Nomads in the desert make ice by exposing a thin water layer to cold air during the night. The icing or freezing of thin layers of water is often also referred to as ice making by nocturnal ( or night time ) cooling, where the surface temperature of water is lowered considerably by radioactive and convective cooling, and it had been practiced extensively in ancient India. To model this process and evaluate the conduction process in water layer, consider a 5-mm thick horizontal layer gets cooled such that its top surface is at temperature of - 5 0C. After a while the water begins to freeze at top surface and the ice front expands downwards through the water layer. Determine the location of solid liquid(ice-water) interface if the bottom surface temperature of the liquid water is at 30C.

Question

State your assumptions for the model and calculations.



GIVEN

• Thickness of the layer(t)= 5 mm

• Surface temperature (Ts)= -50C=268 K

• Water temperature(Tw)= 30C= 276 K FIND

Location of solid liquid interface .

ASSUMPTIONS

• 1 Dimensional steady state heat transfer

• Constant properties throughout time

• Negligible radiation

• Negligible convection by liquid.

SKETCH

Answer 1

If x is the distance of solid liquid interface from liquid surface, the energy balance over the interface gives



Thus the interface is at distance of 0.77 mm from liquid surface or 4.23 mm from ice surface.