Analytic solutions for heat conduction in functionally graded circular hollow cylinders with time-dependent boundary conditions

Sen-Yung Lee, Chih Cheng Huang

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

An analytic solution method, without integral transformation, is developed to find the exact solutions for transient heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions. By introducing suitable shifting functions, the governing second-order regular singular differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions. The exact solution of the system with thermal conductivity and specific heat in power functions with different orders is developed. Finally, limiting studies and numerical analyses are given to illustrate the efficiency and the accuracy of the analysis.

Original languageEnglish
Article number816385
JournalMathematical Problems in Engineering
Volume2013
DOIs
Publication statusPublished - 2013 Sep 3

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Circular Cylinder
Circular cylinders
Heat Conduction
Analytic Solution
Heat conduction
Boundary conditions
Differential equations
Exact Solution
Transient Heat Conduction
Singular Differential Equations
Integral Transformation
Power Function
Specific Heat
Thermal Conductivity
Variable Coefficients
Specific heat
Thermal conductivity
Limiting
Differential equation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

Cite this

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abstract = "An analytic solution method, without integral transformation, is developed to find the exact solutions for transient heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions. By introducing suitable shifting functions, the governing second-order regular singular differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions. The exact solution of the system with thermal conductivity and specific heat in power functions with different orders is developed. Finally, limiting studies and numerical analyses are given to illustrate the efficiency and the accuracy of the analysis.",
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AB - An analytic solution method, without integral transformation, is developed to find the exact solutions for transient heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions. By introducing suitable shifting functions, the governing second-order regular singular differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions. The exact solution of the system with thermal conductivity and specific heat in power functions with different orders is developed. Finally, limiting studies and numerical analyses are given to illustrate the efficiency and the accuracy of the analysis.

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