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

Suneet Singh, Prashant K. Jain, Rizwan-Uddin

Research output: Contribution to journalArticle

Abstract

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-θ) 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.

Original languageEnglish (US)
Pages (from-to)144-154
Number of pages11
JournalNuclear Engineering and Design
Volume241
Issue number1
DOIs
StatePublished - Jan 2011

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Cholestenones
Boundary conditions
boundary conditions
boundary condition
Conjunctival Diseases
Dysostoses
Micelles
Heat conduction
Multilayers
integral transformations
annuli
conductive heat transfer
Interceptive Orthodontics
Middle Ear
Eigenvalues and eigenfunctions
Hot Temperature
Ordinary differential equations
heat sources
eigenvectors
differential equations

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Mechanical Engineering
  • Safety, Risk, Reliability and Quality
  • Materials Science(all)
  • Nuclear and High Energy Physics
  • Waste Management and Disposal

Cite this

Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions. / Singh, Suneet; Jain, Prashant K.; Rizwan-Uddin.

In: Nuclear Engineering and Design, Vol. 241, No. 1, 01.2011, p. 144-154.

Research output: Contribution to journalArticle

Singh, Suneet; Jain, Prashant K.; Rizwan-Uddin / Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions.

In: Nuclear Engineering and Design, Vol. 241, No. 1, 01.2011, p. 144-154.

Research output: Contribution to journalArticle

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