In this paper the authors present the experimental results of the effects of tip clearance on the thermal and hydrodynamic performance of a shrouded pin fin array. The authors have employed the most modern experimental techniques to obtain their results. This is indeed an excellent experimental work. The authors refer to two cases of existing similar experimental work, where pin fins have been used for cooling purposes: (a) cooling of turbine’s blades in aircraft engines and (b) cooling of electronic equipment. A comprehensive discussion with regard of turbines’ experiments, it can be found in the recent book by Han et al. (1). On the other hand, the authors’ work can be useful to manufacturers that produce ready made electronic coolers found in the market as CF-512, BF-02, etc.
Experimental endeavors are costly and time consuming, while analytical solutions of extended surface heat transfer requires only mathematical skills. Most of the analytical results have been obtained, assuming the surface heat transfer coefficient constant. In this respect the heat transfer community is indebted to experimentalists for providing valuable information that can be used to obtain more realistic mathematical results. However, experimentalists often, as in the present case, have to use analytically obtained results. For example, the authors employed mathematical results obtained previously by Kraus and Bar-Cohen, authors’ Ref. [20]. It is also apparent that rudimentary theoretical background of fin analysis is a prerequisite for any experimental endeavor, for designing an experiment. Therefore, there is a blend between experiment and analysis.
In the following, discussion we offer some suggestions that might help the authors, and for the sake of the readers, to improve the representation of their results. These comments refer: to the authors’ mathematical expressions (Eqs. (9)–(12)), and to evaluation of the pin fins’ performance (fin efficiency).
Let us now discuss Eqs. (11), (12a), (12b) that were derived by K-B. In spines and longitudinal fins analysis it is advantageous to locate the origin of the coordinate, , at the tip of the fin. However, symbol , in their nomenclature, that represents the distance between the tip and the base of the fin, is not correct. As is shown in the Fig. 3.10 of K-B, symbolizes the distance between a fictitious tip, (determined by ), and the base of the fin, while the symbol , (that does not appear in the author’s nomenclature but only in the pertinent equations), represents the distance from the fictitious tip to the tip of pin. Therefore, the distance depends on the parameter , while . Thus, the extremely complicated expression for the dimensionless temperature, Eq. (3.73) in K-B, involves the distances the and , instead of the given parameters and . All of this enormously complicated formulation by K-B could have been circumvented if one selects the real tip to be the origin of coordinates, . For this particular case, the pertinent equations, given below, are taken from Ref. 4.
Finally, it is necessary for those who are in involved in any fin analysis or experiment endeavor, at the end they should always compare the heat transferred by the fin, to the heat that would have been transferred from the fin’s base area in the absence of the fin. This ratio was introduced by Gardner (6), as fin effectiveness. The later could be calculated using the average heat transfer coefficient determined experimentally, and the results will be on the conservative side, because in the bare surface, where the heat transfer coefficient can be easily determined from known formulas, would be larger. It has been also shown in Refs. 2 3 that, for straight fins and spines the effectiveness is equal to , which poses restrictions on the values of Bi, that was neglected by the authors.
I may suggest further, that the authors extend their experimental work to the following two other important problems. The first one is the case where fins are used in heat exchangers, and the second the in arrays of fins. Notice that the boundary conditions in the first are constant temperature and insulated tip, and in the second the temperatures are specified. With regard of the second problem that authors should consult (11).
I hope these comments will help the authors to improve the presentation and to design their new experiments.
In the following I will refer to the author’s Ref. [20] as K-B.
