`Mathematical Problems in EngineeringVolume 2006, Article ID 48542, 13 pageshttp://dx.doi.org/10.1155/MPE/2006/48542`

## Levenberg-Marquardt application to two-phase nonlinear parameter estimation for finned-tube coil evaporators

1Products Research & Development, Tecumseh do Brasil Ltda, P. O. Box 54, São Carlos, SP CEP 13565-900, Brazil
2Department of Mechanical Engineering, São Paulo State University, (UNESP), P. O. Box 31, Ilha Solteira, SP CEP 15385-000, Brazil

Received 30 August 2004; Revised 19 June 2005; Accepted 7 July 2005

Copyright © 2006 S. S. Bueno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A procedure for calculation of refrigerant mass flow rate is implemented in the distributed numerical model to simulate the flow in finned-tube coil dry-expansion evaporators, usually found in refrigeration and air-conditioning systems. Two-phase refrigerant flow inside the tubes is assumed to be one-dimensional, unsteady, and homogeneous. In the model the effects of refrigerant pressure drop and the moisture condensation from the air flowing over the external surface of the tubes are considered. The results obtained are the distributions of refrigerant velocity, temperature and void fraction, tube-wall temperature, air temperature, and absolute humidity. The finite volume method is used to discretize the governing equations. Additionally, given the operation conditions and the geometric parameters, the model allows the calculation of the refrigerant mass flow rate. The value of mass flow rate is computed using the process of parameter estimation with the minimization method of Levenberg-Marquardt minimization. In order to validate the developed model, the obtained results using HFC-134a as a refrigerant are compared with available data from the literature.