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DISCUSSION

Discussion: “Second Law Analysis of Laminar Viscous Flow Through a Duct Subjected to Constant Wall Temperature” (Sahin, A. Z., 1998, ASME J. Heat Transfer, 120 , pp. 76–83) OPEN ACCESS

[+] Author and Article Information
M. M. Awad

Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, Newfoundland, A1B 3X5, Canadaawad@engr.mun.ca

J. Heat Transfer 129(9), 1302 (Mar 17, 2007) (1 page) doi:10.1115/1.2745836 History: Received February 12, 2007; Revised March 17, 2007

Abstract

In the paper Sahin, A. Z., 1998, “Second Law Analysis of Laminar Viscous Flow Through a Duct Subjected to Constant Wall Temperature  ” ASME J. Heat Transfer, 120(1), pp. 76–83, there are many errors in equations, values, etc. The errors will be summarized below.

Based on the definition of the dimensionless temperature difference (τ)Display Formula

τ=TwToTw
(1)
For Tw=373K (Table 1) and To=293K (Tables 2a, and 3a), τ=0.214>τ=0.00.2 (Table 1). Thus, the range of τ in Table 1 must be τ=0.00.25.

Based on Eqs. (8) and (9), then Eq. (10) must beDisplay Formula

ψ={ln(1τe4Stλ1τ)τ(1e4Stλ)+18fτEcStln(e4Stλτ1τ)}(1e4Stλ)
(2)
The major error in Eq. (10) leads to other many errors in the equations. First, Eq. (14) must beDisplay Formula
ψ={ln(1τe4Π11τ)τ(1e4Π1)+8τΠ2ln(e4Π1τ1τ)}(1e4Π1)
(3)
Second, Eq. (17) must beDisplay Formula
ψ={ln(1τe4Π11τ)τ(1e4Π1)+8τΠ2[ln(e4Π1τ1τ)+(bTrefa)ln(e4Π1τ1τ)4(bTwa)Π1]}(1e4Π1)
(4)
Third, Eq. (20) must beDisplay Formula
ψ={ln(1τe4Π11τ)τ(1e4Π1)+32Π20lΠ1lTwToTrefnTn1exp[B(1T1Tref)]dx}(1e4Π1)
(5)
Finally, Eq. (22) must beDisplay Formula
ψ=ψ(1e4Π1)
(6)

These errors in the above equations lead to errors in values in both figures and tables. For example, values of dimensionless entropy generation (ψ) are incorrect and must be calculated again based on the correct form of Eqs. (14), (17), and (20), respectively. In addition, based on the correct form of Eq. (22), values of dimensionless entropy generation (ψ) must be greater than values of modified dimensionless entropy generation (ψ) at the same modified Stanton number (Π1) (not as shown, ψ<ψ at the same Π1, in Figs. 2 and 3, Tables 2a and 3a).

On p. 81 (second column), the total dimensionless entropy change using Eq. (14) becomesDisplay Formula

ψ=32(τΠ2)Π1(1e4Π1)
(7)
On pp. 81 and 82 (Tables 2b, 3b), values of To are in K, not in °C.

In addtion, Sahin (1) made a second law comparison for optimum shape of duct subjected to constant wall temperature and laminar flow. In this paper, the following error is found.

For laminar flow the thermal entry length may be expressed as (2-3):Display Formula

(xfd,tDH)lam0.05ReDHPr
(8)
From Table 1, the hydraulic diameter (DH) for circular duct geometry can be expressed asDisplay Formula
DH=2πAc
(9)
Combining Eqs. (8) and (9), we obtainDisplay Formula
(xfd,t)lam0.1πAcReDHPr
(10)
From Table 2, (Ac)max=6×107m2 and Pr=7. From Figs. 1–7, (ReDH)max=3000. Thus,Display Formula
(xfd,t)lam0.1π6×107(3000)(7)0.92m
(11)

The above value is greater than the length of the duct: L=0.1m (Table 2). This indicated that the flow is still in thermal entrance laminar region and does not reach fully developed laminar region. This error is repeated for other duct geometries such as square, triangle, etc. As a result, the assumption of the fluid is fully developed laminar as it enters the duct in all types of geometry is not acceptable.

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Copyright © 2007 by American Society of Mechanical Engineers
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