Numerical solutions to equations:
Many practical problems in engineering involve complex boundary conditions and variable properties that cannot be solved analytically, creating the need for a numerical solution. Numerical methods require setting up equations that can be solved with different numerical schemes, unlike analytical solutions which are derived by solving the governing differential equations together with the boundary conditions. According to Cengel (1998), results obtained with numerical methods are flexibility and a better model of the system in consideration is obtained.
The numerical scheme that will be used in this work is the finite element method.