International Journal of Thermal Sciences 48 (2009) 1184–1195 Contents lists available at ScienceDirect International Journal of Thermal Sciences www.elsevier.com/locate/ijts Optimal design of a plate heat exchanger with undulated surfaces A.G. Kanaris, A.A. Mouza, S.V. Paras ∗ Laboratory of Chemical Process and Plant Design, Department of Chemical Engineering, Aristotle University of Thessaloniki, Univ. Box 455, GR 54124, Thessaloniki, Greece article info abstract Article history: Received 17 January 2008 Received in revised form 12 September 2008 Accepted 5 November 2008 Available online 28 November 2008 Keywords: Plate heat exchanger Sustainable design CFD Optimization Response surface methodology The purpose of this study is to suggest a general method for the optimal design of a plate heat exchanger (PHE) with undulated surfaces that complies with the principles of sustainability. A previously validated CFD code is employed to predict the heat transfer rate and pressure drop in this type of equipment. The computational model is a three-dimensional narrow channel with angled triangular undulations in a herringbone pattern, whose blockage ratio, channel aspect ratio, corrugation aspect ratio, angle of attack and Reynolds number are used as design variables. To limit the number of simulations needed, the Box– Behnken technique is employed. An objective function that linearly combines heat transfer augmentation with friction losses, using a weighting factor that accounts for the cost of energy, is employed for the optimization procedure using response surface methodology (RSM). New correlations are provided for predicting Nusselt number and friction factor in such PHEs. The results are in very good agreement with published data. Finally, optimal design specifications are suggested for a range of Re for two values of the weighting factor.  2008 Elsevier Masson SAS. All rights reserved. 1. Introduction The need for designing process equipment that complies with the principles of economic and ecological sustainability (sustain- able design) acted as a driving force towards the evolution in the design of plate heat exchangers (PHE). The advantages of a PHE over conventional heat transfer equipment also increased their ac- ceptance in two-phase flow applications. They are commonly used in process and power industries for a wide range of temperatures due to their compactness, close temperature approach and ease on inspection and cleaning [1,2]. The plates of these heat exchangers comprise some form of near-sinusoidal corrugations in a herring- bone (or chevron) pattern, a design commonly used for PHEs as it is considered the most successful type [3]. It is known [4] that there are two mechanisms for the augmentation of heat transfer, which are also accompanied by pressure loss increase; inducing flow separation and reattachment, and increasing the wall skin friction. When two of these plates are arranged and placed abut- ting, a channel with complicated passages is formed. Due to the breakup and reattachment of boundary layers, secondary flows and small hydraulic diameter of the flow passages, high heat transfer coefficients are achieved. This allows a small requirement in sur- face area, up to one third that of a shell-and-tube heat exchanger for a given duty [4], thus reducing the cost, overall volume and space requirement for the exchanger. Nevertheless, the series of periodic changes in flow direction induces a significant resistance * Corresponding author. E-mail address: paras@cheng.auth.gr (S.V. Paras). to the flow and increases the friction losses. It is therefore appar- ent that, in order to come up with an optimal design, a ‘compro- mise’ between heat transfer and pressure drop must be set. As the plate patterns greatly influence both hydraulic and thermal perfor- mance, the final design is certainly dependent on the initial choice of the plate pattern. The majority of the performance data on this type of equipment are considered proprietary, in a highly competitive PHE market. Thus, the lack of data in open literature has held back the devel- opment of a more generic design model for the corrugated plates of a PHE, even though there are studies referring to the effect of several geometrical parameters on the heat transfer coefficient and the friction factor. For instance, Focke et al. [5] and Heavner et al. [6] provide empirical equations based on experimental data regarding the effect of the corrugation inclination angle on the per- formance of an industrial PHE. Martin [3], in a theoretical approach using the generalized Lévêque equation, provide correlations based on chevron angle for predicting friction factor and Nusselt num- ber in typical PHEs, with limited accuracy (±40%) [4]. Numerical work has also been performed; either on representative elements or in complete conduits. For example, Mehrabian and Poulter [7] study the flow inside a furrow of a PHE with sinusoidal corru- gations, while Hossain and Sadrul Islam [8] study similar control volumes for three different corrugation shapes. Moreover, Asako et al. [9] study the case of rounding the corrugations in wavy pas- sages with constant plate spacing using a numerical approach for low Reynolds numbers. There is an increasing interest on the study of various geomet- rical parameters of the modulated pattern of the plates with the 1290-0729/$ – see front matter  2008 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2008.11.001