3 answers

Solve the following Heat Equation: Show the details ofyour work: (30%) D.E. Ut(x,t) = c2uxx(x,t), 0 < x < ZTt,

Question:

Solve the following Heat Equation: Show the details ofyour work: (30%) D.E. Ut(x,t) = c2uxx(x,t), 0 < x < ZTt, 0 < t B C. Ux(0,t) = ux(2T,t) = 0, 0 < t 1. C_ u(x,0) = x(2t x)_ 0 < x < ZTt


Answers

If $u(x, t)=e^{a t} \sin (b x)$ satisfies the heat equation $u_{t}=$ $u_{x x},$ find the relationship between $a$ and $b$

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Hello. In this problem we have two systems. The 1st 1 is a. With an initial temperature of T. Hey and another system B.

Also with temperature T. B. When both are in thermal contact with each other. So now we have a new system and the wretched equilibrium and the temperature of equilibrium S. T.

C. So if we are giving a piece of info about their magnitude of this temperature or how it compares to other temperature, we can say some piece of information regarding the initial temperatures of the two systems here. So first we have to keep in mind the fact that the temperature flows or the heat flows from that body with greater temperature. So heat flows from hot objects too cold objects for the higher temperature to the lower temperature. So here in case A We're being told that the temperature C.

Is less than the temperature eight. So what does this mean? The temperature that the system reached equilibrium and is less than the initial temperature of Aid. Which means that object has lost some heat or some energy. And uh it reached a lower temperature. And in that way we know that heat flow from A to B.

And this means that actually the temperature of object A. Was initially higher than the temperature of object B. Let's now look at the 2nd case. In the 2nd case, we are being told that the temperature C. Of the equilibrium is larger than the temperature of object A.

Which means here that object A increased in temperature meaning that it received some energy. And this energy definitely came from the contact it made with object B. So he flows from B to A. In that case, and this means that the temperature of object A. Was initially less than the temperature of object B.

So that's the answer, and that's our judgment in case A. And that's it in case B..

It hit conduction question where we have a UTI equal Choda on for square You x x and then were given the function you equal with you Ive Omanis and foursquare case grabbed de times With this I I'm the k Thanks and we need to verify if this function is the solution to this in question are not here. Let's find ah, duty first So you they will be a big me a variable So doesn't will be the constant now Therefore, I'm a ghenda each other bound minutes and first crack a scrap the on by the general management they multiply by the derived from the power it could u minus and from square hey square attempting to sigh Okay, x, we can rewrite history is a minus and for square a square each of the performers and foursquare case square Okay, times windows under Okay x So the next thing going to find me in the year X It would equal Jew now expertly the variable Therefore just want to be the constants Or have Obama's and far square case quiet day and only do that the cycles Yukos I off the i X and tempt with uh, do you agree with them that they ANC's well respected the ANC's included. OK, so I have to get enough run here and now the new x X We do the same thing and then we actually get now Ah, minus K square each of the months and four square is a square the and no time sigh I'm the guy X and now it would have, uh, on foursquare you x x which will get echo judo minus and foursquare K square E J minus And first crack a square day. I'm sign off the X. So we see this in examining Jenna Jaap de here.

So it was just very fighters and is correct here..

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