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1. ### Solving the heat equation with complicated boundary conditions

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...
2. ### Solving the heat equation with complicated boundary conditions

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...
3. ### Solving the heat equation with complicated boundary conditions

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.
4. ### Solving the heat equation with complicated boundary conditions

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...
5. ### Solving the heat equation with complicated boundary 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...
6. ### How is Finite Difference Method?

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...
7. ### Showing That the Modified Bessel Function of the First Kind is a Solution

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.
8. ### Showing That the Modified Bessel Function of the First Kind is a Solution

Sorry, the actual left hand side I have are those two terms inside the sum multiplied by (x/2)^2k+v. All inside the sum.
9. ### Numerical Solutions to Coupled ODEs with Boundry Values at Opposite Ends

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.
10. ### Showing That the Modified Bessel Function of the First Kind is a Solution

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...