Abstract
The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM) to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.
Highlights
The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces
We show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient
The obtained equation is analogous to the radiative transfer equation (RTE) with the approximation of local thermodynamic equilibrium, which was employed to study the phonon transport inside solids.[9]
Summary
Using G by essentially represents the temperature.[5] The dashed line denotes the diffusive incident energy flow GD while the dash-dot line corresponds to the nonlocal source GB. Compared to GD, GB contributes more to the total incident energy flow Gt, which is indicated using the dotted line. The profile of Gt suggests that the temperature of the wall and the adjacent thin film is not necessarily to be continuous This is verified by the linearized solution shown in the thin solid line calculated from. In this case, of 10−4, as indicated in the inset
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