Theoretical prediction of longitudinal heat conduction effect in cross-corrugated heat exchanger J.H. Doo a , M.Y. Ha a,⇑ , J.K. Min b , R. Stieger c , A. Rolt c , C. Son a a School of Mechanical Engineering, Pusan National University, San 30, Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea b Rolls-Royce and Pusan National University Technology Centre in Thermal Management, Pusan National University, San 30, Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea c Strategic Research Centre, Rolls-Royce plc, P.O. Box 31, Derby DE24 8BJ, United Kingdom article info Article history: Received 13 September 2011 Received in revised form 22 February 2012 Accepted 22 February 2012 Available online 18 April 2012 Keywords: Longitudinal heat conduction Conjugate heat transfer Cross-corrugated heat exchanger abstract In the elementary heat exchanger design theory, the longitudinal heat conduction through the heat trans- fer plate separating hot and cold fluid streams is neglected, and only the transverse heat conduction is taken into account for the conjugate heat transfer problem. In the cross-corrugated heat exchanger, the corrugated primary surface naturally leads to the highly non-uniform convective heat transfer coef- ficient distribution on opposite sides of the plate. In such a case, the longitudinal heat conduction may play a significant role in the thermal coupling between high heat transfer regions located on opposite sides of the plate. In the present study CFD is used to perform a quantitative assessment of the thermal performance of a cross-corrugated heat exchanger including the longitudinal heat conduction effect for various design options such as different plate thickness and corrugation geometry for a typical operating condition. The longitudinal heat conduction effect is then predicted by the theoretical method using the ‘ network-of-resistance’ in the wide range of the heat exchanger design space. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction In the elementary heat exchanger design using effectiveness- NTU or log-mean temperature difference (LMTD) methods [1], the longitudinal heat conduction (LHC) through heat transfer plates is neglected and only the transverse heat conduction (THC) in the direction normal to the plate surface is taken into ac- count. However, the large scale (or end-to-end) LHC effects of the whole heat exchanger matrix have been introduced by many researchers in recent years [2–8]. In their work, it was reported that the large scale LHC effect results in the deterioration of the thermal performance in terms of the conduction effect factor which accounts the degree of the heat transfer deterioration by LHC for a specified NTU in most heat exchanger types. The deteri- oration becomes most significant in a very high NTU heat exchang- ers such as cryocoolers [3]. In 2007, Ciofalo [9] introduced local effects of the small scale LHC in plate heat exchangers which acts at the length scale of the unit cell. Using the ‘network-of-resistance’ as the approximated theoretical model, the overall heat transfer coefficient (overall HTC) including the small scale LHC effect was predicted for the 2D simple conjugate heat transfer problem, which was validated by numerical simulations. Most plate type heat exchanger matrices are made up of a very large number of unit cells which denote a geometrically periodic element of the whole matrix. Corrugated plates separating hot and cold fluid streams are used not only to improve the convective heat transfer due to the generation of the secondary flow and intensification of the turbulent mixing but also to increase the surface area and thus the compactness of heat ex- changer matrices. The secondary flows such as the flow separation, recirculation and impingement induce highly non-uniform HTCs on opposite surfaces of the corrugated plate. In such a case, the thermal performance predicted on the basis of the elementary heat exchanger design theory would be over-predicted. Cross-corrugated heat exchangers are proposed for application in compact thermal management systems due to their relatively high thermal effectiveness, aerodynamic performance and thus their potential for light weight designs. The investigations on var- ious geometrical shapes of the primary surface have been carried out in order to improve the aero- and thermal performances of the heat exchanger [10–19]. The corrugated primary surface heat exchanger has a highly non-uniform HTC distribution and as a re- sult the longitudinal heat conduction plays a significant role in the thermal coupling between high heat transfer regions located on opposite sides of the plate. In the present study the quantitative estimation of the thermal performance considering the longitudinal heat conduction effect is performed for various design options of the cross-corrugated heat exchanger such as the plate thickness and corrugation geometries 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.03.054 ⇑ Corresponding author. Tel.: +82 51 510 2440; fax: +82 51 515 3101. E-mail address: myha@pusan.ac.kr (M.Y. Ha). International Journal of Heat and Mass Transfer 55 (2012) 4129–4138 Contents lists available at SciVerse ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt