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Research Papers: Thermal Systems

# A New Approach to Thermal Analysis of a Multilayered Cylindrical Structure With Imperfect Bonds and Internal Heat Source

[+] Author and Article Information
M. Bakhtiari

Department of Mechanical Engineering,
Iran University of Science and Technology,
Narmak, Tehran 16844, Iran
e-mail: m.bakhtiari@isme.ir

K. Daneshjou

Department of Mechanical Engineering,
Iran University of Science and Technology,
Narmak, Tehran 16844, Iran
e-mail: kjoo@iust.ac.ir

R. Alibakhshi

Department of Mechanical Engineering,
Iran University of Science and Technology,
Narmak, Tehran 16844, Iran
e-mail: r_alibakhshi@cmps2.iust.ac.ir

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 16, 2015; final manuscript received June 13, 2016; published online August 2, 2016. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 138(12), 122801 (Aug 02, 2016) (8 pages) Paper No: HT-15-1734; doi: 10.1115/1.4034038 History: Received November 16, 2015; Revised June 13, 2016

## Abstract

In the present research, a new and straightforward mathematical model, named augmented state-space method, is introduced to solve the heat conduction equation for a multilayered orthotropic hollow cylinder with bonding imperfection in the presence of heat source. Since such problems including heat source are inherently inhomogeneous and complex, augmented state-space method converts these inhomogeneous equations into homogeneous ones. The transient solution will be achieved by present method based on laminate approximation theory in the Laplace domain, and then the solutions obtained are retrieved into the time domain by applying the numerical Laplace transform inversion. All material properties can be considered to vary continuously within the cylinder along the radial direction with arbitrary grading pattern. Based on the proposed method, the solution of heat conduction problem can be also obtained for general boundary conditions which may be included various combinations of arbitrary temperature, flux, or convection. Due to lack of any data on the transient thermal analysis corresponding to problems with imperfect bonds in the cylindrical coordinate system $(r,θ),$ comparison is carried out with the available results for the three-layer semi-circular annular region with perfect bonds in the literature. Finally, the influence of orthotropy and interface imperfection on the distribution of the temperature field for three-layer hollow cylinder, in which the second layer is made of orthotropic functionally graded material (FGM), will be visualized.

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## Figures

Fig. 1

Mechanical model of jth layer of cylindrical structure

Fig. 2

Transient temperature distribution in radial direction at θ=π/2

Fig. 3

Hollow three-layer annular region example problem

Fig. 4

Contours of temperature distribution in r and θ directions: (a) η=0.4, (b) η=1, (c) η=2

Fig. 5

Temperature distribution in radial direction for different values of contact resistance: (a) R = 0.3 × 10−4, (b) R = 0.8 × 10−4, (c) R = 2 × 10−4, (d) R = 5 × 10−4

Fig. 6

Transient temperature distribution for different values of θ and η at r = 0.8

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