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8.5.4 Composition-Dependent Thermal Conductivity for Multicomponent Mixtures

If you are modeling a flow that includes more than one chemical species (multicomponent flow), you have the option to define a composition-dependent thermal conductivity. (Note that you can also define the thermal conductivity of the mixture as a constant value or a function of temperature, or using kinetic theory.)

To define a composition-dependent thermal conductivity for a mixture, follow these steps:

1.   For the mixture material, choose mass-weighted-mixing-law or, if you are using the ideal gas law, ideal-gas-mixing-law in the drop-down list to the right of Thermal Conductivity. If you have a user-defined function that you want to use to model the thermal conductivity, you can choose either the user-defined method or the user-defined-mixing-law method for the mixture material in the drop-down list.

The only difference between the user-defined-mixing-law and the user-defined option for specifying density, viscosity and thermal conductivity of mixture materials, is that with the user-defined-mixing-law option, the individual properties of the species materials can also be specified. (Note that only the constant, the polynomial methods and the user-defined methods are available.)

figure   

If you use ideal-gas-mixing-law for the thermal conductivity of a mixture, you must use ideal-gas-mixing-law or mass-weighted-mixing-law for viscosity, because these two viscosity specification methods are the only ones that allow specification of the component viscosities, which are used in the ideal gas law for thermal conductivity (Equation  8.5-6).

2.   Click Change/Create.

3.   Define the thermal conductivity for each of the fluid materials that comprise the mixture. You may define constant or (if applicable) temperature-dependent thermal conductivities for the individual species. You may also use kinetic theory for the individual thermal conductivities, if applicable.

4.   If you selected user-defined-mixing-law, define the thermal conductivity for each of the fluid materials that comprise the mixture. You may define constant, or (if applicable) temperature-dependent thermal conductivities, or user-defined thermal conductivities for the individual species. For more information on defining properties with user-defined functions, see the separate UDF Manual.

If you are using the ideal gas law, the solver will compute the mixture thermal conductivity based on kinetic theory as


 k = \sum_i \frac{X_i k_i}{\sum_j X_j \phi_{ij}} (8.5-6)

where


 \phi_{ij} = \frac{\left [ 1 + \left ( \frac{\mu_i}{\mu_j} \r... ...8 \left ( 1 + \frac{M_{w,i}}{M_{w,j}} \right ) \right ]^{1/2}} (8.5-7)

and $X_i$ is the mole fraction of species $i$.

For non-ideal gases, the mixture thermal conductivity is computed based on a simple mass fraction average of the pure species conductivities:


 k = \sum_i Y_i k_i (8.5-8)


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