In this case, the cooling is dominated by convection and thermal diffusion. Using this equation, calculate the cooling curve for coffee using the explicit and implicit methods. For both methods, use a variety of time step sizes to examine how the solution depends on step size. Also, compare this to analytic results. Assignment Required Data None.
Procedure Determine the analytic solution to the coffee cup equation.
Write a forward Euler method solution to this problem. Write a backward Euler method solution to this problem. Using any software package or language, use our solvers and your analytic solutions to integrate the equation over the time range O to 15 minutes using the specified initial conditions and step sizes. Create a single of plots using your favorite plotting package with these results. This plot should have a total of 9 curves - one analytic, four explicit, four implicit.