New Temperature and Heat Loss Charts for One-Dimensional, Transient Heat Conduction

Abstract

New temperature and heat loss charts have been created for one-dimensional, transient conduction. In the new charts, time is scaled by a weighted sum of the lumped capacitance time scale tLC and the diffusion time scale tdiff: tref=a tLC+b tdiff, where a and b are constants. As the Biot number approaches zero, the diffusion time scale is much smaller than the lumped capacitance time scale (tdiff≪tLC), so the new time scale is equivalent to the lumped capacitance time scale. As the Biot number approaches infinity, the diffusion time scale is much larger than the lumped capacitance time scale (tdiff≫tLC), so the new time scale is equivalent to the diffusion time scale. Using the new time scale, the dimensionless temperature excess and heat loss fraction can be compactly presented in a single plot. The new time scale and associated plots cast new light on some fundamental aspects of the study of conductive heat transfer, and simplify the design process.