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TECHNICAL BRIEFS

A Discussion of Transpiration Cooling Problems through an Analytical Solution of Local Thermal Nonequilibrium Model

[+] Author and Article Information
J. H. Wang1

Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Jinzhai Road No. 96 Hefei 230027 Anhui, P. R. China

H. N. Wang

Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Jinzhai Road No. 96 Hefei 230027 Anhui, P. R. China

1

Corresponding author; e-mail: jhwang@ustc.edu.cn

J. Heat Transfer 128(10), 1093-1098 (Apr 12, 2006) (6 pages) doi:10.1115/1.2345434 History: Received November 27, 2005; Revised April 12, 2006

To study transpiration cooling problems, an analytical solution of the local thermal nonequilibrium (LTNE) model with the second or third boundary conditions is presented. This solution is obtained through neglecting the thermal conduction of the fluid coolant in porous media. By the analytical solution, two problems are investigated. At first, the parameters which influence transpiration cooling effects are analyzed, and the analysis indicates that the cooling effects are dominated by coolant mass flow rate, the Biot number at the hot surface of porous plate, and the Biot number in the pores. Second, the error caused by the assumption of the local thermal equilibrium (LTE) model is quantitatively discussed, and the variation trend of the LTE error is analyzed. Based on the analytical solution and the error analysis, a quantitative criterion to choose the LTNE or LTE model is suggested, and the corresponding expression is also given in this paper.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Heat exchange between fluid coolant and solid matrix

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Figure 2

Solid temperature θs∣Y=1 at hot surface with coolant mass flow rate and the Biot number in the pores at the second BC

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Figure 3

Solid temperature θs∣Y=1 variation with the coolant mass flow rate and the Biot numbers under the third BC. (a)Bih=20 (b) Bih=200.

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Figure 4

The LTE error variation with the coolant mass flow rate and the Biot number in the pores

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Figure 5

The LTE and LTNE regions divided by the curve fitted using the analytical solution

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