Thin Film
Thin films of fluid can be considered as boundaries of thickness significantly smaller than the typical lengths of the overall model.
General Formulation
With this formulation, heat transfer is modeled in the whole film, including its thickness. An additional 1D segmented line represents the thickness in the thin film. In this extra dimension, the governing equation is derived from Equation 4-60 to give:
(4-80)
(4-81)
where Ts is an auxiliary dependent variable defined on the product space. The remaining quantities are recalled below:
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ρ is the density (SI unit: kg/m3)
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Cp is the heat capacity (SI unit: J/(kg·K))
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k is the thermal conductivity (SI unit: W/(m·K))
•
Qf is the heat source applied to the film (SI unit: W/m3)
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df is the film thickness (SI unit: m)
The constraint T = Ts is specified on each side of the extra dimension to connect T to Ts.
See Thin Film (Heat Transfer Interface) and Fluid (Heat Transfer in Shells Interface) with Thin film model set as General for more information about the boundary feature solving Equation 4-80 and Equation 4-81.
Thermally Thin Approximation
The thermally thin approximation is derived from Equation 4-63 to Equation 4-65. Inside the thin layer, the heat equation becomes:
(4-82)
(4-83)
where df is the film thickness (SI unit: m). The heat source Qf is a density distributed in the layer while q0 is the received out-of-plane heat flux.
In 2D, Equation 4-73 and Equation 4-74 have an additional factor, dz, to account for the out-of-plane thickness.
From the point of view of the domain, the following heat source, derived from Equation 4-65, is received from the layer:
(4-84)
See Thin Film (Heat Transfer Interface) and Fluid (Heat Transfer in Shells Interface) with Thin film model set as Thermally thin approximation for more information about the boundary feature solving Equation 4-82. See The Heat Transfer in Films Interface for more information about the physics interface solving Equation 4-84.