Potato Farmer

Quote:

"How long does it take to cook a potato? Consider a cylindrical potato, sliced into thin slices with thicknesses L = 1 cm, much smaller than the diameter of the slices (so that the heat flux into the potato is through its two cut surfaces). The potato slices are at room temperature, 20 deg (Celsius), initially. Then they are dropped into boiling water, which is at 100 deg (Celsius). They are cooked when the temperature inside the potato everywhere is at least 75 deg (Celsius). Note, the heat diffusivity of a russet potato (Rao, et. al 1975) is about k = 1.84 times 10^-7 m^2/s. Write down the boundary-value, initial-value problem statement. Solve for the steady-state solution. Solve for the transient solution. Put it all together to get the full solution. For small times, the first term in the infinite series solution is much much larger than the other terms. Use that approximation to determine the time for the whole potato slice to be at 75 deg F. "

- saibur

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