Problem
Consider the problem of diffusion in the annular region shown in Fig. 14.7, which is in solid body rotation at frequency 
. At the inner face at 
while at the outer face at 
In cylindrical coordinates, this is a one-dimensional problem whose exact solution can be obtained. However, we intend to solve for 
in the square region R, using the 
coordinate system, and then the problem is two-dimensional. The quantity 
is the diffusion coefficient. Such a procedure for artificially formulating two-dimensional problems with known analytical solution and the present problem were introduced by Runchal (1972). The relevant dimensional variables are
the problem is governed by the equation
Diffusion in a rotating annular region. |
the exact solution to the problem being
The grid layout on R may be a Cartesian grid-mesh. Compare the accuracy of the computed solution using a finite volume formation. The results are to be compared for an 
grid-mesh.
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