Assuming that the heat lost is neglegible and the aluminum block has reached steady state, would the following be the correct derivation of the formula (1D heat equation)?
[tex]\frac{\partial^2 T}{\partial z^2}=0\iff T(z)=az+b .[/tex]
By Fourier's Law, [tex]\kappa\frac{\partial T}{\partial z}=h(TS),[/tex]
where S is the room temperature, and [tex]\kappa[/tex] and h are constants. Letting [tex]T(0)=T_0[/tex], then the temperature at any point may be obtained. Is the Fourier's Law correctly written? Thanks in advance.
