You place a 4cm diameter ice-cube into a large bowl of water at constant temperature 15oC, and find that it melts in 10 minutes. (a) Predict the size of the ice-cube as a function of time. You need to consider the rate of heat flow into the ice-cube through its surface, and therefore the rate at which its mass changes with time. Try to express the rate of change of ice-cube size as a simple first-order differential equation. (b) What is the heat transfer coefficient between the ice-cube and the water? (c) Estimate how long it takes the ice-cube to melt in water of different constant temperature T. Hints: Treat the ice-cube as a sphere fully immersed in the water. Assume the water is well-mixed and remains at its constant temperature of 15oC throughout the melting, so that the rate-limiting process is the heat flow at the ice-water boundary. Assume the temperature of the un-melted ice is 0oC. The ice has density 916 kg/m3 , and the latent heat of melting ice is 334 kJ/kg.
You place a 4cm diameter ice-cube into a large bowl of water at constant temperature 15oC, and find that it melts in 10 minutes. (a) Predict the size of the ice-cube as a function of time. You need to consider the rate of heat flow into the ice-cube through its surface, and therefore the rate at which its mass changes with time. Try to express the rate of change of ice-cube size as a simple first-order differential equation. (b) What is the heat transfer coefficient between the ice-cube and the water? (c) Estimate how long it takes the ice-cube to melt in water of different constant temperature T. Hints: Treat the ice-cube as a sphere fully immersed in the water. Assume the water is well-mixed and remains at its constant temperature of 15oC throughout the melting, so that the rate-limiting process is the heat flow at the ice-water boundary. Assume the temperature of the un-melted ice is 0oC. The ice has density 916 kg/m3 , and the latent heat of melting ice is 334 kJ/kg.
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