Recent content by nrhoades

My computer keeps locking up. Haha.

it's actually (c + dz + ez^2)*T"(z) + a*T(z) + b = 0 T(z=0) = Ts T'(z=Z) = 0 Don't let my explanation confuse you; forget the axial direction x for now; right now I'm solving a one dimensional ODE (radially only) with lots of constants, shown above. I'm scared of the word "Bessel"...

Good questions. I am investigating the properties of a sensor I am making, which involves the simultaneous interactions of convective heat transfer, joule heating, and potential theory. I am trying to build an analytic model that approximates all of these physics for simple geometries, namely a...

Is there an analytic solution for: y"(c+dx+ex^2) + ay + b = 0, y (x=0) = Ts y'(x=L) = 0 where a,b,c,d,e are all constants?

I FDM'ed this too and I agree. For some reason it wasn't obvious to me at first. Thanks.

pmsrw3: Last one... Quickly, can you do: y'' = 0 y'(x=0) = inf y(x=L) = a I don't know if this is possible. Thanks!

Thanks! Thread closed!

What do you get when a is negative?

I simultaneously found the solution. The form is T(x) = C1*cos(sqrt(a)*x) + C2*sin(sqrt(a)*x) - b/a where C1 = Ts + b/a, C2 = C1*tan(sqrt(a)*L) Your solution looks like it takes this form after some trig flexing. Thanks!

pmsrw3, very close! Please see the following two plots: The equation you gave models the homogenous boundary problem exactly, which is: Txx + aT = -b, T(x=0) = Ts, T(x=L) = 0 (first plot) What I need is the solution to the NON-homogenous boundary problem: Txx + aT = -b, T(x=0) = Ts...

I've made a lot of simplifications to a Joule-heating problem I'm working on. I'm struggling to solve the following one-dimensional, one variable ODE: Txx + aT = -b with boundary conditions T(x=0) = Ts (Dirichlet) Tx(x=L) = 0 (Neumann) I've learned that this is a non-homogeneous...