Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

In the present study nonstationary mathematical model of single-crystal wafer of molecular $beta$-diketonate sublimation is constructed. It is supposed that the wafer is on the metal holder, which is situated on the bottom wall of the plane slotted channel. An inert heated gas with given constant velocity and temperature flows along the channel. $beta$-diketonate wafer is heated due to convective heat emission of gas, radiation from upper channel wall and heat emission of heated holder. As a result a wafer material sublimation, vaporization and vapor transfer by inert gas (argon) are happened.

On these assumptions the problem is reduced to solving nonstationary heat conduction equations for the $beta$-diketonate wafer and holder with boundary conditions of convective heat and mass transfer taking into account kinetics of vaporization at sublimation surface, flow mating condition on the wafer-holder interface and on the bottom surface of the holder, and initial temperature distribution in the system under consideration.

In concordance with physical and mathematical models on the basis of collocation and least-squares (CLS) method the numerical algorithm is developed for solving the problem of heat and mass transfer in process of $beta$-diketonate sublimation. In contrast to previously developed variants of CLS method the proposed algorithm is intended for solving nonstationary PDEs. At every discrete time level in each cell in space the solution is a linear combination of basic functions which belong to the class of second order polynomials. Time derivative is approximated with first order. In the model considered the domain with motile exterior bound, where the sublimation is happened, is divided into two subdomains: holder and $beta$-diketonate wafer. The heat conduction equations with different thermal diffusivity coeffitients corresponding to materials of holder and wafer are solved in these subdomains by CLS method. The equation of bound motion is integrated to calculate the vapored mass of $beta$-diketonate since the velocity of bound motion is determined through the process parameters at each time step. Thereby the bound position is determined explicitly at all time steps.

This study was performed under financial support of RFBR and SB RAS integration project No 2000-60.2.

Note. Abstracts are published in author's edition

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