Heat Conduction Transfer Functions: General one-entry Tables for six two-dimensional Solids of Different Geometric Shapes

In this paper we face up to the evaluation of the heat conduction transfer functions for six different classes of homogeneous solids of similar shape. The TFs are proposed in a generalized form so as to be applied to the whole family of objects having the same geometry. This is achieved by handling the governing conduction equation in terms of dimensionless variables such as the Biot number (Bi) and the Fourier modulus (Fo). Then by choosing the dimensionless time interval according to the sampling theorem, namely as a function of Bi, the TFs coefficients may be scheduled in the form of suitable one-entry tables. The selected incremental steps meet the requirement of grading the temperature responses within a 10 % maximum deviation. Since for engineering purposes a 5 % error range will normally suffice, the TFs coefficients tables can be used without the necessity of tedious temperature interpolations. Each of the six TFs tables is referred to some relevant points of the solid field such as the central and boundary ones.