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.

Issue Section:
Conduction Heat Transfer
Keywords:
Conduction, Numerical Methods, Transient & Unsteady Heat Transfer
Topics:
Heat conduction, Transfer functions, Transient heat transfer, Corners (Structural elements), Finite element analysis, Heat transfer, Numerical analysis, Polynomials, Shapes, Temperature, Theorems (Mathematics), Transient analysis, Transients (Dynamics)
1.
Brunello, P., and Nonino, C., 1987, “Thermal Response Factors for Heating Panels in Buildings,” Proceedings of the XVII International Congress of Refrigeration, Vol. E, pp. 115–120.
2.
Jury, E. I., 1964, Theory and Applications of the z-Transform Method, John Wiley, NY.
3.
Marcotullio, F., and Ponticiello, A., 1993, “Determination of Transfer Functions in Multidimensional Heat Conduction by Means of a Finite Element Technique,” Numerical Methods in Thermal Problems, Lewis, R. W. et al., eds., Vol. VIII, Part 1, pp. 226–236, Pineridge Press Limited, Swansea, UK.
4.
Marcotullio, F., and Ponticiello, A., 1994, “Generalized Heat Conduction Transfer Functions in Two-Dimensional Linear Systems of Assigned Geometry,” Advanced Computational Methods in Heat Transfer III, Wrobel, L. C. et al., eds., pp. 35–42, Computational Mechanics Publications, Southampton, Boston.
5.
Mascheroni
R. H.
,
Sanz
O. D.
, and
Dominguez
M.
,
1987
, “
A New Way to Predict Thermal Histories in Multidimensional Heat Conduction: the z-Transfer Function Method
,”
Int. Comm. of Heat & Mass Transfer
, Vol.
14
, pp.
81
–
90
.
6.
Stephenson, D. G., and Mitalas, G. P., 1971, “Calculation of Heat Conduction Transfer Function for Multilayer Slabs,” ASHRAE Transactions, Part 2, pp. 117–126.
7.
Zienkiewicz, O. C., 1977, The Finite Element Method, McGraw-Hill, London.
This content is only available via PDF.
Copyright © 1997
 by The American Society of Mechanical Engineers
You do not currently have access to this content.