In this model we considered a scenario similar to that occurring in a microchemical reactor with heat transfer in the flowing direction. The governing equation is the heat equation:
we then posed the conditions:
Because the conditions are determined at the two boundaries of this one-dimensional reactor this is an ODE with boundary value conditions. We solved this model with a finite difference method. Transforming the differential equation into a difference equation gives:
We then partitioned our model into a set of equally spaced points, and constructed a linear algebraic equation from the differential equations relating to those points.
The solution for temperature along the model is:
Click below for our results:
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