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Thermal diffusivity of non-flat plates using the flash method


A. Salazar1, R. Fuente1, E. Apiñaniz1 and A. Mendioroz1

1Fisika Aplikatua I Saila, Euskal Herriko Unibertsitatea, Spain

Keywords: flash method
property: thermal difussivity
material: non-flat slabs

The flash method [1] is one of the most acknowledged techniques used to measure the thermal diffusivity. In fact, in many countries it is currently considered as a standard for thermal diffusivity measurements of solid materials. This technique consists of heating the front surface of an opaque sample by a brief light pulse and detecting the temperature evolution at its rear surface. Then, thermal diffusivity is obtained by measuring the time corresponding to the half maximum of the temperature rise; this parameter depends only on the sample thickness and thermal diffusivity through the following simple formula: t1/2=0.1388 L2/D. Therefore, the flash method is a fast way for calculating the thermal diffusivity.

Up to now, the flash method has only been applied to flat samples. The aim of this work is to extend this method to non-flat slabs. In particular, we will study plates with cylindrical and spherical shapes. First, we develop a theoretical model to calculate the temperature rise above the ambient at the rear surface of cylindrical and spherical plates illuminated by a uniform and brief light pulse. The theoretical model indicates that the effect of the curvature is almost negligible, so the expression normally used for flat samples can also be applied to cylindrical and spherical plates that are not extremely curved. Accordingly, a curvature limit for the application of the expression for flat samples is established.

In order to confirm the validity of the model, flash measurements on lead foils of cylindrical shape have been performed. This material is very suitable for our aim because it has high ductility and malleability and it can be easily shaped. In addition, it has a high thermal conductivity so that the influence of heat losses can be neglected. We have measured the rear surface temperature rise of several lead foils of the same thickness (2 mm) but different curvatures (ratio between the thickness and the inner radius) from 0 up to 0.57. Only for this last one a small overestimation of the thermal diffusivity was found. In summary, in this paper we have demonstrated theoretically and experimentally that the flash method can be extended to non-flat plates, provided their curvature is smaller than 0.5.

This work has been supported by the Ministerio de Ciencia e Innovación (MAT2008-01454).

References
  1. W. J. Parker, R. J. Jenkins, C. P. Buttler, and G. L. Abbott, J. Appl. Phys. 32, 1679 (1961)

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