Increasing of accuracy for engineering calculation of heat transfer problems in two layer media
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 v...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vilnius Gediminas Technical University
2005-06-01
|
| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/9672 |
| _version_ | 1818893338927955968 |
|---|---|
| author | H. Kalis I. Kangro |
| author_facet | H. Kalis I. Kangro |
| author_sort | H. Kalis |
| collection | DOAJ |
| description | 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.
First Published Online: 14 Oct 2010 |
| first_indexed | 2024-12-19T18:11:01Z |
| format | Article |
| id | doaj.art-c22a27c3274746b58aec3b2a3230b1de |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T18:11:01Z |
| publishDate | 2005-06-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-c22a27c3274746b58aec3b2a3230b1de2022-12-21T20:11:19ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102005-06-0110210.3846/13926292.2005.9637280Increasing of accuracy for engineering calculation of heat transfer problems in two layer mediaH. Kalis0I. Kangro1Institute of Mathematics , Latvian Academy of Sciences and University of Latvia , Akadēmijas laukums 1, Riga, LV‐1524, LatviaDepartament of engineering science , Rēzekne Higher Education Institution , Atbriivosanas aleja 90, Rezekne, LV‐4601, LatvijaIn 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. First Published Online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/9672heat transferlayered medianumerical methodsmathematical modelling |
| spellingShingle | H. Kalis I. Kangro Increasing of accuracy for engineering calculation of heat transfer problems in two layer media Mathematical Modelling and Analysis heat transfer layered media numerical methods mathematical modelling |
| title | Increasing of accuracy for engineering calculation of heat transfer problems in two layer media |
| title_full | Increasing of accuracy for engineering calculation of heat transfer problems in two layer media |
| title_fullStr | Increasing of accuracy for engineering calculation of heat transfer problems in two layer media |
| title_full_unstemmed | Increasing of accuracy for engineering calculation of heat transfer problems in two layer media |
| title_short | Increasing of accuracy for engineering calculation of heat transfer problems in two layer media |
| title_sort | increasing of accuracy for engineering calculation of heat transfer problems in two layer media |
| topic | heat transfer layered media numerical methods mathematical modelling |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/9672 |
| work_keys_str_mv | AT hkalis increasingofaccuracyforengineeringcalculationofheattransferproblemsintwolayermedia AT ikangro increasingofaccuracyforengineeringcalculationofheattransferproblemsintwolayermedia |