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TUBULAR: Tubular Reactor Model

from the NEP Collection

Source: K. Meerbergen and D. Roose, Katholieke Universiteit Leuven, Belgium
Discipline: Computational fluid dynamics

The conservation of reactant and energy in a homogeneous tube of length L in dimensionless form is modeled by

L/v dy/dt= -1/P_{e_m}d^2y/dX^2 +dy/dX+D y exp(gamma-gamma T^(-1)); L/v dT/dt = -1/P_{e_h}d^T/dX^2 +dT/dX+beta(T-T_0)-bDy exp(gamma-gamma T^(-1))

where y and T represent concentration and temperature and 0<=X<=1 denotes the spatial coordinate. The boundary conditions are y'(0)=P_{e_m} y(0), T'(0)=P_{e_h} T(0), y'(1)=0 and T'(1)=0. Central differences are used to discretize in space. For X^T=[y_1,T_1,y_2,T_2,...y_{N/2},T_{N/2}], the equations can be written as dot(x)=f(x). The parameters in the differential equation are set to Pem = Peh = 5, B = 0.5, gamma = 25, beta = 3.5 and D = 0.2662. One seeks the rightmost eigenvalues of the Jacobian matrix A=df/dx. A is a banded matrix with bandwidth 5.

Matrices in this set:

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