Solid Cylinder Key Problem

Reconsider the Bat plate (key problem) now for an infinitely long cylinder of diameter 2R. The exact analytical solution of this problem (see, for example, Ex. 5.8 of Reference 1) may be implicitly expressed as 

The heat transfer Q over a time interval (0, r) and per unit length of this cylinder relative to the initial internal energy of the cylinder per unit length, 

The one-dimensional charts for a flat plate and an infinitely long cylinder can be used to determine the temperature of a cylinder of finite length. It can be shown that the dimensionless unsteady temperature of a solid cylinder of height 2H and diameter 2R may be expressed as the product of the dimensionless temperature of a flat plate of thickness 2H and the temperature of an infinitely long cylinder of diameter 2R, 

Reconsider Ex, 3.10 for a finite solid cylinder of height 2H — 5 cm and diameter 2R—S cm. We have already obtained, for a flat plate of thickness 2H = 5 cm, 

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