Abstract
Non-equilibrium energy transfer takes place for thin films when thermal disturbance is introduced. In this case, phonon transport inside the film governs the heat transport and temperature distribution in the film. In the present study an attempt is made to formulate and illustrate the phonon transfer in micro-scale silicon film of various shapes incorporating the non-orthogonal coordinate system. Successful application of the discrete-ordinates method to the solution of the equation for phonon radiative transport in non-orthogonal coordinates requires the application of various numerical techniques connected to the finite-difference method. The numerical solution of the equation for phonon transfer in non-orthogonal coordinate is introduced via adapting the discrete ordinate method. Phonon intensity distribution in the thin film is presented in terms of equivalent equilibrium temperature. It is found that film shape has significant effect on equivalent equilibrium temperature distribution inside the film. The validation study demonstrates that the code developed solving the equation for phonon transport is also applicable to the phonon transport in non-orthogonal coordinate system.
Highlights
Non-equilibrium energy transfer takes place when the size of the heat transferring becomes comparable to the mean free path of the solid material
An attempt is made to illustrate such application of equation for phonon transport via solving various problems related to the phonon transfer in the micro-scale two-dimensional silicon film of various shapes
It is demonstrated the successful application of the discrete-ordinates method to the solution of the equation for radiative phonon transport in non-orthogonal coordinates
Summary
Non-equilibrium energy transfer takes place when the size of the heat transferring becomes comparable to the mean free path of the solid material. The phenomenon of radiative transfer occurs in many physical situations such as the radiative heat transfer between surfaces through a participating media, conduction heat transfer through diffusive-ballistic phonons in thin films, neutron transport etc In all these cases, the transport equations are very similar. In the author knowledge the RTE has not been solved by means of the DOM in non-orthogonal coordinates and the present study is an attempt to illustrate such an application by solving various problems related to the phonon transfer in micro-scale silicon film of various shapes. Successful application of the discrete-ordinates method to the solution of the equation for radiative transport in non-orthogonal coordinates, which requires the application of various numerical techniques connected to the finite-difference method. The derivatives of the polar and azimuthal angles are defined as [16], BJ − DG BC − AD
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