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Question: 41 an ice cube is set on a metal table...

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4-1. An ice cube is set on a metal table outside in Arizona during July. How long will it last? The average air temperature is 45°C, and the wind is blowing at 80 km/hr a) Assume that 5 sides of the ice cube with initial edge length (L) of 5 cm, are heated by convection, with a convective heat transfer coefficient (h) of 200 W/m2 C. What is the initial rate of heat absorption through convection? b) How much heat is initially gained from the surroundings to the 5 exposed sides due to radiation heat exchange? You may assume that the emissivity () of the ice is 0.98 c) The thickness (8) of the paper plate separating the ice cube from the thick table is 1 mm. The thermal conductivity (k) of paper is 0.05 W/m-K. Assuming that the table is at the same temperature as the air, what is the initial rate at which heat is absorbed by the ice via conduction through the plate? d) The product of the mass and the enthalpy of fusion of the ice cube defines the total amount of energy required to melt it. If we assume that the ice remains cubic as it melts, and that the table temperature is not significantly changed during the process, we arrive at the following equation for the time dependent edge length (L) of the ice cube table ice The density (p) and enthalpy of fusion (A) of ice are 917 kg/m3 and 334 kJ/kg respectively. Use the above relation, and the given properties to determine how long it will take to melt the ice cube. [Hint: Notice that L is a function of time that is L(t). Differentiate the left-hand side of the equation, then solve for dL/dt.]

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