Chester, thanks for your help, but I may just go ahead and simplify the BCs such that I use a sol-air temperature rather than explicitly include radiation effects.
I've just solved the problem where I have 1-D space with one end's temperature fixed to zero and the other has convection term...
This is a problem of personal interest. The boundary conditions are not the same on both sides, and the heat fluxes on the boundaries contain radiation, solar, and convective components. Radiation is 4th order in T. The convective terms contain T raised to the third power (empirical correlation...
Correct. The heat fluxes at the boundaries are dependent on temperatures at the boundaries, and they vary with time. This is an example of what the heat flux would like:
q''(t)=constant*(T(0,t)^4-Toutdoor(t)^4)... where T(0,t) is unknown and Toutdoor(t) is known.
The actual boundary conditions of interest specify the heat fluxes; however, the heat fluxes are dependent on the temperatures on the boundaries, which are also unknown.
I just also include T(0,t) and T(L,t) being non-zero and positive. Is it wrong of me to impose those Dirichlet conditions...
Hi, it is easy solving these PDEs with the idealized homogeneous BCs they throw out in class, but I am having some difficulty solving the transient problem posed in the images below. I have tried working through it, but I don't have confidence in the result. I overlook the solution when the...
I'm going to take a finite difference linear and non-linear PDE course next semester. I'm wondering how enjoyable the material is, and how difficult it may be. I'm actually looking forward to the fact there may only be one test throughout the semester, if any, and it's a mid-term. The rest of...
Thank you for the response.
I just realized I made a mistake by changing the index, resulting in that denomintor. I eventually obtained a series that converged to 0.
Thank you again.
COMSOL is a great software application I use to solve systems of non-linear and coupled ODE's and PDE's.
It's very user-friendly, and it uses finite element method to numerically solve the systems. Not sure if you have access to it, but I figured I'd suggest it if you could use it.
Hello,
I am in the process of showing that the modified Bessel function, I_v(x), is a solution to the modified Bessel equation,
x^2*y''+x*y'-(x^2+v^2)*y=0
I have differentiated the MBF twice and plugged it into show that the left hand side is in fact 0.
After a good amount of work...