An inverse problem to estimate temperature dependent heat capacity under convection processes
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Abstract.
Solutions of the heat capacity versus temperature in a one-dimensional slab have been studied for different types of dependency (lineal, sinusoidal, piece-wise and rectangular) under boundary conditions of natural and forced convection on both sides of the slab. The input data of this inverse problem are the temperature history ("measurements") at a particular location within the slab, obtained by adding a specified random error to the set of temperatures which are the solution of the direct problem. No prior information is used as regards the temperature-dependent functional forms of the unknown heat capacity. In all cases, a piece-wise function is used to approach the solution. Using a programming routine that minimises a classical predefined functional, successive stretches of this piece-wise function are obtained step by step by (i) fixing its length and (ii) increasing or decreasing its slope. The Network Simulation Method is used to solve both the direct and inverse problems. No mathematical manipulations of the finite-difference differential equations are required by the programmer, since they are contained in the computer code used in the method. The basic network for the inverse problem, which is basically the same as for the direct problem, is easy to design and has very few devices. Several examples are shown to prove the accuracy and effectiveness of the proposed method.
Keywords
Inverse Problem Nusselt Number Natural Convection Rayleigh Number Forced ConvectionReferences
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