Differential Equations Boundary Conditions

Question

If there are two heat flux given, one at x=0 and the other at x=0.2, how can an expression for the variation of temperature be obtained? thermal conductivity is given to be k=20 W/mk, the surface area is 15m^2, and the temperature distribution is dT^2/dx^2=0. At x=0, the heat flux is 40000 W/m^2 while at x=0.2, the heat flux is 25000 W/m^2. I was able to solve for C1, but I am stuck with trying to solve for C2 since there is no temperature given. Is there a way to solve this without any given temperature?

Thank you in advance.

Answer 1

The given equation T''(x) = 0 has definite integrals T'(x) = T'(0) = T'(L), where L = 0.2m. The boundary conditions are kT'(0)=40000W/m² and kT'(L)=25000W/m², but these requirements are inconsistent with T'(0) = T'(L), so something seems to be mis-stated in your question. Also the "surface area" is of what surface? The univariate equation T''(x) = 0 doesn't imply a particular shape. Please check the problem statement, and if it is stated as given then provide its source and I will investigate.