The evaporator section of a refrigeration unit consists of thin-walled, 10-mm-diarneter tubes through which refrigerant passes at a temperature of - 18°C. Air is cooled as it flows over the tubes, maintaining a surface convection coefficient 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 refrigerators 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_∞= 20°C and natural convection maintains a convection coefficient 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/m 3 and a latent heat of fusion of 334kJ/kg.