Research Papers: Electronic Cooling

Passive Heat Transfer in Solid-State Lighting: Relaxing the Boussinesq Approximation Analytically in the Vertical Channel

[+] Author and Article Information
Thomas D. Dreeben

Osram Sylvania Corporate Innovation,
71 Cherry Hill Drive,
Beverly, MA 01915
e-mail: thomas.dreeben@sylvania.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 10, 2015; final manuscript received November 11, 2015; published online January 12, 2016. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 138(4), 041401 (Jan 12, 2016) (11 pages) Paper No: HT-15-1537; doi: 10.1115/1.4032176 History: Received August 10, 2015; Revised November 11, 2015

Analytical relations between the heat flux, temperature rise, thermal boundary layer thickness, and characteristic velocity have been derived for the two-dimensional vertical channel, without use of the Boussinesq approximation. Results have been put into the context of well-established scaling behavior in the literature. In addition, useful implications of the analytical results have been described, including a criterion to determine the suitability of a heat-sink configuration to a particular application.

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Fig. 1

Common solid-state lamps with different thermal approaches including fins

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Fig. 2

Geometry of a heated vertical channel of moderate aspect ratio. It consists of two vertical heated parallel fins with air in between. An unheated plenum beneath the channel enables more physical inlet conditions.

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Fig. 3

Simulation output of temperature above ambient buoyant flow in the heated vertical channel, shown together with air velocity vectors. Fin temperature in this simulation is 114 °C above ambient.

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Fig. 4

Simulation output of vertical air velocity for buoyant flow in the heated vertical channel

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Fig. 5

Simulation output of horizontal velocity for buoyant flow in the vertical channel

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Fig. 7

Simulation results. Fin temperature rise above ambient as a function of heat flow using the Boussinesq approximation (Eq. (7)) compared with the fully compressible formulation (Eq.(1)).

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Fig. 11

Analytical thermal boundary layer thickness compared with its equivalent taken from the simulation

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Fig. 10

Simulation results for air temperature rise above ambient with a 3 mm fin gap and 0.4 W power

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Fig. 9

Comparison of simulation results with the analytical result of Eq. (25). Dependence of fin temperature above ambient on fin gap, at 0.4 W of heat flow.

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Fig. 8

Comparison of simulation results with the analytical result of Eq. (25). Dependence of fin temperature rise above ambient on heat flow.

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Fig. 12

Analytical model output for the short vertical channel. Dependence of the convection coefficient on key parameters fin height and temperature difference, with α = 2.5.



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