Apply the finite difference method to find the algebraic representation of the governing equations for each node.

Application of ODEs in chemical reaction engineering
Reactions in series are commonly occurring in chemical engineering. This task is an open-ended assignment regarding the application of advanced mathematics in analyzing the reaction kinetics in a series of reactions. To keep the flow of the solution at a consistent level, use the below set of reactions in a batch reactor and find the changes of concentration over time for all the species via the general mole balances approach. Solve the resulting ODEs using three methods stated below and compare the results via MATLAB:
𝐴 𝑘1
→ 𝐵 𝑘2
→ 𝐶
a) The analytical solution using the exponential functions
b) Laplace transformation pathway with presumed initial conditions
c) Numerical methods and approximation of derivations
d) Using parameter tuning in your programming, obtain various trends under which B
concentration peaks and degrades. What parameters influence this behaviour and how?
Dr A. Taheri, University of Greenwich
2
Applications of PDEs in 2d conductive heat transfer
For a two-dimensional heat transfer in the figure below, find the temperature at the four internal
nodes while addressing the questions:
a) Derive the governing equations for heat transfer under steady-state conditions .
b) Apply the finite difference method to find the algebraic representation of the governing
equations for each node.
c) Pick a temperature for each side of the sample within the given range and calculate the temperatures at the internal nodes. Use two different methods for solving simultaneous eqiations in MATLAB.
d) Create 9 internal nodes  and find the temperature distributions in that case.
Research the suitable approaches to build the resulting equation system and solve it using
MATLAB to obtain the temperatures.