IJPAM: Volume 106, No. 4 (2016)

SOLUTION OF HEAT CONDUCTION PROBLEM WITH
DISCONTINUOUS BOUNDARY CONDITIONS IN
NONHOMOGENOUS MOVING CYLINDER USING MAPLE

G.R. Gasimov$^1$, Z.A. Abusutash$^2$
$^1$Faculty of Applied Mathematics
Baku State University
23, Zahid Khalil, Baku, AZERBAIJAN
$^{2}$Department of Mathematics
Faculty of Science
Damietta University
New Damietta, 34517, EGYPT


Abstract. This paper presents a heat conduction problem with discontinuous boundary conditions in nonhomogeneous moving entire cylinder, which moves on the axis oz with any movement law $z=S(t)$. The temperature field is determined in the cylindrical coordinates system linked with motionless cylinder as a system in a single movement. Using the method inversion of the unit function $\eta(t-S^{-1}(z))$, method a sequence of integral transformations like Fourier transform with respect to $z$, Hankel transform with respect to $r$, Bessel functions theory,general integral transforms theory, a solution in the form of the series is obtained.

And in order to illustrate theoretical results in this paper,we wrote special programming in Maple program and for a special cases, where numerical solutions were presented with explained graphics and discussed.

Received: December 11, 2015

AMS Subject Classification: 35K05, 35A22, 33C10, 44A05, 42A38, 68N15

Key Words and Phrases: heat conduction problem, Maple program, general integral transforms theory, sequential integral transformation method,bessel functions theory

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DOI: 10.12732/ijpam.v106i4.14 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 4
Pages: 1127 - 1150


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).