Numerical tool for the inverse estimation of the heat capacity temperature-dependent using Pspice

Abstract

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.

In this paper a variant of the Sequential Function Specification Method has been used together with Network Simulation Method as the numerical method to solve an inverse problem associated with the determination of the heat capacity. It has been developed a software application for estimation the temperature dependence of heat capacity using the Qt platform and programming language Visual C++. A set of temperatures measured at different points of the medium (obtained by means the numerical solution of the direct problem) and a random error affected by a normal distribution are used for evaluation of the classical functional that compares these temperatures with the temperatures obtained numerically at each step , and so an iterative least-squares approach function is obtained (heat capacity) by straight sections (piecewise function). No prior information is used for the functional forms of the unknown specific heat, because this problem is considered a function estimation problem. A special device that generates a piecewise temperature-dependent function is required in conjunction with a programming routine. The Network Simulation Method is the numerical method used, with a design of the network model easy and has very few electric devices. The software developed is used to run the network so that no mathematical manipulations are required. The effect of different parameters over the numerical solution has been studied. The results confirm that it is possible to estimate the heat capacity (or specific heat when the density is known) using experimental temperature history and a procedure inverse based in an iterative process.