Analytical versus numerical calculations of physical problems. The benefits of its combination

Abstract

The disadvantage of the pure application of numerical approaches, however, is the fact, that the physicals laws behind are not so easy to visualize, the results art not so easy to generalize, and the storage of the information requires mostly an extensive amount of data. This paper would like to show at some examples the advantages of the combination of both methods. The key part of this approach is the calculation of the heat transfer by the Finite Volume Method (FVM) and the approximation of the calculated data by the so‐called “simplified equations”. These simplified equations were received by analytical solutions of the basic heat conduction equation. The required adaptation of the numerical results was done with properly adapted fitting algorithms on the basis of the elaborated analytical solutions, a process which was leading to an enormous reduction of data. As a result it became possible to describe the applied tasks by a few characteristic constants.

Another approach for an analytical solution with a numerical calculation process is the determination of the so‐called “properties of mixed magnitudes”. As an example this principle has been applied for the numerical calculation of electrical multi conductor containing cables. This process allowed the prediction of the thermal behavior of any cable harness with the required precision.

Darbe nagrinejamas analitinis metodas, temperatūros pasiskirstymo elektros laiduose bei ju pluoštuose uždaviniams spresti. Analitinis metodas yra pritaikytas šilumos laidumo koeficientams paskaičiuoti daugiasluoksneje medžiagoje – elektros laidu pluošte.Temperatūros pasiskirstymui atskirame elektros laidininke paskaičiuoti yra pritaikytas baigtiniu tūriu metodas. Turint tikslias atskiro laidininko temperatūros vertes, toliau laidu pluošto temperatūru vertes galima skaičiuoti analitiškai, ivedus proporcingumo koeficientus šilumos laidumo dydžiui rasti. Tokia procedūra duoda galimybe gauti efektyvu algoritma, skirta spresti šilumos pernešimo uždavinius atskiruose laiduose tiek ju pluoštuose su skirtingais skerspjūviais.

Key words:

• mathematical modeling
• heat transfer
• electrical cables