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Study of thermal flows from two-dimensional, upward-facing isothermal surfaces using a laser speckle photography technique

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Abstract

A laser specklegram or speckle photography technique allows a direct measurement of surface temperature gradients and provides a full field interrogation with an extremely high resolution from a single data taking. The specklegram technique has been successfully applied to investigate the natural convection heat transfer from an upward-facing isothermal plate. For a plate with a large aspect ratio of 15, both local and global Nusselt numbers have been determined from the direct measurement of local temperature gradients. The Rayleigh number, based on the length scale equivalent to the ratio of the surface area to the perimeter, has been varied from 9.0 × 103 to 4.0 × 104. The present result for the global heat transfer has shown that a 1/5-power law, i.e., Nu = C1 Ra 1/5, correlates the data more properly whilst previously published results showed a large scatter in the exponent, ranging from 1/8-power to 1/4-power. The proportional constant, C1 has been determined to be 0.56 which shows a fairly good agreement with previously published theoretical results. The laser specklegram technique has shown a strong potential as a powerful and convenient method for an experimental assessment of natural convection heat transfer problems. The specklegram technique at the same time has eliminated the deficiencies of both the mass transfer analogy technique and the classical heat transfer measurement technique.

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Abbreviations

a :

characteristic length scale defined as a = A/P where A is the surface area and P is the perimeter of the plate edge [mm]

AR:

aspect ratio [L/H]

c :

defocusing distance [mm]

d :

image distance of Young's fringes from speckle negative

h :

thermal convection coefficient [W/m2 · K]

\(\overline h\) :

average thermal convection coefficient [W/m2 · °C]

H :

width of the test section measured perpendicular to the optic axis [mm]

k :

thermal conductivity [W/m · K]

L :

length of the test section measured parallel to the optical axis [mm]

n :

index of refraction

Nu :

local Nusselt number [ha/k]

\(\overline {Nu}\) :

global Nusselt number \([\overline h a/k]\)

Pr :

Prandtl number [θv/α]

q :

heat flux per unit area [W/m2 · s]

Ra :

Rayleigh number \(\left[ { \equiv \frac{{g\beta (T_{w{\text{ }}} - {\text{ }}T_e )a^3 }}{{\alpha v}}} \right]\)

s :

fringe spacing [mm]

Sc :

Schmidt number [θv/D]

T :

temperature [K]

α:

thermal diffusivity [m2/s]

β:

volumetric coefficient of expansion (1/T∞)

v :

kinematic viscosity of air [m2/s]

λ:

wavelength of helium-neon laser [632.8 nm]

Δ:

amount of speckle dislocation

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Authors and Affiliations

  1. Department of Mechanical Engineering, Texas A&M University, 77843-3123, College Station, Texas, USA

    K. D. Kihm & S. K. R. Cheeti

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  1. K. D. Kihm
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  2. S. K. R. Cheeti
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Kihm, K.D., Cheeti, S.K.R. Study of thermal flows from two-dimensional, upward-facing isothermal surfaces using a laser speckle photography technique. Experiments in Fluids 17, 246–252 (1994). https://doi.org/10.1007/BF00203043

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