### SIMPLE METHODS OF ENGINEERING CALCULATION FOR SOLVING STATIONARY 2 –D HEAT TRANSFER PROBLEMS IN MULTILAYER MEDIA

H. Kalis, I. Kangro

#### Abstract

There are well-known different numerical methods for solving the boundary value problems for partial differential equations. Some of them are: finite difference method (FDM), finite element method (FEM), boundary element methods (BEM), and others. In the given work two methods FDM and BEM for the mathematical model of stationary distribution of heat in the multilayer media are considered. These methods were used for the reduction of the two-dimensional heat transfer problem described by a partial differential equation to a boundary – value problem for a system of ordinary differential equations. (ODEs). Such a procedure allows obtaining simple engineering algorithms for solving heat transfer equation in mulyilayer domain. In the case of three layers the system of ODEs is possible for solving analytically.

#### Keywords

Poisson’s type partial differential equation; two dimensional heat transfer problem

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#### References

H.Kalis Effective finite-difference scheme for solving some heat transfer problems with convection in multilayer media. In: International Journal of Heat and Mass Transfer, 2000, vol.43, 4467-4474.

H.Kalis and I.Kangro. Simple algorithms for the calculation of heat transport problem in plate. Mathematical modelling and analysis, Vilnius “Technika”,2001, vol. 6, N 7, 85 –95.

H.Kalis Finite-difference scheme for solving of some heat transfer problems with convection in multilayer media. In: Proc. Of the 2-nd int. conference “Finite-difference methods: theory and applications’’, vol.2, Minsk 1998, Belarus, 50-55.

H.Kalis, I.Kangro. Simple methods of engineering calculation for solving heat transfer problems. In: Mathematical Modelling and Analysis, Vilnius “Technika”, 2003, vol. 8, N 2.

DOI: https://doi.org/10.17770/etr2003vol1.1991

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