**:** ..
**:**
**:** 73
**:** ,
**:** 2018
**:** .. // . 73. .: , 2018. .184-194. URL: https://doi.org/10.25728/ubs.2018.73.9

** :** , , , ,

** (.):** heat equation, finite-difference method, Gaussian elimination, continuous furnace, heating section

**:** . , , 2- 3- . - .

** (.):** This paper describes modeling the process of slab heating in continuous furnaces. The process is described using mathematical model consisting of parabolical type partial derivative equation with second and third type boundary conditions. The finite-difference approximation is used to solve the problem. Further, the system of linear algebraic equations is solved by the Gauss method. Because of the complexity of the solution, the software "Modeling of the process of slabs heating in methodical furnaces" was developed. Programming in the integrated environment of Microsoft Visual Studio 2010 in the programming language C #. She gives an opportunity to obtain a numerical and graphical result. Thus, the paper presents a model for heating slabs in methodical seals, which yields an adequate result and can be applied by technologists in setting suitable operating conditions for the furnace.

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