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Research Papers: Forced Convection

Benchmark Solutions for Slip Flow and H1 Heat Transfer in Rectangular and Equilateral Triangular Ducts

[+] Author and Article Information
C. Y. Wang

Departments of Mathematics and Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: cywang@mth.msu.edu

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received March 5, 2012; final manuscript received August 30, 2012; published online December 28, 2012. Assoc. Editor: Sujoy Kumar Saha.

J. Heat Transfer 135(2), 021703 (Dec 28, 2012) (8 pages) Paper No: HT-12-1084; doi: 10.1115/1.4007576 History: Received March 05, 2012; Revised August 30, 2012

Accurate analytic solutions for the fully developed slip flow and H1 heat transfer in rectangular and equilateral triangular ducts are presented. Both velocity slip and temperature jump have significant influences on the Poiseuille and Nusselt numbers. These exact solutions serve as benchmark cases for other methods, whether analytic, approximate, or numerical.

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Figures

Grahic Jump Location
Fig. 1

(a) Cross section of the rectangular duct and (b) cross section of the equilateral triangular duct

Grahic Jump Location
Fig. 2

(a) Constant velocity lines (b = 0.5, λ = 1); from inside: w = 0.46, 0.42,…; maximum velocity is 0.4764 at the center. (b) Constant temperature lines (b = 0.5, λ = 1, γ = 1); from inside: − τ = 0.18, 0.16,…; minimum temperature is −0.1990 at the center.

Grahic Jump Location
Fig. 4

(a) Constant velocity lines (λ = 1); from inside: w = 0.9, 0.8,…; maximum velocity is 0.9167 at the center. (b) Constant temperature lines (b = 0.5, λ = 1, γ = 1); from inside: −τ = 0.6, 0.5,…; minimum temperature is −0.6979 at the center.

Grahic Jump Location
Fig. 3

Constant velocity lines (b = 0.5, λ = 1) using constant slip assumption. From inside: w = 0.44, 0.40, 0.36.

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