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Technical Brief

Thermal Spreading Analysis of Rectangular Heat Spreader

[+] Author and Article Information
S. M. Thompson

Assistant Professor
Department of Mechanical Engineering,
Carpenter Hall,
P.O. Box 9552,
Mississippi State University,
Mississippi State, MS 39762

H. B. Ma

C. W. LaPierre Professor
Department of Mechanical and
Aerospace Engineering,
University of Missouri,
Columbia, MS 65211

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 2, 2013; final manuscript received January 20, 2014; published online March 11, 2014. Assoc. Editor: Bruce L. Drolen.

J. Heat Transfer 136(6), 064503 (Mar 11, 2014) (8 pages) Paper No: HT-13-1332; doi: 10.1115/1.4026558 History: Received July 02, 2013; Revised January 20, 2014

A unique nondimensional scheme that employs a source-to-substrate “area ratio” (e.g., footprint), has been utilized for analytically determining the steady-state temperature field within a centrally-heated, cuboidal heat spreader with square cross-section. A modified Laplace equation was solved using a Fourier expansion method providing for an infinite cosine series solution. This solution can be used to analyze the effects of Biot number, heat spreader thickness, and area ratio on the heat spreader's nondimensional maximum temperature and nondimensional thermal spreading resistance. The solution is accurate only for low Biot numbers (Bi < 0.001); representative of highly-conductive, two-phase heat spreaders. Based on the solution, a unique method for estimating the effective thermal conductivity of a two-phase heat spreader is also presented.

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Figures

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Fig. 1

Typical thermal spreading configuration with heat source, spreader and sink

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Fig. 2

Top view of square-on-square heat spreader/source configuration in Cartesian space

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Fig. 3

Profile view of square-on-square heat spreader/source configuration in Cartesian space

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Fig. 4

Profile view of first octant of square-on-square heat spreader/source configuration in Cartesian space (with symmetry boundary conditions)

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Fig. 5

Nondimensional temperature field (θ*) on bottom, heated plane of heat spreader for various area ratios (A*) and Bi = 0.0001, τ = 0.01

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Fig. 6

Maximum temperature ratio (θR) along half-length of bottom, heated plane of heat spreader for various area ratios (A*) for Bi = 0.0001 (top), Bi = 0.0005, and Bi = 0.001 (bottom) with τ = 0.01

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Fig. 7

Maximum temperature ratio (θR) along half-length of bottom, heated plane of heat spreader for various Biot numbers (Bi) with A* = 0.0001 and τ = 0.01

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Fig. 8

Nondimensional, maximum temperature versus nondimensional heat spreader thickness for various area ratios at Bi = 0.0001

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Fig. 9

Nondimensional, maximum temperature versus nondimensional heat spreader thickness for various area ratios at Bi = 0.0005

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Fig. 10

Nondimensional, maximum temperature versus nondimensional heat spreader thickness for various area ratios at Bi = 0.001

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Fig. 11

Nondimensional, maximum temperature versus area ratio for various nondimensional heat spreader thicknesses at Bi = 0.0001

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Fig. 12

Nondimensional, maximum temperature versus area ratio for various nondimensional heat spreader thicknesses at Bi = 0.0005

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Fig. 13

Nondimensional, maximum temperature versus area ratio for various nondimensional heat spreader thicknesses at Bi = 0.001

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Fig. 14

Nondimensional thermal spreading resistance versus area ratio for various nondimensional heat spreader thicknesses at Bi = 0.0001

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Fig. 15

Nondimensional thermal spreading resistance versus area ratio for various nondimensional heat spreader thicknesses at Bi = 0.0005

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Fig. 16

Nondimensional thermal spreading resistance versus area ratio for various nondimensional heat spreader thicknesses at Bi = 0.001

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Fig. 17

Dimensionless thermal spreading resistance (ψsp*) of heat spreader versus area ratio (A*) and nondimensional thickness (τ) for Bi = 0.0001

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Fig. 18

Nondimensional thermal spreading resistance and dimensional thermal spreading resistance versus area ratio for τ = 0.01, Bi = 0.001, L = 0.05 m, and k = 400 W/m K

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Fig. 19

Nondimensional, maximum temperature versus Biot number for various area ratios at τ = 0.01

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