A Method for Determining Self-Similarity: Transient Heat Transfer with Constant Flux


  • Charles Monroe University of California
  • John Newman University of California


This simple example demonstrates the physical significance of similarity solutions and the utility of dimensional and asymptotic analysis of partial differential equations.  A procedure to determine the existence of similarity solutions is proposed and subsequently applied to transient constant-flux heat transfer. Short-time expressions follow from  expansion of the Laplace transform and similarity transformation when the outer wall is considered far away. Comparison of these results illustrates the connection between a semi-infinite geometry and short-time behavior.

Author Biographies

Charles Monroe, University of California

Charles Monroe recently completed his graduate study at the University of California, where he investigated dendrite formation in lithium/polymer batteries with Dr. Newman. He earned a BS from Princeton University in 1999, received the 2002 Dow Award for Excellence in Teaching, and was granted a doctoral fellowship for 2003 by the Shell Foundation. Recently, he joined the Department of Chemistry at Imperial College, London, as a Research Associate.

John Newman, University of California

John Newman joined the Chemical Engineering faculty at the University of California, Berkeley, in 1963, and has been a faculty senior scientist at Lawrence Berkeley National Laboratory since 1978. His research involves modeling of electrochemical systems, including industrial reactors, fuel cells and batteries, and investigation of transport phenomena through simulation and experiment.