Simple Algorithm's for the Calculation of Heat Transport Problem in Plate

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.

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“…Using a method of finite volumes [1][2][3][4], we would find the finite-difference scheme of 1  N equations on a joint of layers in the form…”

Section: Methods Of Finite Volumes and Fdmmentioning

confidence: 99%

Simple Methods of Engineering Calculation for Solving Stationary 2 –D Heat Transfer Problems in Multilayer Media

Kalis

Kangro

2006

ETR

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“…We use the method of finite volumes [3] for approximation of the differential problem. We consider N + 1 grid points in the x− direction…”

Section: The Exact 3-points Finite-difference Schemementioning

confidence: 99%

Increasing of Accuracy for Engineering Calculation of Heat Transfer Problems in Two Layer Media

Kalis

Kangro

2005

Mathematical Modelling and Analysis

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In this paper we study the simple algorithms for modelling the heat transfer problem in two layer media. The initial model which is based on a partial differential equation is reduced to ordinary differential equations (ODEs). The increase of accuracy is shown if instead of first order ODE initial value problem ([4, 5]) the second order differential equations is taken. Such a procedure allows us to obtain a simple engineering algorithm for solving heat transfer equations in two layered domain of Cartesian, cylindrical (with axial symmetry) and spherical coordinates (with radial symmetry). In a stationary case the exact finite difference scheme is obtained. Šiame straipsnyje yra nagrinejami paprasti dvisluoksnes srities šilumos laidumo problemos modeliavimo algoritmai, keičiant diferencialines lygtis dalinemis išvestinemis i paprastas diferencialines lygtis. Parodoma, kad didesnio tikslumo pasiekimui, vietoje pirmos eiles paprastu diferencialiniu lygčiu pradinio uždavinio nagrinejamos antros eiles diferencialines lygtys. Ši proced ura leidžia gauti paprasta inžinerini dvisluoksies srities šilumos laidumo lygties sprendini stačiakampeje, cilindrineje (su ašiu simetrija) ir sferineje (su spinduline simetrija) koordinačiu sistemoje. Tiksli baigtiniu skirtumu schema buvo sudaryta stacionariam atvejui.

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“…. The exact vector finite -difference scheme for given vector -function F can be obtained in similar [2,5] In the non-stationary case ( )…”

Section: The Exact Vector 3 -Points Finite Diffe Rence Scheme In the mentioning

confidence: 99%

“…The calculation of heat transfer in a ground layer and in an atmosphere [10] is possible. It is possible to find out the algorithm for describing the temperature changes depending on time for surfaces on fibbers glasses at its heating without radiation [3] and with radiation [4,5], the algorithm for calculation of a temperature mode in a wall of a building with linings taking into account an opportunity of there heating [6,7]. Here it is very important to find simple algorithms for engineering -technical calculations, which are characterized by the sufficient accuracy of calculations, by the simplicity of calculations (with an opportunity of use of mathematical systems of a high level, for example, Mathematica, Maple, Matlab, etc.…”

Section: Introductionmentioning

confidence: 99%

Simple Methods of Engineering Calculations for Solving Transfer Problems of Multi – Substances in Horizontal Layer

Kalis

Kangro

2005

ETR

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We consider the simple algorithms in the modelling of the transfer problem of different substances (concentration, heat, moisture, and e. c.) in plate. The approximations of corresponding initial – boundary value problem of the system of the partial differential equations (PDE) is based on the finite volume method. This procedure allows one to reduce the 2-D transfer problem described by a PDE to initial value problem for a system of ordinary differential equations (ODE) of the first or second order. In the stationary case the exact finite – difference vector scheme is obtained.

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Simple Algorithm's for the Calculation of Heat Transport Problem in Plate

Cited by 3 publications

References 1 publication

Simple Methods of Engineering Calculation for Solving Stationary 2 –D Heat Transfer Problems in Multilayer Media

Simple Methods of Engineering Calculation for Solving Stationary 2 –D Heat Transfer Problems in Multilayer Media

Increasing of Accuracy for Engineering Calculation of Heat Transfer Problems in Two Layer Media

Simple Methods of Engineering Calculations for Solving Transfer Problems of Multi – Substances in Horizontal Layer

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