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Research Papers: Conduction

# Heat Transfer in Thin Multilayered Plates—Part I: A New Approach

[+] Author and Article Information
T. K. Papathanasiou1

School of Applied Mathematics and Physical Sciences, Department of Theoretical and Applied Mechanics, National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou Campus, 15773 Athens, Greecethpapath@lycos.com

S. I. Markolefas

School of Applied Mathematics and Physical Sciences, Department of Theoretical and Applied Mechanics, National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou Campus, 15773 Athens, Greecemarkos34@gmail.com

S. P. Filopoulos

School of Applied Mathematics and Physical Sciences, Department of Theoretical and Applied Mechanics, National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou Campus, 15773 Athens, Greecesfilop@gmail.com

G. J. Tsamasphyros

School of Applied Mathematics and Physical Sciences, Department of Theoretical and Applied Mechanics, National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou Campus, 15773 Athens, Greecetsamasph@central.ntua.gr

1

Corresponding author.

J. Heat Transfer 133(2), 021302 (Nov 02, 2010) (9 pages) doi:10.1115/1.4002630 History: Received July 23, 2009; Revised September 23, 2010; Published November 02, 2010; Online November 02, 2010

## Abstract

We present a new model for the determination of temperature distributions in thin plates consisting of many different layers. The method uses both continuous and discrete approaches. The derived set of equations is based on a continuous representation of heat transfer phenomena at the midplane of each layer, whereas it facilitates a discrete process for introducing ply to ply, through thickness, heat transfer. For the steady state case, the resulting equations are of the Helmholtz type. Methods of solutions for the resulting system are discussed, and comparisons with the first order lamination theory are presented in a benchmark example.

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## Figures

Figure 1

Thin multilayered plate

Figure 2

Energy conservation for a characteristic volume of the plate

Figure 3

(a) Ply to ply heat transfer approximation. (b) Convection loses approximation.

Figure 4

A thin plate consisting of two different plies A and B

Figure 5

Temperature profile at the interface and comparison of the present method with the FOL theory (case I)

Figure 6

Temperature profile at the interface and comparison of the present method with the FOL theory (case II)

Figure 7

In depth temperature distribution at four different cross sections (case I)

Figure 8

In depth temperature distribution at four different cross sections (case II)

Figure 9

Performance of the present method and FOL theory with respect to ‖•‖DL norm (case I)

Figure 10

Performance of the present method and FOL theory with respect to ‖•‖DL norm (case II)

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