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RESEARCH PAPERS: Conduction

# Nonstationary Heat Conduction in Complex-Shape Laminated Plates

[+] Author and Article Information
Alexander N. Shupikov

A.N. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, 2/10 Dm. Pozharsky Street, Kharkov 61046, Ukraineshupikov@ipmach.kharkov.ua

Natalia V. Smetankina, Yevgeny V. Svet

A.N. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, 2/10 Dm. Pozharsky Street, Kharkov 61046, Ukraine

J. Heat Transfer 129(3), 335-341 (Jun 19, 2006) (7 pages) doi:10.1115/1.2427073 History: Received September 07, 2005; Revised June 19, 2006

## Abstract

Based on the immersion method, an analytical solution has been obtained for the problem of nonstationary heat conduction in laminated plates of complex plan shape when they are heated with interlayer film heat sources. The temperature distribution over the thickness of each layer is represented in the form of an expansion in a system of the orthonormal Legendre polynomials and, in the plate plane, it is represented as trigonometric series expansions. Temperature fields were investigated in a five-layer plate for conditions of convective heat exchange with the environment. The method suggested can be applied for designing heating systems and determining temperature stresses in laminated glazing for different vehicles

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## Figures

Figure 1

Laminated plate

Figure 2

Auxiliary plate

Figure 3

Plan shape of plate

Figure 4

Temperature distribution over plate thickness 1—1s, 2—10s, 3—102s, 4—103s, 5—105s, 6 — solution of stationary problem, 7 — solution obtained by FEM at the point of time τ=102s, and 8 — solution obtained by FEM at the point of time τ=104s

Figure 5

Temperature distribution on surface Ωt at the point of time τ=102s: 1—+14.3°C, 2—+14.2°C, 3—+12°C, 4—0°C, 5—−13°C, 6—−13.5°C, and 7—−14.1°C

Figure 6

Temperature distribution on surface Ω1 (surface with heat source) at the point of time τ=102s: 1—+23°C, 2—+22°C, 3—0°C, 4—−12°C, 5—−12.7°C, and 6—−12.9°C

Figure 7

Temperature distribution on surface Ωb at the point of time τ=102s: 1—+7.1°C, 2—+6°C, 3—+5.5°C, 4—+5°C, and 5—+4.1°C

Figure 8

Temperature distribution on surface Ωt at the point of time τ=104s: 1—+22°C, 2—+21°C, 3—0°C, 4—−10°C, 5—−14°C, 6—−15.2°C, and 7—−15.3°C

Figure 9

Temperature distribution on surface Ω1 (surface with heat source) at the point of time τ=104s: 1—+32.4°C, 2—+31°C, 3—0°C, 4—−13°C, 5—−13.2°C, 6—−14°C, and 7—−14.1°C

Figure 10

Temperature distribution on surface Ωb at the point of time τ=104s: 1—+25.4°C, 2—+22°C, 3—+9°C, 4—+5°C, and 5—+4°C

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