Abstract—In the present paper the design of plate heat exchangers is formulated as an optimization problem considering two mathematical modelling. The number of plates is the objective function to be minimized, considering implicitly some parameters configuration. Screening is the optimization method used to solve the problem. Thermal and hydraulic constraints are verified, not viable solutions are discarded and the method searches for the convergence to the optimum, case it exists. A case study is presented to test the applicability of the developed algorithm. Results show coherency with the literature. Keywords—Plate heat exchanger, optimization, modeling, simulation. NOMENCLATURE ܣ ௉ Plate effective area, m 2 ܣ ̿ Eigenvalues and eigenvectors matrix  Average thickness channel, m ܤ ത Binary vector  ௣ Heat capacity, J/kg·K ܥ ௥ Heat capacity ratio ܥ ̅ Coefficients vector ܧExchanger effectiveness, % IS Initial set of configurations  ௉ Plate thermal conductivity, W/m·K ܮ ௉ Plate length, m ܯ ሶ Mass flow rate, kg/s ܯ ന Tri-diagonal matrix  Number of channels per pass  ஼ Number of channels  ௉ Number of plates  Number of transfer units OS Optimal set of configurations  Number of passes RS Reduced set of configurations ݏ ௜ Binary parameter for flow direction ݐ ௉ Plate thickness, m  Global heat transfer coefficient, W/m 2 ·K ݒFluid velocity inside channels, m/s  ௉ Plate width, m  ௛ Binary parameter for hot fluid location ݖ ௜ Eigenvector of the tri-diagonal matrix Greek symbols ߙHeat transfer coefficient ߚAngle of inclination of the F. A. S. Mota was with the State University of Maringá, Brazil. He is now with the National Institute for Space Research (INPE), São José dos Campos, Brazil (e-mail: ravag@deq.uem.br). M. A. S. S. Ravagnani is with the State University of Maringá, Brazil. (e-mail: author@lamar. colostate.edu). E. P. Carvalho is with the State University of Maringá, Brazil. ∆ Pressure drop, Pa η Normalized plate length θ Dimensionless fluid temperature ߣEingevalue of the tri-diagonal matrix Φ Enlargement factor of the plate area ϕ Parameter for feed connections position Subscripts ݋ Cold fluid ܥܥCountercurrent ݋ ݐHot fluid  Generic element  Inlet  Generic element ݋ ݐݑOutlet Superscripts I Odd channels of the heat exchanger II Even channels of the heat exchanger  ݔMaximum  Minimum I. INTRODUCTION HE competitive pressures and the increasing interest in the energy conservation and reduction of the environmental impacts have changed the focus on the industrial processes for the use of heat exchangers with high effectiveness. Although the plate heat exchanger (PHE) is classified at the lower end of compactness, it offers several advantages and unique characteristics when compared with compact heat exchangers. It is due to the flexible thermal design (the plates can simply be added or removed to attend different demand of heat duty and processing), cleaning facilities to maintain extreme hygiene conditions (necessary when food, pharmaceutical or other kind of products are processed), good temperature control (necessary in cryogenic uses) and better performance in heat transfer [1]. Due to its characteristics it became ideal for diary, pharmaceutical, food and drink industries [2]. In the present paper we developed an optimization algorithm based on the screening method to find the optimal set of configurations for a specified plate heat exchanger. II. MATHEMATICAL MODELING Before presenting the two modeling approaches we shall introduce five parameters for characterization of the PHE configuration:  ஼ ,  ூ ,  ூூ , ߶ ,  ௛ . These parameters were showed in Gut and Pinto [3]. Number of channels ( ஼ ): The space between two adjacent plates is a channel. The end plates are not considered, thus the number of channels of a PHE is the number of plates minus one (Fig. 1). The odd-numbered channels belong to side I, and the Comparative Analysis of Two Modeling Approaches for Optimizing Plate Heat Exchangers Fábio A. S. Mota, Mauro A. S. S. Ravagnani, E. P. Carvalho T World Academy of Science, Engineering and Technology International Journal of Physical and Mathematical Sciences Vol:8, No:3, 2014 629 International Scholarly and Scientific Research & Innovation 8(3) 2014 scholar.waset.org/1307-6892/10002329 International Science Index, Physical and Mathematical Sciences Vol:8, No:3, 2014 waset.org/Publication/10002329