Question

The evaporator section of a refrigeration unit consists of thin-walled, 10-mm-diameter tubes through which refrigerant passes at a temperature of −18°C. Air is cooled as it fows over the tubes, maintaining a surface convection coeffcient of 100 W/m2 ⋅ K, and is subsequently routed to the refrigerator compartment. (a) For the foregoing conditions and an air temperature of −3°C, what is the rate at which heat is extracted from the air per unit tube length? (b) If the refrigerator’s defrost unit malfunctions, frost will slowly accumulate on the outer tube surface. Assess the effect of frost formation on the cooling capacity of a tube for frost layer thicknesses in the range 0 ≤δ ≤ 4 mm. Frost may be assumed to have a thermal conductivity of 0.4 W/m ⋅ K. (c) The refrigerator is disconnected after the defrost unit malfunctions and a 2-mm-thick layer of frost has formed. If the tubes are in ambient air for which T[infinity] = 20°C and natural convection maintains a convection coeffcient of 2 W/m2 ⋅ K, how long will it take for the frost to melt? The frost may be assumed to have a mass density of 700 kg/m3 and a latent heat of fusion of 334 kJ/kg

Answer 1

This answer explains how to calculate the rate of heat extracted from the air per unit tube length, the effect of frost formation on the cooling capacity of a tube, and the time it takes for frost to melt. It provides detailed explanations and formulas for each calculation.

Step-by-step explanation:

(a) To find the rate at which heat is extracted from the air per unit tube length, we can use the formula for heat transfer by convection: Q = h × A × ΔT, where Q is the heat transfer rate, h is the surface convection coefficient, A is the surface area, and ΔT is the temperature difference. The surface area can be calculated using the diameter and length of the tube. Substitute the given values into the formula to find the answer.

(b) The effect of frost formation on the cooling capacity of a tube can be assessed by considering the additional thermal resistance introduced by the frost layer. Use the formula for thermal resistance to calculate the resistance added by the frost layer. The cooling capacity can then be determined by dividing the temperature difference by the total thermal resistance.

(c) To find how long it will take for the frost to melt, we need to calculate the amount of heat energy required to melt the frost and then divide it by the rate of heat transfer. The amount of heat energy can be found using the mass of the frost, its latent heat of fusion, and the thickness of the frost layer. Substitute the given values into the formula to find the answer.