Multidimensional Transient Conduction Analysis by Generalized Transfer Functions Tables

Abstract

This work provides a general tool for accurate multidimensional transient analysis by means of polynomial heat conduction transfer functions (CTF) which are valid for the whole class of objects having the same geometric shape. With this aim the governing conduction equations were turned into dimensionless variables, such as the well known Biot number (Bi) and Fourier modulus (Fo), and thereafter handled through a finite-element technique to create the CTF with respect to any arbitrary point of the conductive field. In addition, by selecting the nondimensional time interval (ΔFo) according to the sampling theorem, i.e., as a function of Bi, the CTF were scheduled in the form of one-entry tables. The Bi incremental values were furthermore assessed to provide, for any input function, temperature histories within equal percent deviations, say 10 percent. Since for many purposes a five percent tolerance will usually suffice, the CTF tables can be used without the necessity of interpolating. As an example, generalized CTF tables are presented for the central and one of the corner points of a cube.

Determination of the thermal resistance of walls through a dynamic analysis of in-situ data

“…3-6 to be obtained are much higher (generally 2-4 times) than the conventional dimensions found in Refs. [8,10]. The reason is that the p value is affected not only by the inherent features of the analysed wall, but also and above all by the ones of the input/output signals (concerning this, we recall that the p value is derived exactly from these signals, as discussed in Section 3.2).…”

“…It allows the thermal resistance to be easily recognised and provides the discrete dynamic response of a linear system (in every respect any complex wall may be considered like that) following an original procedure described first in [8], generalised recently in [9] and used several times for accurate thermal analyses in multi-dimensional bodies [9,10]. It is interesting to point out that the obtained result, although shows some part-expected similarities with the ISO 9869, is able to identify the wall without performing further calculations and manipulations.…”