Solve the system using n nodes and finite difference approximation

The partial differential equation governing this system is:

*(²/² + ²/²) = 0 (1)

The first term in equation 1 represents the distribution of chemical due to dispersion. The second term quantifies the chemical reaction involving the consumption of the chemical. The parameter values are reported in Table 1.

Table 1. Parameter values. Parameter Symbol Unit Value Reaction rate min^-1 0.1 Dispersion coefficient m² min^-1 0.5 Reactor length m 30 Reactor width m 10

Perform the following tasks:

1) Solve system reported in Eq. 1 using n nodes and finite difference approximation for ²/² AND ²/²

Boundary conditions according to the conditions reported in figure 1 are as follows:

=40 =0 0

2) Determine the number of nodes to obtain an acceptable solution of the spatial distributions of the chemical concentration. Once the optimal number of nodes are determined, compare the simulations obtained with 50%, 100% and 200% of the base case value of the model parameters: and . Discuss the results.

The partial differential equation governing this system is 30 40 1 Open boundary c= 100 Wall 10 Figure 1. Boundary conditions of the reactor The first term in equation 1 represents the distribution of chemical due to dispersion. The second term quantifies the chemical reaction involving the consumption of the chemical. The parameter values are reported in Table 1 Table 1. Parameter values. Value Parameter Reaction rate Dispersion coefficient Reactor length Reactor width Svmbol Unit min mmn 30 10 Perform the following tasks: 1) Solve system reported in Eq 1 using n nodes and finite difference approximation or ay Boundary conditions according to the conditions reported in figure 1 are as follows c=40 ac 0