Question

An ice chest 50 cm long by 40 cm wide by 30 cm high comprised of 3 cm thick Styrofoam having thermal conductivity k = 0.033 W/m°C is filled with ah ice/ water mixture containing 45 kg of ice. The ice / water mixture is separated from the lid by 1 cm of air. The temperature of the surrounding air and the surface on which the ice chest is resting is 30° C, The temperature of the inner surface of the ice chest in contact with the ice / water mixture may be assumed to be 0° C. The heat transfer coefficient at the surface of the ice chest exposed to the air is 20 W/m °C. The thermal contact resistance between the ice chest and the surface on which it is resting is 0.15 m °C/W. Given that the heat of fusion of ice is 333.7 kJ/kg, how long it would take for the ice to melt completely?

Answer 1

Ans. We assume one dimensional steady state heat transfer with constant and unboom Material properties - Conservation of energy A Est = Ein - Eout + Eg TO ЛТ H-0. 3m 1 AT d=0.03m . 7 YKW=o.um KL-SoCm L=0.5m It we bocus on the control volume the chost (deished Lines DESH = 45 kg. 333.7 kJ inside - 15016.5 k ] = 1.50165 x 107] Page :

ave I-D the steady state condition top throught and bour sides. So, a = 9 - k.dT À = dx = 0.033 x (8-0)k m . 0.03 m q" = 8.8 W m2 q=Q". A q". [2 (LL-d). (H-d) + (n -d). (H-d)) + ((L-d).(N-d) ma +98.8 W [2(0:47 x 0:27) + (0:37 x 0.27)] + (0.47 * 0.37) 8.8 m2 / 2 (10.1264 + 0-0994)) + 0.1739] -8.8 W [ongoon 0-6275] q=5.522 W m2 V m2 - 5.522 I 15000 200 Page: 2

Under the steady assumption Est- Ein - Eout + Eg = q. Dt. in At - sEst q = 1.50165 X107 ) 5.522 %s = 0.27193951X 1075 & 31.4744 days. Page: 3