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Technical Brief

Modeling of Heat Transfer in an Aluminum X-Ray Anode Employing a Chemical Vapor Deposited Diamond Heat Spreader

[+] Author and Article Information
David J. Stupple

Torr Scientific Ltd.,
Unit 11, Pebsham Rural Business Center,
Pebsham Lane,
Bexhill-on-Sea,
East Sussex TN40 2RZ, UK
e-mail: d.stupple@torrscientific.co.uk

Victor Kemp

Mecway Ltd.,
1 Goring Street,
Thorndon,
Wellington 6011, New Zealand
e-mail: victor@mecway.com

Matthew J. Oldfield

Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: m.oldfield@surrey.ac.uk

John F. Watts

Professor
Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: j.watts@surrey.ac.uk

Mark A. Baker

Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: m.baker@surrey.ac.uk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 7, 2018; final manuscript received June 26, 2018; published online August 28, 2018. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 140(12), 124501 (Aug 28, 2018) (5 pages) Paper No: HT-18-1373; doi: 10.1115/1.4040953 History: Received June 07, 2018; Revised June 26, 2018

X-ray sources are used for both scientific instrumentation and inspection applications. In X-ray photoelectron spectroscopy (XPS), aluminum Kα X-rays are generated through electron beam irradiation of a copper-based X-ray anode incorporating a thin surface layer of aluminum. The maximum power operation of the X-ray anode is limited by the relatively low melting point of the aluminum. Hence, optimization of the materials and design of the X-ray anode to transfer heat away from the aluminum thin film is key to maximizing performance. Finite element analysis (FEA) has been employed to model the heat transfer of a water-cooled copper-based X-ray anode with and without the use of a chemical vapor deposited (CVD) diamond heat spreader. The modeling approach was to construct a representative baseline model, and then to vary different parameters systematically, solving for a steady-state thermal condition, and observing the effect on the maximum temperature attained. The model indicates that a CVD diamond heat spreader (with isotropic thermal properties) brazed into the copper body reduces the maximum temperature in the 4 μm aluminum layer from 613 °C to 301 °C. Introducing realistic anisotropy and inhomogeneity in the thermal conductivity (TC) of the CVD diamond has no significant effect on heat transfer if the aluminum film is on the CVD diamond growth face (with the highest TC). However, if the aluminum layer is on the CVD diamond nucleation face (with the lowest TC), the maximum temperature is 575 °C. Implications for anode design are discussed.

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References

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Figures

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Fig. 1

(a) The beveled tip of a typical X-ray anode as used in a commercial XPS system, with (b) a cutaway view showing the recessed diamond heat spreader, one of several cooling fins and internal water cooling

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Fig. 2

An overview of the mesh used as the basis of the analysis. (Color variations within components (e.g., within aluminum) are visual aids to facilitate the modeling process.

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Fig. 3

A previously published temperature-dependent TC profile of CVD diamond used in the baseline FEA model [11,12]. The curve has been extrapolated to higher temperatures (above 270 °C).

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Fig. 4

Baseline model modified to have direct cooling of the diamond underside

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Fig. 5

The copper-bodied model (right) has a maximum steady-state temperature 613 °C, whereas the baseline model with the diamond heat spreader (left, same temperature scale) has maximum 301 °C

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Fig. 6

Effect of varying TCs of components, and the convection coefficient of the cooling water. The steep curves indicate those thermal properties that have the greatest effect on the aluminum temperature.

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Fig. 7

The peak temperature of the aluminum for different dimensions in the model. The aluminum temperature of the baseline model is highly sensitive to the thickness of the aluminum layer (steep curve).

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Fig. 8

A comparison of vertical and horizontal temperature profiles in models with and without a diamond heat spreader. The profiles are taken from the top/center of each model. While the temperatures are higher without a heat spreader, the temperature gradients are quite similar.

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Fig. 9

A schematic diagram of the heat flux through a central section of the anode tip, with the anode tip center at top left. For clarity, the heat flux magnitude range of 0–1.5 MW m−2 is chosen, such that the highest fluxes near the center of the tip (top left) are not shown. The section shown is from the heat spreader model; the model with no heat spreader shows a similar pattern. The flux magnitude is proportional to arrow length.

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