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Lesson 14. PROBLEMS ON PLANCK’S EQUATION
Module 2. Food freezing
Lesson 14
PROBLEMS ON PLANCK’S EQUATION
Example 14.1
Find out the diameter of the spherical product being frozen in an airblast wind tunnel. The initial product temperature is 10^{0}C & cold air in the tunnel is at 12^{0}C. The product density is 1000 kg/m^{3} and the convective heat transfer coefficient for the air blast is 50 W/m^{2}K. The thermal conductivity of the product is 1.25 W/mK and the initial freezing temperature is 2^{0}C. The latent heat of fusion is 300 kJ/kg. Freezing time is 2.2 hrs. (Use Plank’s Equation).
Example 14.2
Example 14.3
A spherical product is being frozen in an air blast wind tunnel. The initial product temperature is 10^{0}C and that of cold air is 15^{0}C. The product has a 7cm diameter with a density of 1000 kg/m^{3} & the convective heat transfer coefficient for the air blast is 50 W/m^{2}K. The thermal conductivity for the frozen product is 1.2 W/mK, the initial freezing temperature is 1.25^{0}C and the latent heat of fusion is 250 kJ/kg. Compute the freezing time.
Example 14.4
Grape juice is being frozen in a 4cm diameter and 10cm tall can in an air blast freezer with 20 W/m^{2}K as a surface heat transfer coefficient. The initial product temperature is 2^{0}C and air used as a freezing medium is 20^{0}C. Estimate the time required to freeze the product to 10^{0}C, using Plank’s Equation. Assume infinite cylinder geometry, T_{F} = 1.8^{0}C and L = 210 kJ/kg.
Example14.5
Find out the diameter of the spherical product being frozen in an airblast wind tunnel. The initial product temperature is 10^{0}C and cold air in the tunnel is at 12^{0}C. The product density is 1000 kg/m^{3 }and convective heat transfer coefficient for the air blast is 50 W/m^{2}K. The thermal conductivity of the product is 1.25 W/mK. The initial freezing temperature is 2^{0}C, the latent heat of fusion is 300 kJ/kg and freezing time is 2 hr. Use Plank’s equation for solving the problem.
Questions
Solve the following problems: 

1. 
Apple juice is being frozen in a 5cm diameter and 12cm tall can in an air blast freezer with 25 W/m^{2}K as a surface heat transfer coefficient. The initial product temperature is 3^{0}C and air used as a freezing medium is 18 ^{0}C. Estimate the time required to freeze the product to 12^{0}C, using Plank’s Equation. Assume infinite cylinder geometry, T_{F} = 2.2 ^{0}C and L = 230 kJ/kg. 
2. 
A spherical product is being frozen in an air blast wind tunnel. The initial product temperature is 15^{0}C and that of cold air is 20^{0}C. The product has a 6 cm diameter with a density of 1050 kg/m^{3} & the convective heat transfer coefficient for the air blast is 75 W/m^{2}K. The thermal conductivity for the frozen product is 1.1 W/mK, the initial freezing temperature is 1.80^{0}C and the latent heat of fusion is 300 kJ/kg. Compute the freezing time. 
3. 
Find out the diameter of the spherical product being frozen in an air blast air tunnel. The initial product temperature is 10^{0}C and cold air in the tunnel is at – 25 ^{0}C. The product density is 900 kg/m^{3} and convective heat transfer coefficient for the air blast is 60 W/m^{2}K. The thermal conductivity of the product is 1.20 W/mK. The initial freezing temperature is – 1.7 ^{0}C. The latent heat of fluid is 250 kJ/kg and freezing time is 180 min. 
4. 
Find out the diameter of the spherical product being frozen in an airblast wind tunnel. The initial product temperature is 10^{0}C & cold air in the tunnel is at 18^{0}C. The product density is 1100 kg/m^{3} and the convective heat transfer coefficient for the air blast is 80 W/m^{2}K. The thermal conductivity of the product is 1.25 W/mK and the initial freezing temperature is 2.2 ^{0}C. The latent heat of fusion is 230 kJ/kg. Freezing time is 3.2 hrs. (Use Plank’s Equation). 
5. 
Find out the diameter of the spherical product being frozen in an airblast wind tunnel. The initial product temperature is 20^{0}C and cold air in the tunnel is at 25 ^{0}C. The product density is 1000 kg/m^{3 }and convective heat transfer coefficient for the air blast is 70 W/m^{2}K. The thermal conductivity of the product is 1.20 W/mK. The initial freezing temperature is 1.2 ^{0}C, the latent heat of fusion is 280 kJ/kg and freezing time is 2.5 hr. Use Plank’s equation for solving the problem. 