HTC

Determination of Heat Transfer Coefficients by Inverse Methods

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 Obiettivo del progetto (Objective)

'In this proposal, we consider the reconstruction of (multi-dimensional) heat transfer coefficients from both steady and transient surface temperature measurement input, and investigate a regularized boundary element method to this inverse problem in a framework that can ultimately be incorporated within industrial computational fluid dynamics codes. The research will be performed by the internationally incoming fellow (visitor, Professor Dinh Nho Hao, Hanoi Institute of Mathematics, Vietnam) in colaboration with the scientisty in charge (host, Professor D. Lesnic, Department of Applied Mathemnatics, University of Leeds, UK). The project combines the efforts of applied mathematicians in collaboration with engineers and industry to impact on solving fundamental inverse problems with practical applications in the reconstruction of heat transfer coefficients. The area of research that this project proposes is fascinating and challenging, with wide applications in the heat transfer and polymer industries, e.g. in cooling of hot steel or glass in fluids or gases, but previously with relatively little theoretical input and numerical computations, especially in higher dimensions. The current state of the art is still very much based on practical experience and technical know-how, despite recent advances in technology. The focus of the present study will be therefore to make progress on such inverse identifications of heat transfer coefficients, which can be time, space or temperature dependent, from all theoretical, numerical, experimental validation and design recommendation aspects. The techniques to be developed will be used to predict the efficiency of industrial devices, based on the inversion of real-life experimental data provided by several laboratories performing heat transfer experiments. This in turn will offer new and revolutionary suggestions for the design of such devices in order to optimize their performance.'

Introduzione (Teaser)

Traditionally, how polymer parts perform under conditions of high heat is determined through extensive empirical work, which is time consuming and costly. EU-funded researchers, aided by the growth of numerical simulations, developed a more systematic approach to predicting their operational efficiency.

Descrizione progetto (Article)

A critical aspect of the approach developed within the 'Determination of heat transfer coefficients by inverse methods' (HTC) project was to determine heat transfer on the surface of polymer parts. To calculate the heat transfer conditions, both surface temperature and heat flux must be estimated. These properties are difficult to determine directly from measurements.

In this light, inverse methods developed by HTC researchers allow estimation of boundary conditions from the thermal history in the interior of the solid. Specifically, the procedure involves measurements of the temperature response inside the particular part, which are subsequently converted into heat flux and temperature at the surface.

This so-called inverse heat conduction method leads to an ill-posed problem, which does not satisfy criteria for the existence, uniqueness and stability of its solution. In the past, many efforts were devoted to obtain a solution that is accurate and not sensitive to noise in the temperature measurements. Additionally, problems examined concerned solely the estimation of boundary heat flux and temperature.

The HTC team focused on heat transfer coefficients, accompanying heat transfer across the solid's surface. They treated the problem of estimating space-, time- and temperature-dependent coefficients both as a linear and a non-linear problem. To obtain a physically realistic solution, a new regularisaton technique was employed, the conjugate gradient method.

A series of numerical experiments were conducted to verify the effectiveness of the method to suppress sensitivity to noise in the computed solution. Initially evaluated for problems arising in the design of polymer structures and products, HTC research will be continued to cover metal casting and finned-tube heat exchangers.

There is significant research still to be conducted in inverse problems theory, but the first steps have been made. More importantly, further applications are expected to be identified through close collaboration with HTC industrial partners. Adoption of efficient computational techniques should contribute to the competitiveness of European industry.