Random heat evolution problem
(5 pts)
A metal bar with a given initial temperature distribution $g(x)$ lies along the unit interval. At time zero, it's left and right endpoints are placed against two large temperature wells. Your task is to sketch the evolution of the resulting temperature flow. Get your specific question by choosing your name from the menu on this webpage.
In your response, you should state your question, draw your solution by hand, and upload an image of the result.
Comments
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by $$g(x)=4x^2−1x.$$ At time $t=0$, its left end is set to temperature 2 and its right end to 0. Here is my (tentative) sketch the temperature distribution at times $t=0$, $t=0.01$, $t=0.1$, and $t=10$.
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by
$$g(x) = 4x^2 - 2x.$$
At time $t =0 $, its left end is set to temperature 1 and its right end to 0. Here is a sketch of the the temperature distribution $u(x,t)$ at times $t = 0$, $t = 0.01$, $t = 0.1$, and $t = 10$.
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by
$g(x) = 4x^2 - 1x$
At time t=0, its left end is set to temperature 3 and its right end to -3. Sketch the temperature distribution at times
t=0,t=0.01,t=0.1, and t=10.
(Redo) A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by: $$g(x)=4x^2-2x$$
At time t=0, its left end is set to t=-3 and the right end t=-1. Sketch of temperature distribution at times t=0, t=.01, t=.1, and t=10 is below:
A metal bar of length 1 with a temperature distribution given by:
$$g(x)=3x^2-1x.$$
At $t=0$ its left end is set to temperature -2 and its right end to 3. Sketch the temperature distribution at time t=0, t=0.01, t=0.1, and t=10.
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
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by
$$g(x) = 4x^2 - 2x.$$
At time $t=0$ its left end is set to temperature -1 and its right end to -3. Sketch the temperature distribution at times $t=0, \: t=0.01, \: t=0.1, \text{ and } t=10.$
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by:
$$g(x) = 5x^2 - 1x .$$
At time t = 0, its left end is set to temperature -2 and its right end to -1. Sketch the temperature distribution at times:
t = 0, t = 0.01, t = 0.1, t = 10.
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by
$g(x) = 4x^2 - 2x$.
At time t=0, its left end is set to temperature 2 and its right end to 0. Sketch the temperature distribution at times
t=0, t=0.01, t=0.1, and t=10
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by:
$$g(x) = 4x^2 - 3x$$
At time $t=0$, its left end is set to temperature $0$ and its right end to $-1$. Sketch the temperature distribution at times:
$$t=0, \: t=0.01, \: t=0.1, \text{ and } t=10$$
We will look at a bar of length $1$ that lies along the unit interval. Its temperature distribution is given by:
$$g(x)=3x^2 - 2x.$$
At time t=0, its left end is set to temperature 3 and its right end to -2. Here is the sketch of the temperature distribution at times $t=0, t=0.01, t=0.1$, and $t=10.$
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by
$$g(x) = 6x^2 - 2x.$$
At time $t=0$, its left end is set to temperature $3$ and its right end to $3$. Sketch the temperature distribution at times
$$t = 0, t = 0.01, t = 0.1, t = 10.$$
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by
$$g(x) = 5x^2 - 1x.$$
At time $t=0$, its left end is set to temperature $0$ and its right end to $-3$. Sketch the temperature distribution at times
$$t=0, t=0.01, t=0.1, t=10.$$
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by
$$g(x) = 3x^2 - 2x$$
At time $t = 0$ its left end is set to temperature 0 and its right end to 3. Sketch the temperature distribution at times: $t = 0,\ t = 0.01,\ t = 0.1,\ t = 10$ .
A metal bar of length 1 lies along the unit interval. Its temperature distribution is $$g(x)=5x^2-4x$$
At t=0, its left end and right end set to temp 0. Sketch the distribution at times $$t=0, t=0.01, t=0.1, and t=10.$$
Given a metal bar of length 1 that lies along the unit interval. Its temperature distribution is
$$g(x)=6x^2 - 4x $$
At t=0, its left end is 3 degrees and right end is -3 degrees.
Sketch the distribution at times
$t=0,t=0.01,t=0.1$,and $t=10.$
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by $$g(x)=6x^2-1x$$.
At time $t=0$, its left end is set to temperature -2 and its right end to 2. Sketch the temperature distribution at times $$t=0,t=0.01,t=0.1, \text{ and } t=10.$$