Commun. Comput. Phys., 12 (2012), pp. 1482-1494.


Study on General Governing Equations of Computational Heat Transfer and Fluid Flow

Wang Li 1, Bo Yu 1*, Yi Wang 1, Xin-Ran Wang 1, Qing-Yuan Wang 1, Wen-Quan Tao 2

1 Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing, 102249, People's Republic of China.
2 Key Laboratory of Thermal Fluid Science and Engineering of MOE, Xi'an Jiaotong University, Xi'an, 710049, People's Republic of China.

Received 22 January 2011; Accepted (in revised version) 28 November 2011
Available online 22 May 2012
doi:10.4208/cicp.220111.281111a

Abstract

The governing equations for heat transfer and fluid flow are often formulated in a general form for the simplification of discretization and programming, which has achieved great success in thermal science and engineering. Based on the analysis of the popular general form of governing equations, we found that energy conservation cannot be guaranteed when specific heat capacity is not constant, which may lead to unreliable results. A new concept of generalized density is put forward, based on which a new general form of governing equations is proposed to guarantee energy conservation. A number of calculation examples have been employed to verify validation and feasibility.

AMS subject classifications: 76M12, 80A20, 68U20

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Key words: SIMPLE algorithm, general form of governing equations, conservation, generalized variable, fluid-solid coupling.

*Corresponding author.
Email: lw286964103@yahoo.com.cn (W. Li), yubobox@cup.edu.cn (B. Yu), wy1031@yahoo.com.cn (Y. Wang), wangxinran719@163.com (X.-R. Wang), qingyuan19871001@126.com (Q.-Y. Wang), wqtao@mail.xjtu.edu.cn (W.-Q. Tao)
 

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