Question

Artificial tissues are made individually and frozen in bulk. These tissues are 10 cm in diameter and 2 mm in thickness. A thin piece of paper is placed between them, and a stack of tissues 1.2 m long is frozen on its side in an air-blast freezer. Cold air at -20°C blows at 1.5 m/s over the stack of tissues. The properties are: unfrozen tissues (ρ = 1060 kg/m3, Cp = 3.5 kJ/kg·K, k = 0.5 W/m·K), frozen tissues (ρ = 950 kg/m3, k = 1.1W/m·K ). The tissues have 75% moisture with an initial temperature of 25°C.

a) Determine the convective heat transfer coefficient in the air-blast freezer.

b) The solutes in the tissues have an effective molecular weight of 225, calculate the tissues’ freezing point temperature.

c) Calculate the time required for the center of the tissues to be chilled from 25°C to the freezing point temperature.

d) Calculate the freezing time of the tissues assuming they are at the freezing point temperature.

Answer 1

At -20°C, properties of air   

Density = 1.395 kg/m^3 , dynamic viscosity = 1.63*10^-5 (N-s/m2)

Reynolds number Re = (1.395*1.5*1.2/ 1.63*10^-5)=1.54*10^5

Since Reynolds number is less than 5*10^5 - Flow is assumed to be laminar

By using formula for convective heat transfer coefficient...

hL/K = 0.332 (Re)^(1/2) * Pr^(1/3)

K of air = 0.02227 W/mk. ( At -20°C)

Pr of air= 0.722

By substituting h = 2.1691 W/m2-K

Average Heat transfer coefficient H = 2h= 4.3382 W/m^2-K

B.The Normal freezing Temperature of tissues is -3°C.

C.

We know that heat transfer from tissue to air will lead to decrease in temperature of tissue to -3°C.