Q$3$

Use an appropriate numerical method to solve for the temperature distribution of a long,

thin rod, shown below, with a length of $16$ cm and following values: $)$

and $t=1\mathrm{.}5sec.$ At $t=0sec,$ the temperature of the rod at nodes $(1),(2),(3),$ and $(4)$ is $19C$

$($initial condition$)$ and the left boundary condition is fixed for all times at $T(0,t)=103C.$ In

addition, the right derivative boundary condition $\frac{\text{d}\text{e}\text{l}\text{T}(4,t)}{\text{d}\text{e}\text{l}\text{x}}$ for all times is given in the table

below for each of the problem sets. Note that the rod is aluminum with $C=0\mathrm{.}2174ca\frac{l}{g*C}$

and $=2\mathrm{.}7\frac{g}{c}{m}^3.$ Find the temperature values on the inner grid points and the right

boundary $($nodes $(1),(2),(3),$ and $(4))$ for $t=3sec.$ The nodes are equally spaced. Use the

dimension of the rod indicated in the figure shown below; the figure itself is not drawn to

scale.

Each student should refer to the table below to see his student ID for the corresponding

problem set he needs to solve. Consider the boundary conditions according to the

problem sets.

$($Note: Use and show the units throughout the solution. Show all the steps in detail$)$

$[10$ points$]$