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# axisymmetric_heat

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# axisymmetric_heat   {  AXISYMMETRIC_HEAT.PDE    This example demonstrates axi-symmetric  heatflow.  The heat flow equation in any coordinate  system is         div(K*grad(T)) + Source = 0.  The following problem is taken from  Zienkiewicz, "The Finite Element Method  in Engineering Science", p. 306 (where  the solution is plotted, but no dimensions  are given). It describes the flow of heat  in a spherical vessel.  The outer boundary is held at Temp=0,  while the inner boundary is held at Temp=100. }   title "Axi-symmetric Heatflow " coordinates

ycylinder("R","Z")   { select a cylindrical coordinate system, with

the rotational axis along the "Y" direction

and the coordinates named "R" and "Z" }

variables

Temp             { Define Temp as the system variable }

definitions

K = 1             { define the conductivity }

source = 0       { define the source (this problem doesn't have one) }

Initial values

Temp = 0         { unimportant in linear steady-state problems }

equations           { define the heatflow equation: }

Temp : div(K*grad(Temp)) + Source = 0

boundaries         { define the problem domain }

Region 1         { ... only one region }

start(5,0)

natural(Temp)=0 { define the bottom symmetry boundary condition }

line to (6,0)

value(Temp)=0   { fixed Temp=0 in outer boundary }

line to (6,3)   { walk the funny stair-step outer boundary }

to (5,3)

to (5,4)

to (4,4)

to (4,5)

to (3,5)

to (3,6)

to (0,6)

natural(Temp)= 0   { define the left symmetry boundary }

line to (0,5)

value(Temp)=100     { define the fixed inner temperature }

arc( center=0,0) to close   { walk an arc to the starting point }

monitors

contour(Temp)     { show contour plots of solution in progress }

plots               { write these hardcopy files at completion }

contour(Temp)     { show solution }

surface(Temp)