Simple methods of engineering calculation for solving heat transfer problems

• Main Authors: H. Kalis, I. Kangro
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2003-03-01
• Series: Mathematical Modelling and Analysis
• Subjects: transfer problems; initial‐boundary value problems; partial differential equations; finite difference method; finite element method
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/9760

There are well‐known numerical methods for solving the initial‐boundary value problems for partial differential equations. We mention only some of them: finite difference method (FDM), finite element method (FEM), boundary element method (BEM), Galerkin type methods and others. In the given work FDM and BEM are considered for determination a distribution of heat in the multilayer media. These methods were used for the reduction of the 1D heat transfer problem described by a partial differential equation to an initial‐value problem for a system of ordinary differential equations (ODEs). Such a procedure allows us to obtain a simple engineering algorithm for solving heat transfer equation in multilayered domain. In a stationary case the exact finite difference scheme is obtained. An inverse problem is also solved. The heat transfer coefficients are found and temperatures in the interior layers depending on the given temperatures inside and outside of a domain are obtained. Paprastieji inžinerinio skaičiaimo metodai šilumos laidumo uždaviniams spręsti Santrauka Darbe nagrinejami du ‐ baigtiniu skirtumu ir kraštiniu elementu ‐ metodai šilumos pasiskirstymo daugiasluoksneje aplinkoje uždaviniams spresti. Šiais metodais dvieju kintamuju uždavinys dalinemis išvestinemis pakeičiamas pradiniu ‐ kraštiniu paprastuju diferencialiniu lygčiu sistemos uždaviniu. Tokia procedūra suteikia galimybe gauti paprastus inžinerinius algoritmus, skirtus spresti šilumos laidumo lygti daugiasluoksneje srityje. Stacionariu atveju imanoma nustatyti tikslu skirtumu schemos sprendini. Darbe nagrinetas atvirkščias uždavinys. Skaitinio eksperimento metu gauti šilumos laidumo koeficientai ir temperatūros vidiniuose sluoksniuose priklausomai nuo išoriniu plokštes duomenu. First Published Online: 14 Oct 2010