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Analysis of the Constitutive Equations Influence on a Model of Roll-Bond Evaporators Used in Domestic Refrigerators

Grant number: 14/09049-5
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): August 01, 2014
Effective date (End): July 31, 2015
Field of knowledge:Engineering - Mechanical Engineering - Thermal Engineering
Principal Investigator:André Luiz Seixlack
Grantee:Raul Maziero Nogaroto
Home Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

This work proposes an analysis of a model to simulate the unsteady refrigerant fluid flow and heat transfer along a roll-bond evaporator installed inside the cabinet of a static household refrigerator. This model is divided into two stages, one for the evaporator and other for the cabinet. The analysis of the evaporator involves the refrigerant flow inside the channel formed by powder-coated aluminum. This channel is separated by fillets that act as a single fin, causing significant heat transfer by conduction in the evaporator plate. The powder-coated aluminum channel is considered as a single vertical flat plate, where conduction heat transfer takes place along horizontal and vertical directions. Heat transfer by free convection and radiation between the evaporator plate and the air inside the cabinet is taken into account. The refrigerant flow inside the channel is divided in two regions: a two-phase flow, of liquid-vapor, and another of single-phase flow, of superheated vapor. The refrigerant flow is assumed to be one-dimensional and a homogeneous flow model is employed for the two-phase flow. The influence of the curvature of the channels on the flow is disregarded, although the pressure drop inside the channels is taking into account. The fundamental equations governing the flow through evaporator are derived from the mass conservation, momentum and energy conservation laws. The heat conduction equation is also solved to obtain the temperature distribution along the evaporator plate. A Finite Volume approach is used to obtain the discretization of the governing partial differential equations and the resulting set of algebraic equations is solved by successive iterations. The mean air temperature inside the cabinet and the temperature of its external and internal surfaces are evaluated by modeling the heat transfer by free convection and radiation only and not the air flow inside the cabinet. The cabinet is taken as a rectangular cavity and heat conduction through the walls is considered to be one-dimensional. The conductive resistance of the internal and external cladding materials, which have high thermal conductivity, is disregarded and the heat conduction through the thermal insulation, which has low thermal conductivity, is analyzed according to a differential formulation. The model allows prediction of the temperature, pressure and enthalpy distributions of the refrigerant along the channel and the evaporator plate temperature distribution, as functions of the geometrical parameters and operating conditions, in both steady and unsteady states. Also, the model is capable of predicting the thermal load, the mean air temperature inside the cabinet and the internal and external walls temperatures. The model was validated by comparing its results with experimental data available in the literature and / or obtained by other models. During the development of this model, it was noted that its results were dependent on the constitutive equations used in the calculation of pressure drop due to friction of the flow through the evaporator, the convective heat transfer coefficient between the refrigerant and internal walls of the evaporator, the convective heat transfer coefficient between the evaporator and the air inside the cabinet, among other parameters. Thus, this work proposes to carry out a sensibility analysis of the model to verify the influence of these correlations on the results obtained and define the set of constitutive equations that result in the lowest average relative difference between the experimental data obtained in the literature, and calculated results.