hadley

The displacement of the midpoint from the equilibrium is approximately -0.324 when t=1.8

A metal bar with length = 1. Temp given by g(x) = 5x^2 - 3x. At t=0, the left end pt is T=-2 and the right end pt is T=-3. Sketch the temp distribution at t=0, t=0.01, t=0.1, and t=10

Correction! I forgot to set the Dirichlet boundary on the circle as well. The temperature at the midpoint of the insulated edge of the triangle is now 0.31130 after 1s.

My Matrix was ;

matrix = [

[0,2,1,3,3],

[3,0,4,3,4],

[1,1,0,1,4],

[1,2,2,0,2],

[4,1,3,2,0]

]

Eigen Ranking ;

My best team being Team 2 by far.

For the condition $k = 0$ and $f = 0$, the steady-state temperature of the lower right corner of the bar is $0.89962.$

Heat flow with a constant internal heat source is governed by $u_t = 3u_{xx} + 3$, $u(0,t) = -4$, $u(1,t) = 5$ Find the steady state temp distribution.

Set $u_t = 0$ which yields $u_{xx} = -1$ ; Integrating twice I get :

$u(x,t) = \frac{-1}{2}x^2 + \alpha(t)x + \beta(t)$

where $\alpha$ and $\beta$ are the two constants. Solving for our initial conditions, the steady state temp distribution function is

$u(x,t) = \frac{-1}{2}x^2 + 9.5x - 4$