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Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions

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Title Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions
 
Creator SINGH, S
JAIN, PK
RIZWAN-UDDIN
 
Subject DIMENSIONAL COMPOSITE SLAB
TRANSIENT ANALYTICAL SOLUTION
TEMPERATURE MODES
ANALYTIC APPROACH
UNSTEADY
CYLINDER
 
Description The separation of variables (SOV) method has recently been applied to solve time-dependent heat conduction problem in a multilayer annulus. It is observed that the transverse (radial) eigenvalues for the solution in polar (r-theta) coordinate system are always real numbers (unlike in the case of similar multidimensional Cartesian problems where they may be imaginary) allowing one to obtain the solution analytically. However, the SOV method cannot be applied when the boundary conditions and/or the source terms are time-dependent, for example, in a nuclear fuel rod subjected to time-dependent boundaries or heat sources. In this paper, we present an alternative approach using the finite integral transform method to solve the asymmetric heat conduction problem in a multilayer annulus with time-dependent boundary conditions and/or heat sources. An eigenfunction expansion approach satisfying periodic boundary condition in the angular direction is used. After integral transformation and subsequent weighted summation over the radial layers, partial derivative with respect to r-variable is eliminated and, first order ordinary differential equations (ODEs) are formed for the transformed temperatures. Solutions of ODEs are then inverted to obtain the temperature distribution in each layer. Since the proposed solution requires the same eigenfunctions as those in the similar problem with time-independent sources and/or boundary conditions a problem solved using the SOV method-it is also "free" from imaginary eigenvalues. (C) 2010 Elsevier B.V. All rights reserved.
 
Publisher ELSEVIER SCIENCE SA
 
Date 2012-06-26T07:43:40Z
2012-06-26T07:43:40Z
2011
 
Type Article
 
Identifier NUCLEAR ENGINEERING AND DESIGN,241(1)144-154
0029-5493
http://dx.doi.org/10.1016/j.nucengdes.2010.10.010
http://dspace.library.iitb.ac.in/jspui/handle/100/14166
 
Language English