Food Engineering

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 air-blast wind tunnel. The initial product temperature is 10⁰C & cold air in the tunnel is at -12⁰C. The product density is 1000 kg/m³ and the convective heat transfer coefficient for the air blast is 50 W/m²K. The thermal conductivity of the product is 1.25 W/mK and the initial freezing temperature is -2⁰C. The latent heat of fusion is 300 kJ/kg. Freezing time is 2.2 hrs. (Use Plank’s Equation).

Example 14.2

Find out the diameter of the spherical product being frozen in an air blast air tunnel. The initial product temperature is 10⁰C and cold air in the tunnel is at -12⁰C. The product density is 1000 kg/m³ and convective heat transfer coefficient for the air blast is 50 W/m²K. The thermal conductivity of the product is 1.25 W/mK. The initial freezing temperature is -2⁰C. The latent heat of fluid is 300 kJ/kg and freezing time is 120 min.

Example 14.3

A spherical product is being frozen in an air blast wind tunnel. The initial product temperature is 10⁰C and that of cold air is -15⁰C. The product has a 7cm diameter with a density of 1000 kg/m³ & the convective heat transfer coefficient for the air blast is 50 W/m²K. The thermal conductivity for the frozen product is 1.2 W/mK, the initial freezing temperature is -1.25⁰C 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/m²K as a surface heat transfer coefficient. The initial product temperature is 2⁰C and air used as a freezing medium is -20⁰C. Estimate the time required to freeze the product to -10⁰C, using Plank’s Equation. Assume infinite cylinder geometry, T_F = -1.8⁰C and L = 210 kJ/kg.

Example14.5

Find out the diameter of the spherical product being frozen in an air-blast wind tunnel. The initial product temperature is 10⁰C and cold air in the tunnel is at -12⁰C. The product density is 1000 kg/m³ and convective heat transfer coefficient for the air blast is 50 W/m²K. The thermal conductivity of the product is 1.25 W/mK. The initial freezing temperature is -2⁰C, 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/m2K as a surface heat transfer coefficient. The initial product temperature is 30C and air used as a freezing medium is -18 0C. Estimate the time required to freeze the product to -120C, using Plank’s Equation. Assume infinite cylinder geometry, TF = -2.2 0C and L = 230 kJ/kg.
2.	A spherical product is being frozen in an air blast wind tunnel. The initial product temperature is 150C and that of cold air is -200C. The product has a 6 cm diameter with a density of 1050 kg/m3 & the convective heat transfer coefficient for the air blast is 75 W/m2K. The thermal conductivity for the frozen product is 1.1 W/mK, the initial freezing temperature is -1.800C 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 100C and cold air in the tunnel is at – 25 0C. The product density is 900 kg/m3 and convective heat transfer coefficient for the air blast is 60 W/m2K. The thermal conductivity of the product is 1.20 W/mK. The initial freezing temperature is – 1.7 0C. 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 air-blast wind tunnel. The initial product temperature is 100C & cold air in the tunnel is at -180C. The product density is 1100 kg/m3 and the convective heat transfer coefficient for the air blast is 80 W/m2K. The thermal conductivity of the product is 1.25 W/mK and the initial freezing temperature is -2.2 0C. 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 air-blast wind tunnel. The initial product temperature is 200C and cold air in the tunnel is at -25 0C. The product density is 1000 kg/m3 and convective heat transfer coefficient for the air blast is 70 W/m2K. The thermal conductivity of the product is 1.20 W/mK. The initial freezing temperature is -1.2 0C, the latent heat of fusion is 280 kJ/kg and freezing time is 2.5 hr. Use Plank’s equation for solving the problem.