Discussion: “Performance and Optimization Analysis for Fins of Straight Taper with Simultaneous Heat and Mass Transfer” (, and , 2004, ASME J. Heat Transfer, 126, pp. 862–868) OPEN ACCESS

[+] Author and Article Information
Panagiotis Razelos

Department of Engineering Science and Physics,  College of Staten Island∕CUNY, 2800 Victory Blvd., Staten Island, NY 10314

J. Heat Transfer 129(9), 1304-1305 (Oct 18, 2006) (2 pages) doi:10.1115/1.2740643 History: Received April 07, 2006; Revised October 18, 2006

In this paper the authors employed a new rather unorthodox approach, and unusual parameterization entirely different from that existing in the literature, to obtain their results. In their abstract, the authors claim to have obtained the performance prediction, i.e., the efficiency and effectiveness, of wet fins, for tapered longitudinal, spines and radial fins. Their lengthy explanation for the obvious differences between wet and dry fins is unnecessary. They further assert to have derived a generalized criterion (what is the meaning of generalized?) for the optimization of the three types of fins they analyze. The authors describe the fins as tapered, shown in their Fig. 1, however the expressions of their profiles such as yyb=f(X,λ) is missing. Also, their keywords refer to dehumidification and heat exchanger that are not used in the manuscript. Moreover, what is conspicuously missing in this paper is the exact description of the mathematical problem they solve. The authors abruptly start with a differential (Eq. (1)), without any boundary conditions, or any other comments such symmetry, etc. In fact this paper lacks the mathematical perspicuousness and rigor required in any such endeavor.

The following comments are addressed to specific sections of the manuscript.

We begin with the authors’ Nomenclature because it contains several errors, thus making the reading of this manuscript extremely difficult. The Nomenclature is a mirror of the symbols found in the text, which is used to explain their meanings to the reader who frequently needs to consult it.

(i) The authors assume the following linear temperature variation of the specific humidity:Display Formula

Considering the values of ω to be specified at the temperatures Tt and Tb, we obtain the following values for of the above constants:Display Formula
The authors’ expression for b1 is incorrect and unless this is a typographical error, this mistake is propagated in their results, although the incautious reader may tempted to ask, are both temperatures, Tb and Tt, that are used in Eq. 2 of this Discussion specified?

(ii) I think Bit=htybk should have been Bit=htytk, although ht is never defined.

(iii) The authors assert “f, g to be functions defined by Eq. (18) and Eq. (19) respectively.” However, Eq. (18) defines the dimensionless volume U, whereas f(Bi,ψ) is defined by Eq. (19), and g(Bi,ψ) by Eq. (20).

(iv) The symbol hm, which appears in the last term on the left-side of the authors’ Eq. (1), has never been defined. Also, the dimensions of q, the actual heat transfer rate, for longitudinal fins should be expressed in watts per meter.

(v) The correct definition of qe is: “the heat transfer from the base of the fin, with the same heat transfer coefficient in its absence.” The assumption for the ideal heat dissipation qi is: “the entire fin is maintained at the base temperature.”

(vi) Q is defined by Eq. (11) not Eq. (10), Qe by Eq. (16) not Eq. (15), Qi by Eq. (14) not Eq. (13), and U by Eq. (18) not Eq. (17).

(vii) The parameter Z0 is recognized as the one which used by Gardner (1) to plot his efficiency graphs and is expressed as the product of the aspect number Lyb and the Bi. The quotient Lyb is always referred in the literature as aspect number, however, the authors’ ψ is the reciprocal, but still defined as the aspect number. As shown in Refs. 2-3 the authors’ parameters Z02=Biψ2 and Bi have physical significances.

(viii) Normally, the solutions should be able to handle any values of the parameter 0λ1, hence the parameters Z1, Z2, and α that, are divided by (1λ), cannot be used unless they are redefined.

(ix) The authors created a huge aggregate of dimensionless parameters, whereas only a few appearing in their results. The principal parameters that are used by the authors in their result are: Z0, Bi, and λ; however, the temperature is independent of Bi.

(i) In this section the authors make the following statements: (1) at any point, the temperature over the fin cross section is assumed to be constant and (2) the transport processes can be rendered one-dimensional (1D) as is conventionally done for dry fins. The authors should be reminded that, in mathematical analyses nothing is conventionally done, but it must be based on certain fundamental principles. In this case, there are certain conditions, known as simplified assumptions, described in Ref. 1, that must be met, in order to allow using the 1D conduction model. For example here, the restrictive condition for using the 1D approach is the small values of the Biot number (of the order of 0.01). As shown in Refs. 2-3, when one employs the 1D approach, the simplified assumptions, insulated tip and the length of arc idealization are valid. Thus the expression 1+(dydx)2 can be eliminated, and the tip boundary condition should be modified accordingly.

(ii) There in no explanation as to why the authors introduce the radius ri in Eq. 1, which for longitudinal fins and spines is zero, and in radial fins the coordinate x varies from 0 to ri, instead of rixrt, which is universally used. In this case an important new parameter is introduced namely the ratio parameter rtri. For example, what is the value of this parameter in the results plotted in the original Fig. 4?

(iii) Now, in any mathematical equation involving symbols with dimensions, like those in Eq. (1), one should always first check if it is dimensionally correct. For longitudinal fins, the dimensions of the left-side and the first right-side terms are kelvin per meter whereas the dimensions of the last term hfg are watts per square meter, with similar contradictions appearing in the other cases. I believe the authors neglected to divide this term with the thermal conductivity k.

(iv) The authors assert that have employed the Chilton Colburn analogy and some algebraic manipulations to derive their Eq. (2). However, the temperature becomes now a function of Y=yyb instead of X=xL. This is indeed a very puzzling operation for mainly two reasons. First, according to the authors’ earlier statement the temperature along this direction is constant. In the other hand, how could the profiles of the fins, which are yyb=f(X), possibly influence the results?

At the beginning of this section the authors engage in a long and unnecessary explanation for the self-evident conceptions, of what is meant by dry fins and their performance. Then they present a few graphs, which in the abstract claim to be design curves, while they only refer to one specific case. I am indeed puzzled how these plots were contracted using those formidable equations ((4)–(20)), with all these dimensionless variables, which as was pointed out earlier, they contain several mistakes? What are exactly the differences between efficiencies and effectiveness with the authors’ over-all counterparts? I believe that their results are incorrect despite the agreement with previous work shown in the original Fig. 2. Moreover, the variation of the effectiveness versus Z0 in their Fig. 4 physically does not make sense. For example, when the value of Z0=0 (absence of the fin), by definition, the effectiveness value is equal to 1 instead of the authors’ 20. To help the authors revise their paper certain additional references are given here.

I regret to say, that due to space limitations of the journal I cannot describe the correct formulation of the problem that the authors should solve.

Copyright © 2007 by American Society of Mechanical Engineers
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