Note on a problem in radial flow

The problem of conduction of heat in a circular cylinder with constant flow at the surface is solved by the Laplace transformation method. A previous solution by Macey is shown to be not exact, but a good approximation, and its region of usefulness is compared with that of the other types of solution. It is shown that Macey's idea can be extended to other boundary conditions, constant temperature, or radiation, the result being that with any of these boundary conditions, and constant initial temperature, corresponding times t₁ for a slab, and t for a cylinder, can be found, such that the temperature distribution in the slab at time t₁ is a good approximation to that in the cylinder at time t. Numerical values of t₁ as a function of t are given.