1 Copyright © 2009 by ASME Proceedings of IMECE2009 2009 ASME International Mechanical Engineering Congress and Exposition November 13-19, Lake Buena Vista, Florida, USA IMECE2009-12359 A MATHEMATICAL BASED DESIGN METHODOLOGY FOR CROSSFLOW HEAT EXCHANGERS Prof. Antonio Dumas Università di Modena e Reggio Emilia, I 42100 Dipartimento di Scienze e Metodi dell’Ingegneria Reggio Emilia, Italy antonio.dumas@unimore.it Ph.D. Ing. Michele Trancossi Università di Modena e Reggio Emilia, ITIS Nobili, Enexergy sc, I 42100 - EAST srl, I 43100 Reggio Emilia, Italy michele.trancossi@unimore.it ABSTRACT This paper presents a theoretical work, in order to apply well tested experimental correlations by Gnielinski to a lumped parameters analysis of cross-flow heat exchanger. It produces an effective set of equations which could be useful and effective in order to produce an accurate design of staggered and in line heat exchangers, but also heat pipes based exchangers. The presented method can help designer of heat exchangers to design and determinate performances of cross flow heat exchangers starting by the physical properties of a pipe (or heat pipe) and using geometrical parameters of the exchanger produces an effective evaluation of performances of the whole exchanger. INTRODUCTION This work indicate a natural development of a precedent PhD thesis [1] which dedicates a chapter to heat exchanger mathematical modelling, both in case of traditional heat exchangers and in the case of heat pipe exchangers. . Thermodynamic literature presents many well confirmed results which permit a reliable description of some transient phenomena concerning transient behaviour of flat and tube heat exchangers. These results are mostly obtained by lumped parameter analysis of heat exchangers [2 - 9]. Based on the transient heat exchanger models presented in literature, the dynamic behaviour of a heat exchanger could be described mathematically by coupled partial differential equations and algebraic equations, depending on the physical properties of the considered system, both in the case of an air to liquid heat exchanger and a heat pipe heat exchanger. Two cases of heat exchangers have been analyzed under a common set of general hypothesis: - Traditional crossflow heat exchangers; - Heat pipe based heat exchangers. Expressing these governing equations several assumptions will be made. They include: „ all physical properties of the air, heat pipe, or tube wall and water are time dependent; „ external walls of the exchanger has a negligible heat exchange, and they could be considered adiabatic; „ the conduction in the circumferential direction is negligible if compared to the conduction in the radial direction; „ the heat pipes could be modelled as a simple conductors with a high conductivity; „ the refrigerant (water) enter and leaves the tube with uniform temperature and velocity profiles; „ Axial conduction of the refrigerant is negligible. In order to simplify the mathematical model it is possible to assume that the local air temperature around the tube, T h , is the average between its inlet and outlet values, so that 0 1 2 h h h T T T + = (1) In a simplified analysis, it is possible to assume: „ convection from hot air to the walls of the exchanger in the hot air side. „ it has been also assumed that the hot gas is dry air, so there is no moist air and condensation outside the tube. CROSS FLOW TUBE HEAT EXCHANGER In order to describe the behaviour of an heat exchanger under transient conditions some additional hypothesis are necessary. The flow of the refrigerant is assumed to be incompressible and fully developed. The heat transfer proceeds from the tube wall to the water inside, without any axial conduction through the water compared to the bulk temperature. The inlet temperature of the water considered here is the bulk temperature. Bibliography presents many set of equations and different mathematical models. In particular, this paper presents a set of equation completely based on Stanton Number.