Fourier heat transfer problem.

[Topher925]

I need help understanding what a math problem is asking for. Its a Fourier heat transfer problem but it just isn't making any sense to me and I don't know what the author is asking for.

Homework Statement

The heat flux through the faces at the ends of a bar is found to be proportional to u_n = $$\partial$$u/$$\partial$$n at the ends. Show that if the bar is perfectly insulated, also at the ends x = 0, x = L, (adiabatic conditions) and the initial temperature is f(x), then

u_x(0,t) = 0 u_x(L,t) = 0 u(x,0) = f(x)

Homework Equations

u(x,t) = A_o + $$\sum$$A_n cos(n$$/pi$$x/L exp[ -(cn$$/pi$$/L)² t]

The Attempt at a Solution

Am I suppose to assume that the initial temp (f(x)) is at x = 0 for this problem and I have to prove that there is no heat flux at both ends of the rod? Or do I assume that the temperature can be what ever at any point of the rod because it won't matter since the heat flux at the ends is 0?

I hate math texts, its like they write in a different language.

 

[lippyka]

The problem is asking you to use the equation provided (u(x,t) = Ao + \sumAn cos(n/pix/L exp[ -(cn/pi/L)2 t]) to show that if the bar is perfectly insulated at both ends with an initial temperature of f(x), then the heat flux at both ends will be 0. This means that the heat flux, ux(0,t) and ux(L,t), must be equal to 0, and the temperature at both ends, u(x,0), must be equal to f(x). So, you must use the equation to prove that the heat flux at both ends is 0, and that the temperature at both ends is equal to f(x).