Mathematical Modelling and Analysis (Sep 2003)
Calculation of the heat transfer in cylindrical wires and electrical fuses by implicit finite volume method
Abstract
The usual wire rating problem is to compute the permissible conductor current so, that the maximum conductor temperature does not exceed a specified value. When numerical methods are used to determine wire rating, an iterative approach has to be used for this purpose. This is accomplished by specifying a certain conductor current and computing the corresponding conductor temperature. The electrical fuse rating problem is to calculate the melting behavior and to match thermo‐electrical characteristic of the wire and fuse in a way that the wire is protected by a fuse in wanted time and current range. Up to now the selection of wires is based on data, which were not particular optimized for automotive applications, where the wire length is typically short and low weight is important. The same, electrical fuses today are designed for a certain current value and do not protect the wire reliable in a wider current range. So, for automobile applications, fuses have to be re‐designed for every single wire to protect it against short circuit currents. Thus, the investigation of thermo‐electrical characteristics of both wires and fuses is necessary. This paper would like to show some examples how to calculate heat transfer in cylindrical wires (cable rating) and electrical fuses (melting behavior) by implicit Finite Volume Method (FVM) [12]. Such a procedure allows us to obtain simple algorithm to investigate thermo‐electrical behavior of electrical conductors. The key part of the paper is the calculation of the heat transfer by implicit Finite Volume Method. In non‐stationary state 1‐D heat conduction equation is solved for both cylindrical and orthogonal coordinates. In stationary state analytical solutions are presented. Šilumos pernešimo uždavinio sprendimas cilindriniuose elektros laiduose ir saugikliuose naudojant neišreikštinį baigtinių turių metodą Santrauka Šiame darbe yra nagrinejamas netiesinis šilumos pernešimo uždavinys siekiant apskaičiuoti temperatūros pasiskirstyma cilindriniuose elektros laiduose bei saugikliuose naudojant neišreikštini baigtiniu tūriu metoda. Žinant temepratūros pasiskirstyma, veliau galima efektyviau išnaudoti elektros laidu skerspjūvius bei patikimau apsaugoti pastaruosius nuo perkrovos sroviu. Ši problema (laidu skerspjūviu minimizavimas) yra labai aktuali ten kur elektros laidinku svoris turi būti minimizuotas (automobiliuose, laivuose ar lektuvuose). Pasiūlyta skaičiavimo metodika supaprastina elektros laidininku šiluminiu‐elektriniu charakteristiku apskaičiavima nestacionariu atveju. Pagrindinis demesys šiame darbe yra skiriamas neišreikštinio baigtiniu tūrio metodo pritaikymui šilumos laidumo uždaviniui spresti. Netiesines lygtys atsirandančios del netiesiniu kraštiniu salyu yra išsprestos naudojant Niutono iteraciju metoda. Stacionariame režime pateikti šilumos pernešimo lygties analitiniai sprendiniai apskaičiuoti temperatūros pasiskirstyma elektros laiduose bei saugikliuose. First Published Online: 14 Oct 2010
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