Technical Briefs

Heat Transfer and Pressure Drop Through Nano-Fin Arrays in the Free-Molecular Flow Regime

[+] Author and Article Information
Michael James Martin

Assistant Professor
Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: mjmartin@lsu.edu

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received June 16, 2012; final manuscript received January 5, 2013; published online July 26, 2013. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 135(9), 091601 (Jul 26, 2013) (5 pages) Paper No: HT-12-1290; doi: 10.1115/1.4024462 History: Received June 16, 2012; Revised January 05, 2013

Gas flow through arrays of rectangular nanofins is modeled using the linearized free-molecular drag and heat transfer equations. These are combined with the one-dimensional equations for conservation of mass, momentum, and energy, and the ideal gas law, to find the governing equations for flow through the array. The results show that the pressure gradient, temperature, and local velocity of the gas are governed by coupled ordinary differential equations. The system of equations is solved for representative arrays of nanofins to find the total heat transfer and pressure drop across a 1 cm chip.

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Fig. 1

Array geometry: (a) fin arrangement and (b) fin cross-section

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Fig. 7

Total heat transfer versus velocity for 5 nm × 5 nm fins

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Fig. 6

Total pressure drop versus velocity for 5 nm × 5 nm fins

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Fig. 5

Velocity, pressure, and temperature changes for 5 nm × 5 nm fins, uo = 0.1 m/s (a) velocity increase, (b) pressure change, and (c) temperature change

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Fig. 4

Velocity and pressure change versus x for 5 nm × 5 nm fins, uo = 0.1 m/s (a) velocity increase and (b) pressure change

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Fig. 3

Velocity and pressure change versus x for 5 nm × 5 nm fins, n = 5 × 109 m−2 (a) velocity increase and (b) pressure change

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Fig. 8

Fin drag versus aspect ratio for a fin with a perimeter of 20 nm, uo = 0.01 m/s



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