. If no functions have been loaded, you will get an error message. Refer to the separate UDF Manual for details on user-defined functions. Isotropic diffusion coefficients can also be defined on a per-scalar basis by selecting defined-per-uds from the drop-down list for UDS Diffusivity in the Materials panel (Figure  8.6.2). This will open the UDS Diffusion Coefficients panel (Figure  8.6.3).

Figure 8.6.2: The Materials Panel
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Figure 8.6.3: The UDS Diffusion Coefficients Panel
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In the UDS Diffusion Coefficients panel, select a scalar equation (e.g., uds-0) and then choose a constant, polynomial, or user-defined function from the Coefficient drop-down list. (For the default fluid (air), the constant diffusion coefficient is $1$ kg/m-s.) If you choose polynomial, the Polynomial Profile panel will open and you can specify your coefficients as a function of temperature. See Section  8.2.1 for details.

When you select the user-defined option, the User-Defined Functions panel will open allowing you to hook a DEFINE_DIFFUSIVITY UDF only if you have previously loaded a compiled UDF library or interpreted a UDF. Otherwise, you will get an error message. Refer to the separate UDF Manual for details on user-defined functions.


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