Problem $4$: Using your feedback and advice but after the fact, making you a guinea pig...

A rigid, cylindrical copper bar with length $\backslash ($ L$=2\backslash$mathrm$\{$~m$\}\backslash )$ and diameter $\backslash (=0\mathrm{.}1\backslash$mathrm$\{$~m$\}\backslash )$ is perfectly insulated on its curved surface. $($Think of it kind of like an electrical wire, except with a much larger diameter and not at all flexible.$)$

A$)$ One end is connected to a surface held at a fixed temperature of $293$ K $.$ The other end is connected to a surface held at a fixed temperature of $325$ K $.$ Use the finite difference method to calculate and plot the temperature profile of the bar.

B$)$ One end remains connected to the $293$ K surface, but the other end is connected to a surface that is programmed to emit a fixed heat flux of $\backslash (4000\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ).$ Use the finite difference method to calculate and plot the temperature profile of the bar.

C$)$ Imagine you now strip the insulation off of the cylindrical bar, and connect only one side to the surface being held at $293$ K $.$ It is exposed to air at $277$ K with a convective heat transfer coefficient of $\backslash ($ h$=20\backslash$mathrm$\{$~W$\}/\backslash$left$(\backslash$mathrm$\{$m$\}^\{2\}\backslash$mathrm$\{$k$\}\backslash$right$)\backslash ).$ If you model the system as only having heat transfer in one direction $($the axial direction$),$ use the finite difference method to find the temperature profile in the bar. $($Make sure you use enough points in your finite difference approximation method to make the result be reasonable.$)$

Please submit your code, an indication of what equations you used, and the plots you generated.