## Solution Library

# 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 95^{0} C by rapid immersion in boiling water at 100^{0} C. the initial temperature of peas is 25^{0} 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/m |
mm |
kW/m |

0.45 |
3.50 |
960 |
10.0 |
0.895 |

** **

- What are the values of thermal diffusivity (m
^{2}/s) and Biot Number? - What is the (dimensionless) unaccomplished temperature change at the desired temperature of 95
^{0}C? - 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.
- 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.
- 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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