- 560

- 2

**1. Homework Statement**

I have a rod of density [tex] \rho[/tex] and lenght [tex] l[/tex]. It's located at [tex]0\leq x\leq l [/tex]. The density of internal energy per mass is [tex]E = c(T-T_0) + E_0 [/tex] where T is the tempertature in Kelvin,[tex] E_0[/tex] is a constant and [tex]c [/tex] is the specific heat capacity. We assume that the temperature is not varying across the rodd. The temperature at the two ends of the rod is [tex] T_0, T_l[/tex]

a) this question was to find the time independet solution to the heatequation

[tex] \frac{\partial T}{\partial t} = \kappa \nabla^2 T[/tex] and I found this one by using the conditions to be

[tex] T(x) = \frac{T_l - T_0}{l}x + T_0[/tex]

b) Find the transport of energy, per unit time, out of a cross-section of the rod at [tex] x = l [/tex].Also find the total thermal energy in the rod.

**2. Homework Equations**

**3. The Attempt at a Solution**

Im thinking that the solution to this probably is a flux integral, but I don't know how to proceed and what to integrate.