[Priyanka Konakandla]

A thin plate is initially at a uniform temperature of 200C. At a certain time t = 0 the
temperature of the east side of the plate is suddenly reduced to 0C. The other surface is
insulated. Use the explicit finite volume method in conjunction with a suitable time step size to
calculate the transient temperature distribution of the slab and compare it with the analytical
solution at time (i) t = 40 s, (ii) t = 80 s and (iii) t = 120 s. Comparison should be shown in a
graphical plot as well as in a tabular form showing the percentage error with the analytical
solution.
Recalculate the numerical solution using a time step size equal to the limit given by the stability
criteria (possibly 8 second or higher) for t = 40 s and compare the results with the analytical
solution.
Solve the problem using the both Crank-Nicholson scheme and fully implicit
scheme and compare the results with analytical results at (i) t = 40 s, (ii) t = 80 s and (iii)
t = 120 s.
With a time step of 8 s, compare the results of all these three schemes (explicit,
implicit and Crank-Nicholson) at time t = 40 s.
The data are: plate thickness L = 2 cm, thermal conductivity k = 10 W/m/K and C =
10x106 J/m3
/K.