4. Consider the problem of unsteady thermal diffusion in a flat plate or rod: in the domain [0 cm < x < 25 cm], initially at a temperature of T(x,0) = T i = 0°C. At time t = 0, the surface of the plate at x = 0 is suddenly placed in water at a temperature of = 25°C. Convective heat transfer between the water to the plate is characterized by: Assume that at 25 cm, it is a sufficient distance that the temperature gradient at that point is negligible. The material properties of the plate and water are: a) Solve this problem using finite volumes and . Use an equispaced grid with 10 control volumes per cm and a TDMA solver. Continue iterating until T(0,t) = 0.99* . Calculate the time taken, ttotal , to reach this point to within one second. Choose your own timestep and show that your timestep is small enough so that ttotal is independent of timestep size. Plot T(x) at t = 0, t = .25*ttotal , t = .5*ttotal , t = .75*ttotal , and t = ttotal Plot T(x = 0), T(x = 12.5 cm), and T(x = 25 cm) as functions of time. Comment on your results and on the suitability of the assumptions you have made in five sentences or less