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RIMNI - An International Journal of Numerical Methods for Calculation and Design in Engineering (Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería) is a peer-reviewed Open Access journal, founded in 1985. RIMNI contributes to the spread of theoretical advances and practical applications of numerical methods in engineering and other applied sciences. RIMNI publishes articles written in Spanish and English. The journal's scope includes Computational and Numerical Models of Engineering Problems, Development and Application of Numerical Methods, Advances in Software, Computer Design Innovations, Educational Aspects of Numerical Methods, Soft Computing, Machine Learning, Artificial Intelligence, etc. RIMNI is an essential source of information for scientists and engineers in numerical methods theory and applications. RIMNI contributes to the interdisciplinary exchange and thus shortens the distance between theoretical developments and practical applications. This journal is published quarterly by Scipedia.

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Abstract

In this paper, we analyse the numerical approximation of the heat transfer problem between two subdomains that we will consider filled with a fluid and separated by a thin solid wall. First of all, we state the problem in the whole domain with discontinuous physical properties. As an alternative and under certain assumptions on the separating walls, a classical Robin boundary condition between the fluid domains is obtained, thus eliminating the solid wall, and according to which the heat flux is proportional to the temperature difference between the two subdomains. Apart from discussing the relation between both approaches, we consider their numerical approximation, considering different alternatives for the first case, that is, the case in which temperatures are also computed in the solid wall.

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This work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity numerical simulations are costly and cannot be used, in general, for real-time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real-time the transient heat equation at the monitored point. In order to apply the reciprocity principle, harmonic analysis is used in the space-frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre-computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post-processing step. This last step can be performed online for real-time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.

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