| 释义 | 
		Heat Conduction Equation--DiskTo solve the Heat Conduction Equation on a 2-D disk of radius  , try to separate the equation using
    | (1) |  
  Writing the   and   terms of the Laplacian in Spherical Coordinates gives
   | (2) |  
  so the Heat Conduction Equation becomes
   | (3) |  
  Multiplying through by   gives
   | (4) |  
  The   term can be separated.  
   | (5) |  
  which has a solution
   | (6) |  
  The remaining portion becomes
   | (7) |  
  Dividing by   gives
   | (8) |  
  where a Negative separation constant has been chosen so that the   portion remains finite
   | (9) |  
  The radial portion then becomes 
   | (10) |  
 
   | (11) |  
  which is the Spherical Bessel Differential Equation.  If the initial temperature is   and the boundarycondition is  , the solution is
   | (12) |  
  where   is the  th Positive zero of the Bessel Function of the First Kind  . |