Research Papers: Conduction

Spreading Resistance in Multilayered Orthotropic Flux Channels With Different Conductivities in the Three Spatial Directions

[+] Author and Article Information
Belal Al-Khamaiseh

Department of Mathematics and Statistics,
Memorial University of Newfoundland,
St. John's, NL A1C 5S7, Canada
e-mail: balkhamaiseh@mun.ca

Yuri S. Muzychka

Fellow ASME
Department of Mechanical Engineering,
Memorial University of Newfoundland,
St. John's, NL A1B 3X5, Canada
e-mail: y.s.muzychka@gmail.com

Serpil Kocabiyik

Department of Mathematics and Statistics,
Memorial University of Newfoundland,
St. John's, NL A1C 5S7, Canada
e-mail: serpil@mun.ca

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 24, 2017; final manuscript received October 29, 2017; published online April 6, 2018. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 140(7), 071302 (Apr 06, 2018) (10 pages) Paper No: HT-17-1227; doi: 10.1115/1.4038712 History: Received April 24, 2017; Revised October 29, 2017

In the microelectronics industry, the multilayered structures are found extensively where the microelectronic device/system is manufactured as a compound system of different materials. Recently, a variety of new materials have emerged in the microelectronics industry with properties superior to Silicon, enabling new devices with extreme performance. Such materials include β-Gallium-oxide (β-Ga2O3), and black phosphorus (BP), which are acknowledged to have anisotropic thermal conductivity tensors. In many of these devices, thermal issues due to self-heating are a problem that affects the performance, efficiency, and reliability of the devices. Analytical solutions to the heat conduction equation in such devices with anisotropic thermal conductivity tensor offer significant computational savings over numerical methods. In this paper, general analytical solutions for the temperature distribution and the thermal resistance of a multilayered orthotropic system are obtained. The system is considered as a multilayered three-dimensional (3D) flux channel consisting of N-layers with different thermal conductivities in the three spatial directions in each layer. A single eccentric heat source is considered in the source plane while a uniform heat transfer coefficient is considered along the sink plane. The solutions account for the effect of interfacial conductance between the layers and for considering multiple eccentric heat sources in the source plane. For validation purposes, the analytical results are compared with numerical solution results obtained by solving the problem with the finite element method (FEM) using the ANSYS commercial software package.

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Grahic Jump Location
Fig. 1

Schematic view of a 3D flux channel layout: (a) top view, (b) cross section view in xz-plane, and (c) cross section view in yz-plane

Grahic Jump Location
Fig. 2

Top view of a 3D flux channel with multiple heat sources along the source plane

Grahic Jump Location
Fig. 6

Analytical centroidal temperature of each heat source inthe multiple heat sources validation study computed as afunction of the number of terms in the summations for hc2=106 W/m2 K

Grahic Jump Location
Fig. 3

Idealized single heat source FET layout: (a) top view and (b) cross section view

Grahic Jump Location
Fig. 4

Analytical centroidal and average temperatures of the single heat source problem computed as a function of the number of terms in the summations for hc2=106 W/m2 K

Grahic Jump Location
Fig. 5

Heat source plane layout of the multiple heat sources problem



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