Scenario $1$ Initial Temperature Distribution

Scenario $3$ Initial Temperature Distribution

Scenario $2$ Initial Temperature Distribution

Scenario $4$ Initial Temperature Distribution

Each graph shows the initial $($time$=0)$ temperature distribution for a metal rod which is insulated along its length and has its ends fixed at the temperature$($s$)$ shown. The system is allowed to come to equilibrium and will be modeled using python. Draw in different colors and label the expected temperature distribution output of the simulation a$)$ shortly after the simulation begins $($time$\backslash$cong $2$s$)$ and b$)$ after a very long time and the system has reached steady$-$state $($time$=\backslash$infty $).$

After the metal rod in scenario $1$ reaches steady$-$state, predict the temperature in the middle of the rod. After the metal rod in scenario $2$ reaches steady$-$state, predict the temperature in the middle of the rod. After the metal rod in scenario $3$ reaches steady$-$state, predict the temperature in the middle of the rod. After the metal rod in scenario $4$ reaches steady$-$state, predict the temperature in the middle of the rod.