Question

During a cold winter, the surface of a river develops a layer of ice of unknown thickness L. Known are the water temperature Ty=4°C, the atmospheric air temperature T=-30°C, and the temperature of the underside of the ice layer To= 0°C. The thermal conductivity of ice is k = 1.88 W/m-K. The convective heat transfer coefficients on the water and air sides of the ice layer are hw = 100 W/m²-K and ha= 50 W/m2-K, respectively. Calculate the temperature of the upper surface of the ice layer, Ts, and the ice thickness L.

Answer 1

Solution Given That -30°c o -Air 9 (T°c) T = 4²6 The -30°c Tri =0°6 kice = 1.88 W/mk h 100 W/m²K hz = 50 W/m²K & Ice (0°C) A Water (4°c) Tzo=? (=? Considering the water ice convective breat transfer- 6 = h, ACTi-Tai) or az ho (Tortzi) or, j = 100 (4-0) a = 400 W/m² Now, considering ice-air convective heat transfer- a = hz ( Tzotz) or, 400 = 50 (T2+39) 8 = T2o +30 Temp. of upper surface T20 = -22°C Am of the ice Conductive Heat transfer through the Ice layer- Now, å = Ki (Ti-Tzo) So, 400 = 48*(0+22)» L= 10134 cm