Introduction to Food Engineering

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Unsteady State Heat Transfer - Biot Number

Learning Outcomes

At the end of this module, you will be able to:

  1. differentiate between unsteady state and steady state heat transfer
  2. describe the concept of infinite size objects
  3. determine Biot number in unsteady state heat transfer
  4. calculate unsteady state heat transfer for conditions involving negligible internal resistance to heat transfer   

In unsteady state heat transfer, the temperature in an object varies with location and time, in contrast to steady state heat transfer where temperature varies only by location. In food processing, numerous situations require the calculation of unsteady state heat transfer, the subject of this module. In the following video, we will gain an appreciation of the need for a mathematical description of temperature in an object undergoing unsteady heat transfer. To simplify, the mathematical analysis, we resort to three geometrical shapes, sphere, infinite cylinder, and infinite slab. We will get an understanding of these shapes in this video.

We consider three different scenarios that cover most of the problems involving unsteady state heat transfer, namely, negligible internal resistance to heat transfer, negligible surface resistance to heat transfer, and finite resistance to heat transfer. To quantitatively differentiate these scenarios, we use a dimensionless number called Biot number. In the next video, we learn how the Biot number is obtained.

When Biot number is less than 0.1, we have a case of negligible internal resistance to heat transfer. In this case, in the next video, we will develop a solution to determine temperature distribution in a solid object as a function of time.


In this module, we were introduced to unsteady state heat transfer. You learned that the underlying mathematical description of unsteady state becomes complicated, but simple methods have been developed to determine temporal and spatial variation of temperature in an object. We examined the concept of using shapes such as an infinite cylinder and an infinite slab. You learned how to determine Biot number and its use in differentiating the location of thermal resistance to heat transfer in and around an object. We developed an expression to describe temperature variation with time for a case of negligible internal resistance to heat transfer.