Transient heat conduction at low Biot numbers: A supplement to Heisler's charts

Abstract

Charts for trasient heat conduction in a cylinder of infinite length, an infinite flat plate, and a sphere are presented for a range of Biot numbers ($\text{1}\text{100}\text{to}\text{1}\text{1000}$) relevant to problems which involve cooling by natural convection. These charts may be easily combined to solve for temperature histories of different bodies, including cylinders of finite length. Analyses of the minute temperature gradient within finite cylinders for the range of Biot numbers studied and the accuracy of a simplified solution, the lumped capacity analysis, are presented in tables for the infinite plate and infinite cylinder; these solutions can be combined to solve for cylinders of finite length.