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The Onedimensional Heat Conduction
Ena Pribisalić (2017)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Computer Science Research Group
Cite this document

Pribisalić, E. (2017). Jednodimenzionalno provođenje topline (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:589094

Pribisalić, Ena. "Jednodimenzionalno provođenje topline." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:589094

Pribisalić, Ena. "Jednodimenzionalno provođenje topline." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:589094

Pribisalić, E. (2017). 'Jednodimenzionalno provođenje topline', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 19 October 2019, https://urn.nsk.hr/urn:nbn:hr:126:589094

Pribisalić E. Jednodimenzionalno provođenje topline [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2019 October 19] Available at: https://urn.nsk.hr/urn:nbn:hr:126:589094

E. Pribisalić, "Jednodimenzionalno provođenje topline", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:589094

Metadata
TitleJednodimenzionalno provođenje topline
Title (english)The Onedimensional Heat Conduction
AuthorEna Pribisalić
MentorSnježana Majstorović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics)
(Computer Science Research Group)
Osijek
Defense date and country2017-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
Abstract
U ovome radu upoznat ćemo se s jednadžbom jednodimenzionalnog provodenja topline, te predstaviti metode pronalaska rješenja u ovisnosti o različitim rubnim uvjetima koji su pritom zadani. Najprije ćemo se upoznati s parcijalnim diferencijalnim jednadžbama, konkretno: linearnim jednadžbama drugog reda. Nakon njihove osnovne klasifikacije, izvest ćemo kanonski oblik paraboličkih jednadžbi kojima pripada upravo jednadžba provođenja topline. Zatim ćemo navesti i detaljno objasniti početne i rubne uvjete koji su sastavni dio problema provodenja topline. Precizno ćemo definirati pojam Fourierovog reda, navesti njegova svojstva, te iskazati osnovne tvrdnje o njegovoj konvergenciji. Taj dio matematičke teorije neophodan je za razumijevanje postupka rješavanja jednadžbe provođenja. U glavnom dijelu rada napravit ćemo izvod jednadžbe jednodimenzionalnog provodenja topline koji se bazira na nekoliko temeljnih fizikalnih zakona. Detaljno ćemo analizirati homogenu i nehomogenu jednadžbu provođenja, te pokazati kako se metodom kompleksifikacije mogu rješavati neki tipovi homogenih jednadžbi. Navest ćemo i nekoliko zanimljivih primjera te ih ilustirati sličicama.
Abstract (english)
In this paper we will introduce the one-dimensional heat conduction problem and present methods for searching a solution, based on different boundary conditions which are imposed on the corresponding eqaution. First, we will get acquainted with partial differential equations, specifically: second order linear equations. After we do the proper classification, the canonical form for parabolic type of equation will be derived, since this is the type of equation that a heat equation belongs to. In the following we will specify and explain in details the initial and boundary conditions which are unavoidable parts of the heat conduction problem. We will define the Fourier series, list their main properties and state several basic theorems regarding their convergence. This part of mathematical theory is essential for understanding the solving process for the heat conduction problem. In the main part of this paper we will derive the heat equation by using some basic physical laws. Then, we will thoroughly analyse the homogeneous and nonhomogeneous equation, show the way in which we can complexify some types of homogeneous problems and give some examples along with their illustrations.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:589094
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2017-10-27 11:03:46