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Research Papers: Experimental Techniques

# An Analytical Model of External Streaming and Heat Transfer for a Levitated Flattened Liquid Drop

[+] Author and Article Information
Sungho Lee

Research and Development Division, Hyundai Motor Company, Yongin 446-912, Korea

Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453sadhal@usc.edu

Alexei Ye. Rednikov

Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453

1

Corresponding author.

J. Heat Transfer 130(9), 091602 (Jul 10, 2008) (8 pages) doi:10.1115/1.2943305 History: Received June 21, 2007; Revised November 05, 2007; Published July 10, 2008

## Abstract

We present here the heat-transfer and fluid flow analysis of an acoustically levitated flattened disk-shaped liquid drop. The interest in this work arises from the noncontact measurement of the thermophysical properties of liquids. Such techniques have application to liquids in the undercooled state, i.e., the situation when a liquid stays in a fluidic state even when the temperature falls below the normal freezing point. This can happen when, for example, a liquid sample is held in a levitated state. Since such states are easily disrupted by measurement probes, noncontact methods are needed. We have employed a technique involving the use of acoustically levitated samples of the liquid. A thermal stimulus in the form of laser heating causes thermocapillary motion with flow characteristics depending on the thermophysical properties of the liquid. In a gravity field, buoyancy is disruptive to this thermocapillary flow, masking it with the dominant natural convection. As one approach to minimizing the effects of buoyancy, the drop was flattened (by intense acoustic pressure) in the form of a horizontal disk, about $0.5mm$ thick. As a result, with very little gravitational potential, and with most of the buoyant flow suppressed, thermocapillary flow remained the dominant form of fluid motion within the drop. This flow field is visualizable and subsequent analysis for the inverse problem of the thermal property can be conducted. This calls for numerical calculations involving a heat-transfer model for the flattened drop. With the presence of an acoustic field, the heat-transfer analysis requires information about the corresponding Biot number. In the presence of a high-frequency acoustic field, the steady streaming originates in a thin shear-wave layer, known as the Stokes layer, at a surface of the drop. The streaming develops into the main fluid, and is referred to as the outer streaming. Since the Stokes layer is asymptotically thin in comparison to the length scale of the problem, the outer streaming can be formally described by an effective slip velocity at the boundary. The presence of the thin Stokes layer, and the slip condition at the interface, changes the character of the heat-transfer mechanism, which is inherently different from the traditional boundary layer. The current analysis consists of a detailed semianalytical calculation of the flow field and the heat-transfer characteristics of a levitated drop in the presence of an acoustic field.

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## Figures

Figure 8

Comparison of the results from an iterative procedure and a Legendre polynomial expansion

Figure 7

Temperature gradient on a dimpled drop surface with a uniform temperature

Figure 6

Temperature gradient at the surface of a sphere with uniform temperature. The x-coordinate is along a meridian from the equator to the top pole.

Figure 5

Boundary layer temperature profiles (Prair=0.7) for the outer streaming flow on a sphere. The corresponding angular locations, θ, in degrees are shown.

Figure 4

Boundary layer velocity profiles for the outer streaming flow on a sphere. The corresponding angular locations, θ, in degrees are shown.

Figure 3

Dimensionless slip-velocity distribution on the dimpled drop surface. The point x0 corresponds to the end of the x-coordinate at the center of the top surface.

Figure 2

Contact point of two curves on the dimpled drop surface. The nearly straight line is a parabola curve describing the dimpled region while the other curve is the circular edge.

Figure 1

Coordinate system for the Stokes layer on the dimpled drop. The broken line indicates an oblate spheroid with an equivalent edge curvature.

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