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Research Papers

Longitudinal-Fin Heat Sink Optimization Capturing Conjugate Effects Under Fully Developed Conditions

[+] Author and Article Information
Georgios Karamanis

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
e-mail: Georgios.Karamanis@tufts.edu

Marc Hodes

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
e-mail: Marc.Hodes@tufts.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received January 10, 2016; final manuscript received July 5, 2016; published online August 23, 2016. Assoc. Editor: S. A. Sherif.

J. Thermal Sci. Eng. Appl 8(4), 041011 (Aug 23, 2016) (7 pages) Paper No: TSEA-16-1005; doi: 10.1115/1.4034339 History: Received January 10, 2016; Revised July 05, 2016

We develop a method requiring minimal computations to optimize the fin thickness and spacing in a fully shrouded longitudinal-fin heat sink (LFHS) to minimize its thermal resistance under conditions of hydrodynamically and thermally developed laminar flow. Prescribed quantities are the density, viscosity, thermal conductivity and specific heat capacity of the fluid, the thermal conductivity and height of the fins, the width and length of the heat sink, and the pressure drop across it. Alternatively, the length of the heat sink may be optimized as well. The shroud of the heat sink is assumed to be adiabatic and its base isothermal. Our results are relevant to, e.g., microchannel cooling applications where base isothermality can be achieved by using a heat spreader or a vapor chamber. The present study is distinct from the previous work because it does not assume a uniform heat transfer coefficient, but fully captures the velocity and temperature fields by numerically solving the conjugate heat transfer problem in dimensionless form using an existing approach. We develop a dimensionless formulation and compute a dense tabulation of the relevant parameters that allows the thermal resistance to be calculated algebraically over a relevant range of dimensionless parameters. Hence, the optimization method does not require the time-consuming solution of the conjugate problem. Once the optimal dimensionless fin thickness and spacing are obtained, their dimensional counterparts are computed algebraically. The optimization method is illustrated in the context of direct liquid cooling.

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References

Figures

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Fig. 1

Unconfined longitudinal-fin heat sink (LFHS)

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Fig. 2

(a) Fully shrouded LFHS and (b) domain

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Fig. 3

λ versus Ω and S

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Fig. 4

Rt versus Ω and S for Si–Water, Rt,asym=0.013°C/W, K=9.3×10−3, and B=1.3×10−2

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