Heat transfer in polymers

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.