Using the Scilab software and the reference data, write a program that determines:
a) The temperatures at the inner nodal points in the system, the position vectors of the
inner nodal points, and the von Neumann stability coefficient as a function of the
dimensions of the plate, the element size, the temperatures at the boundaries, the
thermal diffusivity of the material, the defined time-step, the total run time, and a vector
containing the temperatures at the inner nodes for the initial conditions of the system
by applying the BTCS method.
$[T,x,y,r] = f (L_x, L_y, h, T(0,y,t), T(L_x, y, t), T(x, 0, t), T(x, L_y, t), a, \Delta t, t_{end}, T(x, y, 0))$
b) The temperatures at the inner nodal points in the system, the position vectors of the
inner nodal points, and the von Neumann stability coefficient as a function of the
dimensions of the plate, the element size, the temperatures at the boundaries, the
thermal diffusivity of the material, the defined time-step, the total run time, and a vector
containing the temperatures at the inner nodes for the initial conditions of the system
by applying the FTCS method.
$[T,x,y,r] = f (L_x, L_y, h,T(0, y, t), T(L_x, y, t), T(x, 0, t), T(x, L_y, t), a, \Delta t, t_{end}, T(x, y, 0))$
c) The surface graph that shows the variation of the temperature with respect to the
position in the plate and a graph that shows the heat map of the temperatures in the
plate for each time-step. The program should also be able to store the snapshots of
the graphs corresponding to each time-step in the simulation.
Results
The results will be based on the stored snapshots of the graphs that must be generated
using the program for each case. Additionally, a video needs to be produced that shows
the evolution of the system using the snapshots for each case.