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Research Papers: Forced Convection

Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions

[+] Author and Article Information
A. Amiri Delouei

Assistant Professor
Mechanical Engineering Department,
University of Bojnord,
Bojnord 9453155111, Iran
e-mail: a.a.delouei@gmail.com

M. Norouzi

Assistant Professor
Mechanical Engineering Department,
University of Shahrood,
Shahrood 3619995161, Iran
e-mail: mnorouzi@shahroodut.ac.ir

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 25, 2014; final manuscript received March 28, 2015; published online June 2, 2015. Assoc. Editor: Peter Vadasz.

J. Heat Transfer 137(10), 101701 (Oct 01, 2015) (8 pages) Paper No: HT-14-1346; doi: 10.1115/1.4030348 History: Received May 25, 2014; Revised March 28, 2015; Online June 02, 2015

The current study presents an exact analytical solution for unsteady conductive heat transfer in multilayer spherical fiber-reinforced composite laminates. The orthotropic heat conduction equation in spherical coordinate is introduced. The most generalized linear boundary conditions consisting of the conduction, convection, and radiation heat transfer is considered both inside and outside of spherical laminate. The fibers' angle and composite material in each lamina can be changed. Laplace transformation is employed to change the domain of the solutions from time into the frequency. In the frequency domain, the separation of variable method is used and the set of equations related to the coefficients of Fourier–Legendre series is solved. Meromorphic function technique is utilized to determine the complex inverse Laplace transformation. Two functional cases are presented to investigate the capability of current solution for solving the industrial unsteady problems in different arrangements of multilayer spherical laminates.

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Figures

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Fig. 1

Schematic of fibers' direction in a multilayer spherical laminate

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Fig. 2

Arrangement of layers in a spherical laminate

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Fig. 3

Steady-state temperature distribution of an isotropic spherical lamina in radial direction for Tout = 500 K,rnl = 1 m, and θ = 45 deg

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Fig. 4

Geometry and thermal boundary conditions of the five-layer spherical composite (ro = 5 m and thickness = 0.5 m)

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Fig. 5

History of the maximum temperature of laminate in (a) different fibers' arrangements and (b) different composite material's arrangements for case 1

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Fig. 6

History of the mean temperature of laminate in (a) different fibers' arrangements and (b) different composite material's arrangements for case 2

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Fig. 7

Temperature (K) distribution in a five-layer spherical laminate at different times for (a) case 1 and (b) case 2. Three-dimensional contours are plotted in radius r=(ro+rnl)/2.

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Fig. 8

Isotherms (K) in the five-layer spherical laminate in r and θ directions at different times for (a) case 1 and (b) case 2

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Fig. 9

Variation of (a) maximum temperature of case 1 and (b) mean temperature of case 2 respect to fibers' angle at different times

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