Estudo teórico experimental da dinâmica de temperatura no interior de uma cavidade cilíndrica.

Abstract

Two methods for solving a direct heat diffusion problem inside a cylindrical enclosure are proposed, each one is applied with a linear and plus a non-linear solution. Besides, a experimental apparatus was developed for theoretical models validation purpose. Furthermore, as an application of the proposed system the inverse analysis (inverse problem) is used to determine the thermal diffusivity of a liquid (water). The physical experimental system consists of a hollow cylinder, made from metal material (aluminum), which is filled with a liquid fluid whose thermal diffusivity we want to estimate. A sensor element (PT 1000) should measure the temperature at the points that it must be acquired and controlled. The controller has to compare the actual temperature value with the desired one and send command to actuator (Peltier module), which is physically in contact with the metallic cylinder, responding by heating or cooling system. The temperature inside the liquid is measured by thermocouples and saved in a file through software. Temperature control must ensure the thermal conditions during the actual experimental procedure, what is also object of this study. Regarding the direct problem, heat conduction model, one-dimensional and cylindrical radial symmetry for the transient response of temperature measured at the center of a cylindrical cavity. Following the formal proceedings, the Generalized Integral Transform Technique is one of the methods used to solve the direct problem and thus determine the theoretical temperature field, yielding results of the standard type. Initially, considering the thermal diffusivity constant (linear problem) and, after, another approach considering a linear dependence of the parameter with temperature. A proposal for alternative solution is done using the Network Simulation Method (NSM), first in the classical version of linear solution, and afterward as an innovative version through the use of an element whose electrical resistance varies linearly with the voltage. In addition, the liquid medium is considered stationary, thus, any convective and radiative exchanges inside the medium are neglected. The feasibility of determining the unknown thermal diffusivity, through the proposed device is inferred by analyzing the mathematical representation of this system by comparing it with the experimental results. A MATLAB software was developed to enable the solution of the parameter estimation, which was solved using the norm minimization of the least-squares by Levenberg-Marquardt algorithm. The results show the feasibility of the proposed system.