Heat transfer and pressure drop in a rectangular channel with diamond-shaped elements Giovanni Tanda * Dipartimento di Termoenergetica e Condizionamento Ambientale, Universit  a degli Studi di Genova, via all'Opera Pia 15/a, I-16145 Genova, Italy Received 13 April 2000; received in revised form 16 October 2000 Abstract Heat transfer and pressure drop experiments were performed for a rectangular channel equipped with arrays of diamond-shaped elements. Both in-line and staggered ®n arrays were considered, for values of the longitudinal and transverse spacings, relative to the diamond side, from 4 to 8 and from 4 to 8.5, respectively. The height-to-side ratio of the diamonds was 4.0. Liquid crystal thermography was used to determine the heat transfer coecients on the surface of the channel endwall) on which the ®ns were mounted. Local variations in heat transfer coecients induced by the arrangements of the diamond-shaped elements were measured and discussed. Correlations giving the average Nusselt number for each ®n con®guration as a function of the Reynolds number were developed. Thermal performance comparisons with data for a rectangular channel without ®ns showed that the presence of the diamond-shaped elements enhanced heat transfer by a factor of up to 4.4 for equal mass ¯ow rate and by a factor of up to 1.65 for equal pumping power. Ó 2001 Elsevier Science Ltd. All rights reserved. 1. Introduction Heat transfer associated with ¯ow over arrays of pin ®ns has been the subject of extensive investigation in the past because of its importance in a wide variety of en- gineering applications, such as compact heat exchangers and the cooling of advanced gas turbine blades and electronic devices. A pin-®n array usually consists of a number of cylinders attached perpendicularly to the bounding duct walls endwalls), with the coolant ¯uid passing cross¯ow over the cylinders. Much of the literature published is devoted to the study of the ¯ow normal to banks of circular cylinders [1±8]. When the cylinder height-to-diameter ratio is very large higher than 4) the ®n geometry is of particular interest in heat exchanger applications, in which the attainment of very high heat transfer coecients is of major concern. The heat transfer rates at the endwalls, and the endwall ef- fects on the ®n surface heat transfer adjacent to the walls, are unimportant. Arrays of pin ®ns with low/in- termediate height-to-diameter ratio from 0.5 to 4) are commonly used in internally cooled gas turbine engine airfoils. Here the pins must be relatively short because of passage size and manufacturing limitations; as a conse- quence, cylinder/endwall interactions are strong and the analysis of the overall thermal performance must include heat transfer from the endwall surface. Indeed, the heat transfer coecients of short pins, which are signi®cantly lower than those of long ®ns, are typically comparable to those at the endwall. Sparrow et al. [1,2] were among the ®rst to investigate the heat transfer performance of in-line and staggered wall-attached arrays of cylindrical ®ns. The longitudinal and transverse spacing-to-diameter ratios were kept ®xed and equal to 3 and 2.6, respectively, while the ®n height varied from 29% to 87.5% of the channel height. The performance comparison between the two dierent ®n arrangements showed that the in-line array provided a higher heat transfer rate than that from the staggered array by a factor of up to 1.2 under conditions of equal pumping power and equal heat transfer area. On the other hand, at a ®xed heat duty and ®xed mass ¯ow rate, International Journal of Heat and Mass Transfer 44 2001) 3529±3541 www.elsevier.com/locate/ijhmt * Tel.: +390-10-353-2881; fax: +390-10-311-870. E-mail address: tanda@ditec.unige.it G. Tanda). 0017-9310/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0017-931001)00018-7