3 Problem 3 (20 Pts) An earthworm is resting cozy underground at a distance of 0.3...
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3 Problem 3 (20 Pts) An earthworm is resting cozy underground at a distance of 0.3 m below the surface in Chicago, IL. The temperature underneath the surface is 20 C and can be assumed uniform throughout. Due to global warming, suddenly the outside temperature drops to -15 C and a lot of snow is dumped on the ground. 1. (10 Pts) After how many days the water surrounding the earthworm will start to freeze? 2. (10 Pts) What is the Fourier number at that time and location? Hint: See slides for the definition of Fourier number which nondimensionalizes time. The thermophysical properties of the earth are: p = 2050 kg/m, k = 0.52 W/(m.k), and c = 1840 J/(kg.K). 3 Problem 3 (20 Pts) An earthworm is resting cozy underground at a distance of 0.3 m below the surface in Chicago, IL. The temperature underneath the surface is 20 C and can be assumed uniform throughout. Due to global warming, suddenly the outside temperature drops to -15 C and a lot of snow is dumped on the ground. 1. (10 Pts) After how many days the water surrounding the earthworm will start to freeze? 2. (10 Pts) What is the Fourier number at that time and location? Hint: See slides for the definition of Fourier number which nondimensionalizes time. The thermophysical properties of the earth are: p = 2050 kg/m, k = 0.52 W/(m.k), and c = 1840 J/(kg.K).
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