The circular boundary in the centre is insulated, meaning there is no temperature gradient in the normal direction of this boundary

The circular boundary in the centre is insulated, meaning there is no temperature gradient in the normal direction of this boundary. Assume ¢ = 1, then the initial temperature is given by

u(z,y, 0) = sin(rz) cos(ry) + Sz.

Using the PDE Modeller app in MATLAB, plot the temperature over the plate at t = 20. Inctude in your submission:

e acolour plot of the final temperatures,

e a plot of the mesh used,

@ copies of the windows of each boundary condition entered,

@ acopy of the window where the PDE is specified,

@ acopy of the window containing the solve parameters used.

4. A thin plate with a hole in the centre, insulated from above and below, has dimensions as

follows:

1 ;

—__|_—_—___—_»}

: +2

e

@1

b

+ ,

:

Assuming the origin is at the bottom left corner, the outer edges are kept. at. temperatures as

follows:

eo u(f.y,é) —OforO< y <2,

e u(2,y,¢) — 10 forO << y <2,

e@ u(x, Q,t) — sin(ax) + 5x for < x < 2, and

e@ u(x,2,t) — sin(ax) + Sr for 0 < x <2.