1. Five reactors linked by pipes are shown in the following figure. The rate of mass flow through each pipe is computed as the product of flow (Q) and concentration (c). At steady state, the mass flow into and out of each reactor must be equal. For example, for the first reactor, a mass balance equation can be written as Q01c01 + Q31c3 = Q15c1 + Q12c1.
a) Write mass balance equations for the remaining 4 reactors. Put the known values in the 5 equations and convert each equation into a form where left hand side contains all the variables and the right hand side the constant term.
b) Express the equations in the matrix form Ax = b. Show each of the three matrices i.e the coefficient matrix, the variable matrix and the constant matrix.
c) Perform LU factorisation of A using MATLAB. Show commands that you run and the lower triangular matrix L, the upper triangular matrix U and the permutation matrix P.
d) Then use L,U,P matrices in MATLAB to find the values of the variables in your equations. Show your commands and their output.
e) If c03 = 60 and c01 = 30, perform the minimum tasks on MATLAB to find the values of the variables. Show your commands and their output.