Simulación numérica mediante analogía termoeléctrica de problemas de transmisión de calor en distintas geometrías con propiedades de los materiales dependientes de la temperatura

Abstract

In solving heat transfer problems, one of the most common approaches is to assume that material properties are constant with temperature. However, in order to model and simulate this type of problems more accurately, it could be interesting to consider the density, thermal conductivity and specific heat of materials varying with temperature. Therefore, in the thesis, the general objective was the implementation of heat transfer problems considering the dependence of material properties on temperature. In this sense, examples and tests with different materials and different geometries were proposed in order to quantitatively and qualitatively evaluate the reduction of errors and, thus, the highest calculation accuracy in the numerical resolution of heat transfer processes. The methodology followed consisted of several distinct phases. First, mathematical models were developed for different geometries (flat wall, cylindrical and spherical) to solve the heat transfer problems, considering in all cases models with temperature-dependent material properties. Secondly, the network models equivalent to the mathematical models previously developed for each of the geometries were designed. In this way, the equivalent circuits were defined for each of the cells associated with each geometry. Then, the network models were programmed in Matlab and Ngspice and the different possibilities for the graphical representation of the solution of the problems were programmed. Before starting the simulations of real problems, the software was validated by means of a laboratory test comparing the results obtained experimentally with the results obtained by the program. For this purpose, three bottles of different materials commonly used in water consumption were taken, with a double objective: firstly, to validate the proposed model with experimental data and, secondly, to study the temperature variation inside the bottle, since this could lead to an increase in the migration of substances to the liquid in plastic materials. The results obtained in the experiment led us to conclude that the software implemented faithfully followed the reality of what happened in the laboratory and was therefore validated favourably After this experiment, problems were simulated with the software for the different geometries. Four different simulations were performed: cylindrical tank with liquid ethanol and AISI 316 stainless steel; spherical tank with liquid CO2 and AISI 304 stainless steel; cylindrical bottle with ammonia and Al 7075 aluminum and Al 6061 aluminum door. For all these examples, the existing effect of considering or not considering temperature-dependent material properties and the error made when considering them constant were compared. As conclusions of the thesis it can be stated, on the one hand, that the variability of the properties of the materials: density, thermal conductivity and specific heat, must be taken into account when simulating heat transfer problems where greater precision in the results is required and, on the other hand, that the program developed in Matlab, allows simulating problems with the geometries: flat, cylindrical and spherical wall considering the properties dependent on temperature, following an equation of degree two at most, thus minimizing the calculation error with respect to that which would be committed considering the constant properties.