Radial or Cross-Channel Diffusion

Use the method of false transients for the Graetz problem in Example 8.4. Specifically, solve the Graetz problem for ajt jV = 0.4 and report your results in terms of the dimensionless temperature 

SOLUTION The heat of reaction and axial diffusion terms are omitted from Equation 8.27 

The velocity profile is parabolic. The inlet boundary condition is T = 0 for all t, the wall boundary condition is T = 1 for all and the problem is axisymmetric. Applying second-order difference approximations to the spatial derivatives gives 

Code for Example 16.2 gives the macro that solves this set of ODEs. Recall that t = 0 is a special case for cylindrical coordinates. 

Unsurprisingly, converged results from this example are identical to converged results from the method of lines solution as generated by Code for Example 8.4. 

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