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Research Papers: Electronic Cooling

Thermal Resistance in a Rectangular Flux Channel With Nonuniform Heat Convection in the Sink Plane

[+] Author and Article Information
M. Razavi

Faculty of Engineering and Applied Science,
Memorial University of Newfoundland,
Street John's, NL A1B 3X5, Canada
e-mail: m.razavi@mun.ca

Y. S. Muzychka

Faculty of Engineering and Applied Science,
Memorial University of Newfoundland,
Street John's, NL A1B 3X5, Canada

S. Kocabiyik

Department of Mathematics and Statistics,
Memorial University of Newfoundland,
Street John's, NL A1C 5S7, Canada

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 7, 2014; final manuscript received June 15, 2015; published online July 21, 2015. Assoc. Editor: Amy Fleischer.

J. Heat Transfer 137(11), 111401 (Jul 21, 2015) (9 pages) Paper No: HT-14-1786; doi: 10.1115/1.4030885 History: Received December 07, 2014

In this paper, thermal resistance of a 2D flux channel with nonuniform convection coefficient in the heat sink plane is studied using the method of separation of variables and the least squares technique. For this purpose, a two-dimensional flux channel with discretely specified heat flux is assumed. The heat transfer coefficient at the sink boundary is defined symmetrically using a hyperellipse function which can model a wide variety of different distributions of heat transfer coefficient from uniform cooling to the most intense cooling in the central region. The boundary condition along the edges is defined with convective cooling. As a special case, the heat transfer coefficient along the edges can be made negligible to simulate a flux channel with adiabatic edges. To obtain the temperature profile and the thermal resistance, the Laplace equation is solved by the method of separation of variables considering the applied boundary conditions. The temperature along the flux channel is presented in the form of a series solution. Due to the complexity of the sink plane boundary condition, there is a need to calculate the Fourier coefficients using the least squares method. Finally, the dimensionless thermal resistance for a number of different systems is presented. Results are validated using the data obtained from the finite element method (FEM). It is shown that the thick flux channels with variable heat transfer coefficient can be simplified to a flux channel with the same uniform heat transfer coefficient.

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Figures

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Fig. 1

A sample of heat sink with variable heat transfer coefficient

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Fig. 2

Example of systems with nonuniform heat sink: (a) ASUS NVIDIA GeForce GT 520 silent low profile graphics card [20] and (b) ASUS R.O.G. Rampage formula motherboard [21]

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Fig. 3

Two-dimensional flux channel with a central heat source and a variable heat transfer coefficient

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Fig. 4

Variable heat transfer coefficient for half of the slab by considering h(x)/ho=1-(x/c)m

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Fig. 5

Variable heat transfer coefficient for half of the slab by considering h(x)/h¯=(m+1)/m[1-(x/c)m]

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Fig. 6

Dimensionless thermal resistance for Bio = 1 and τ = t/c = 0.1

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Fig. 7

Dimensionless thermal resistance for Bio = 1 and τ = t/c = 0.5

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Fig. 8

Dimensionless thermal resistance for Bio = 10 and τ = t/c = 0.1

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Fig. 9

Dimensionless thermal resistance for Biavg = 0.1 and τ = t/c = 0.1

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Fig. 10

Dimensionless thermal resistance for Biavg = 1 and τ = t/c = 0.1

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Fig. 11

Dimensionless thermal resistance for Biavg = 1 and τ = t/c = 0.5

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Fig. 12

Dimensionless thermal resistance for Biavg = 10 and τ = t/c = 0.1

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Fig. 13

Dimensionless thermal resistance for Biavg = 100 and τ = t/c = 0.1

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Fig. 14

Left: 2D flux channel with dimensionless thickness of τ = 0.1 and right: 2D flux channel with dimensionless thickness of τ = 0.5

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