I have also the same as you, only not with the identity matrix on the left side( do I need this?) and with a²b²-Ra on the left bottom in the matrix. I think it is correct with minus instead of plus(like you have).
Then I get the following eigenvalues and eigenvectors:Squareroot= SQ
λ1=SQ(α²*b²...
I see now that in my first thread I miss the derivative sign on the G, it is suppose to be (Ra/b³) *G' !
So the system I have written in my latest thread(the one over here) is the correct one!
So my system is
F'' - (α^2 * b^2 * F ) = (Ra / b)*G'
G'' - (α^2 * b^2 +Ra)*G = F'*bIf I say that F'=H and G'=I, I have the following system:
F'=H
G'=I
H' - α^2*b^2*F = (Ra/b)*I
I' - (α^2*b^2 - Ra)*G =b*HIf I write my system as a matrix looking like: x'=Ax, I have:
F' 0...
Svein: Yes, what you suggested is correct
Bigfooted: Yes it is the system then
The_wolfman: I have tried your solutions but cannot solve it that way. I have read some other similar papers where their soulution to both F and G are functions of sinh and cosh, but I cannot seem to find such a...
Hello :)I have a system which consists of two coupled ODEs for which I want to solve.F'' *(1/b²) - α²*F = Ra*(1/b³)*G
G'' *(1/b²) - α*²G + Ra*(1/b²)*G = F'(1/b)
In these two equations F(z) and G(z) both depend on z. b is a constant, Ra is the rayleigh number which I need to keep as Ra in my...
No it is not a homework, it is my master thesis. In order to write out the system in a 8x8-matrix I need all the variables in T.
Top and bottom of the cylinders are impermeable and perfectly heat conducting. The sidewalls are impermeable and insulated. I am to see how natural convection cells...
I am looking at natural convection between two coaxial cylinders. Between them there are to layers of different height and permeability, which I will change in my calculations and see how this effects my solution.
Originally, after doing a permutation to the steady state solution, and after...
Hello!
I have a question about an equation.
I have an equation which is a boundary condition to a problem I have concerning fluid flow in a layered porous medium. I have a equation where my only variable is the temperature T, and I have 10 boundary conditions with it. In order to solve the...