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

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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.