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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)PUBLIC ACCESS

[+] Author and Article Information

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

$τ=Tw−ToTw$
(1)
For $Tw=373K$ (Table 1) and $To=293K$ (Tables $2a$, and $3a$), $τ=0.214>τ=0.0−0.2$ (Table 1). Thus, the range of $τ$ in Table 1 must be $τ=0.0–0.25$.

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

$ψ={ln(1−τe−4Stλ1−τ)−τ(1−e−4Stλ)+18fτEcStln(e4Stλ−τ1−τ)}(1−e−4Stλ)$
(2)
The major error in Eq. (10) leads to other many errors in the equations. First, Eq. (14) must beDisplay Formula
$ψ={ln(1−τe−4Π11−τ)−τ(1−e−4Π1)+8τΠ2ln(e4Π1−τ1−τ)}(1−e−4Π1)$
(3)
Second, Eq. (17) must beDisplay Formula
$ψ={ln(1−τe−4Π11−τ)−τ(1−e−4Π1)+8τΠ2[ln(e4Π1−τ1−τ)+(bTrefa)ln(e4Π1−τ1−τ)−4(bTwa)Π1]}(1−e−4Π1)$
(4)
Third, Eq. (20) must beDisplay Formula
$ψ={ln(1−τe−4Π11−τ)−τ(1−e−4Π1)+32Π2∫0lΠ1lTw−ToTrefnTn−1exp[B(1T−1Tref)]dx}(1−e−4Π1)$
(5)
Finally, Eq. (22) must beDisplay Formula
$ψ′=ψ(1−e−4Π1)$
(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

$ψ=32(τΠ2)Π1∕(1−e−4Π1)$
(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

$(xfd,tDH)lam≈0.05ReDHPr$
(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
$(xfd,t)lam≈0.1πAcReDHPr$
(10)
From Table 2, $(Ac)max=6×10−7m2$ and $Pr=7$. From Figs. 1–7, $(ReDH)max=3000$. Thus,Display Formula
$(xfd,t)lam≈0.1π6×10−7(3000)(7)≈0.92m$
(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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