40 



IOWA ACADEMY OF SCIENCE Vol. XXV, 1918 



and that the can is suddenly immersed in a bath which is main- 

 tained at a constant temperature. 



t20 



Fig. 1. 



The general differential equation of symmetrical heat con- 

 duction in a right circular cylinder expressed in cylindrical co- 

 ordinates is 



9V . 9'V 

 IT 3Z* 



■U) 



V being the variable temperature at any point in the cylinder, r 

 the perpendicular distance of this point from the axis of the cyl- 

 inder, z the distance from the center of the cylinder along the axis 



of the base of r, and k the diffusivity . I -= r; rs — r — i 1 



I density x specmc heaty 



of the material, and t the time^. 



The initial conditions which must be satisfied under the as- 

 sumed ideal conditions are that 



V = o at r == a (2) 



and v=o at z=±\ (3) 



and v=Vo at every point of the cylinder when t=o (4) 



where a is the radius of the cylinder, 2 1 the length, and Vq the 

 initial temperature of the cylinder. 



