Recent content by shreddinglicks

I guess I see what you mean. So the heat is diffusing to left and right causing the hump I'm seeing with that left curve.

I followed what you said. I checked my solution over more than once. I derived the solution for a non-homogeneous problem with the external boundaries at constant temperature. I don't like the curve I have on the left. There is a weird hump in it. The image shows a graph from MATLAB at t=1...

By time evolution you mean the thermal diffusivity has to be in the spatial equation?

With a quick online search I see that most sources state that the boundary condition at the interface of two materials in contact having contact resistance is -ksub1*u'sub1 = -ksub2*u'sub2 =q usub1 - usub2 = R*q I've tried to produce a solution consisting of two equations, each describing the...

Thanks for the responses. I'll respond back with my attempts.

I have FEA results for this. I'm trying to see if this problem can be solved by hand with reasonable accuracy.

I'll try that approach.

Interesting. I have FEA results for this problem. I wanted to see if there was a way to get the solution using a pencil and paper. I'll try what you have here and see what I get.

But what about a pipe of this shape being broken up into three pieces. Two cantilevers and one pin-pin. Is it possible to sum the individual natural frequencies to get the frequency of the entire pipe? Does plane matter if the natural frequency is scalar?

I'm trying to find the natural frequency of a pipe that is roughly z shaped (two 90 degree bends). Is it possible to break this pipe up into three straight pieces and model each piece as a beam experiencing transverse vibration? For example, modeling the end segments as cantilevers and the...

Yes, exactly as you said. du/dx and h is a constant. I realized I made an error. The conditions are actually I'll fix it also on the original post. It's what you have but y instead of x. The problem is, this gives an answer where for all y when u(0,y)=0 when x should be zero, x does not...

I've tried a few things. I did one method to try to accomplish the removal of the -70 in the derivative boundary condition. It came out as below. When plotting it however it gave a solution that didn't make sense.

Interesting. I tried to apply what is shown in 11.4.2. How would I solve for A and B that is shown in 11.4.1?

I've been studying a few books on PDE's, specifically the heat equation. I have one book that covers this topic in cylindrical coordinates. All the examples are applied to a solid cylinder and result in a general Fourier Bessel series for 3 common cases that can be found easily with an online...

Let's say it's a light water reactor fueled by uranium 233. The goal is to convert enough uranium 233 from Thorium 232 to breakaway from uranium 235. So a conversion rate of 1 or slightly over 1.