Numerical Methods in Transient Heat Conduction : 3rd Report, One-Dimensional Problems in Cylindrical Co-Ordinate System

Abstract

In this paper, the following problems about one-dimensional transient radial heat conduction in cylindrical co-ordinate system are discussed: (1) Difference equations of explicit type for boundary conditions of no flux across the surface, prescribed heat flux across the surface, linear heat transfer at the surface, non-linear heat transfer, contact with a well-stirred fluid or perfect condutor, and the surface of separation of two media of different conductivities are given. (2) The truncation errors by those difference equations are shown in series expansion. (3) The stability conditions of those difference equations are shown. (4) The effective domain covered with those difference equations is shown, by comparing them with difference equations for one-dimensional rectangular co-ordinate system which are given in our former report. (5) at_min/(Δr)²≥0.4∼2.6, t<min>/Δt≥6 are shown to be of sufficient conditions for the above difference equations, to obtain numerical solutions of accuracy within 2∼3% of the maximum temperature change.