An Analysis of Turbulent Free-convection Heat-transfer

Bayley, F. J.

doi:10.1243/pime_proc_1955_169_049_02

Cited by 70 publications

(33 citation statements)

References 2 publications

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“…A study of the literature shows strong correlation of these data points with other experiments using horizontal plates, allowing the same formula to be used for flat and vertical sides of the actuator [14][15][16][17]. Hence the following new formula extension can be made to the range of the Rayleigh number correlation to the Nusselt number by using a best fit approximation to the lower bound of the Rayleigh number range, …”

Section: Figure (3) Low Rayleigh Number Correlations To Vertical Platesmentioning

confidence: 91%

Transfer function characterization of thermally-actuated displacement-amplified micro-electromechanical systems (MEMS)

et al. 2006

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In this paper the dynamics of MEMS devices is explored, which characterizes the behavior of a thermallyactuated MEMS in order to perform a system identification enabling controlled operation of the micro-device. By considering the input to the system is the current/voltage and the output is the amplified mechanical displacement, a transfer function, TF, is derived which includes energy losses due to the imperfect energy conversion from electric to thermal, and which correspond to various phenomena, such as convection, radiation and conduction -accounting for a Joule-effect temperature less than the ideal one. This TF also includes the relationship between temperature and the mechanical deformation of both "active and passive" flexure hinges, which are thermally-actuated and which contribute to the kinematics of the output motion of the micro-device. This TF model is validated by means of experimental data from an actual displacement-amplification MEMS which was fabricated by means of the PolyMUMPs surface machining technology.A exp = total actuator exposed area A s = actuator cross-sectional area c = actuator specific heat coefficient E in = energy input E out = energy output F uni = actuator unidirectional force Gr 2L = Grashoff number for full actuator length h = average convective heat transfer coefficient h r = linear radiation heat transfer coefficient I = current input k a = actuator thermal conductivity k med = medium's thermal conductivity L = ½ actuator length L Nu2 = Nusselt number for full actuator length P in = Power input in q & = volumetric power input R = actuator resistance R t = thermal contact resistance for conduction Re 2L = Reynolds number for full actuator length S = actuator conduction shape factor T = actuator temperature T med = medium's temperature Smart Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/15/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx T sub = substrate layer temperature T x=-L = surface temperature at base end of actuator (x = -L) T x=L = surface temperature at drive end of actuator (x = L) V = voltage input V ol = total volume of actuators α T = actuator coefficient for linear thermal expansion (CLTE) ε = actuator emissivity ε uni = actuator unidirectional strain ρ = actuator density σ = Stefan-Boltzmann constant σ T = actuator thermal stress

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Section: Figure (3) Low Rayleigh Number Correlations To Vertical Platesmentioning

confidence: 91%

Transfer function characterization of thermally-actuated displacement-amplified micro-electromechanical systems (MEMS)

et al. 2006

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“…2. Bayley [2], Oosthuizen [3], and Kato et al [4] utilized approximate, onedimensional momentum and energy balances with the eddy diffusivities postulated to be equal and an explicit function of y' only. 3.…”

Section: Prior Workmentioning

confidence: 99%

Turbulent Free Convection from a Vertical, Isothermal Plate

Lin

Churchill

1978

Numerical Heat Transfer, Part B: Fundamentals

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The temperature and velocity fields adjacent to mi kothermal, vertical plate have been calcuhted by finitedifference methods using the time-averaged equations af conservation. Effective diffurivities for turbulent tmnsfer were computed from differential balances for the turbulent kinetic energy and the rate of dksipation of turbulent energy. using the empirical coefficients previousIfZGluated for forced convection together with an additional Prandtl-numberdependent coefficient associated with the buoyant production of turbulent kinetic energy. Although the turbulent boundary hyer almost approaches an asymptotic condition, the slight development requires a two-dimensional solution proceeding from the leading edge through the laminar and turbulent regimes. It was necessary to trigger the transition from laminar to turbulent motion, but the ultimate turbulent behavior was found to be independent of the point of triggering. The computed velocity fields, temperature fields, and rates of heat transfer are in agreement with prior experimental data for air within their uncertainty. Excellent wreement was also obtained with the data for water, and fair agreement with the data for spindle oiL

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“…Several investigators have calculated such flows using integral methods including Eckert and Jackson [l], 2 Bayley [2], and more recently, Kato, et al [3]. Although the results of these calculations agree well with available experimental data with respect to the heat transfer, the assumed velocity and temperature profiles have been shown to be in error particularly the 1/7 power law profiles of Eckert and Jackson.…”

Section: Introductionmentioning

confidence: 98%

“…(The solution of Kato does not assume profiles of velocity and temperature but assumes an eddy diffusivity distribution from which mean profiles of velocity and temperature are deducted.) More recently several investigators: Cebeci and Khattab [4], Mason and Seban [5], and Noto and Matsumoto [6] have obtained numerical 1 Present address: Department of Mechanical Engineering, Washington State University, Pullman, Wash. 2 Numbers in brackets designate References at end of paper. Contributed by The Heat Transfer Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS, and presented at the National Heat Transfer Conference, St. Louis, Mo., August 9-11,1976.…”

Section: Introductionmentioning

confidence: 99%

Application of a K-ε Turbulence Model to Natural Convection From a Vertical Isothermal Surface

Plumb

Kennedy

1977

Journal of Heat Transfer

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A K-e turbulence model similar to that proposed by Jones and Launder is applied to the calculation of the turbulent natural conuectiue boundary layer on a vertical, isothermal surface. Conservation equations for the turbulent kinetic energy, dissipation rate of turbulent kinetic energy, and mean square temperature fluctuations are solved numerically along with the turbulent momentum and energy equations using the Spalding-Patankar boundary layer method. Various model constants and wall functions, and wall terms were tested. The results are compared with available experimental data and found to be in reasonable agreement.

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An Analysis of Turbulent Free-convection Heat-transfer

Cited by 70 publications

References 2 publications

Transfer function characterization of thermally-actuated displacement-amplified micro-electromechanical systems (MEMS)

Transfer function characterization of thermally-actuated displacement-amplified micro-electromechanical systems (MEMS)

Turbulent Free Convection from a Vertical, Isothermal Plate

Application of a K-ε Turbulence Model to Natural Convection From a Vertical Isothermal Surface

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