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Calculation of Thermal Diffusivity and Biot Number of a Process

Question

A process for preserving peas involves heating them quickly to a high temperature by immersion in boiling water. In a particular case, peas with an average diameter of 10.0 mm are to be heated to an average temperature of 950 C by rapid immersion in boiling water at 1000 C. the initial temperature of peas is 250 C. properties for the peas and of the system are given below:

 

Thermal conductivity

Heat capacity

Density

Diameter

Heat transfer coefficient

W/m-K

kJ/kg-K

Kg/m3

mm

kW/m2-K

0.45

3.50

960

10.0

0.895

 

  1. What are the values of thermal diffusivity (m2 /s) and Biot Number?
  2. What is the (dimensionless) unaccomplished temperature change at the desired temperature of 950 C?
  3. Assuming that the surface temperature of the peas remains constant at the temperature of the boiling water, how long will it take to reach the desired temperature? Explain how you found the value and comment on whether this is a reasonable assumption.
  4. It is found that peas with a diameter of 8 mm require about 34 seconds to be heated in a similar manner. Use this result to estimate how long it will take to heat the 6 mm peas.
  5. If the thermal conductivity of the 10 m pea is 45 W/m-K instead (other properties remain the same) , what will be average temperature of the peas after they are put into the boiling water for 10 seconds and how much energy is transferred to one hundred of such within this 10 seconds?

 

Summary: This question belongs to heat transfer and discusses about a process for preserving peas. Explains thermal diffusivity, energy transferred and Biot Number.

Answer is in image format

 

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