Duhamel integral form for the interface heat flux between bubble and liquid

Nail S. Khabeev

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Duhamel integral form for the interface heat flux between bubble and liquid

机译：气泡和液体之间的界面热通量的Duhamel积分形式

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The solution of heat equation inside oscillating gas bubble with moving boundary was obtained by Fourier's method. The integral formula for interface heat flux, containing theta-function in the integrand was derived. The kernel of the integral is represented by a series of exponential functions, and a simple analytic approximation obtained earlier is used for it with high accuracy. The asymptotic expression for the interface heat flux in the Duhamel integral form with rooted kernel was derived. The vapor bubbles were also considered. In this case the major problem is external heat problem in liquid. It is shown that the asymptotic expression for the heat flux at the interface in the case of gas bubbles has the similar structure as the heat flux from the vapor bubble surface to the liquid. In both cases it is Duhamel integral with rooted kernel.

机译：利用傅里叶法求出了带有运动边界的振荡气泡内部的热方程解。推导了界面热通量的积分公式，该积分公式中包含theta函数。积分的核由一系列指数函数表示，并且对其使用了较早获得的简单解析近似，具有很高的精度。推导了带有根核的Duhamel积分形式的界面热通量的渐近表达式。还考虑了汽泡。在这种情况下，主要问题是液体中的外部热量问题。结果表明，在气泡的情况下，界面处的热通量的渐近表达式与从蒸气表面到液体的热通量具有相似的结构。在这两种情况下，它都是带有根核的Duhamel积分。

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来源
《International Journal of Heat and Mass Transfer》 |2007年第26期|p.5340-5343|共4页
作者
Nail S. Khabeev;
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作者单位

Department of Mathematics, University of Bahrain, P. O. Box 32038, Bahrain;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类热力工程理论;热学;
关键词
heat flux; duhamel integral; gas bubble; vapor bubble;

机译：热通量;Duhamel积分;气泡;蒸气泡;

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机译：分层液体之间的热传递通过界面鼓泡。

Duhamel integral form for the interface heat flux between bubble and liquid

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