GATE ME 2016 Set 3 — Question 53
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Heat Transfer → Conduction → Lumped Parameter System
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Question
A cylindrical steel rod, in diameter and in length is first heated to and then immersed in a water bath at . The heat transfer coefficient is . The density, specific heat and thermal conductivity of steel are , , and , respectively. The time required for the rod to reach is ________ seconds.
Correct answer
42 to 45
Solution
To determine the time required for the rod to cool to , we first evaluate if the lumped heat capacity analysis is applicable by calculating the Biot number ().
Given and :
Since , the lumped analysis is valid.
Substituting the given values (, , ):
Using the long rod approximation () yields . Both results fall within the specified range of to .
1.Characteristic Length ():
For a cylinder of radius and length :Given and :
2.Biot Number ():
Since , the lumped analysis is valid.
3.Lumped Analysis Equation:
Substituting the given values (, , ):
Using the long rod approximation () yields . Both results fall within the specified range of to .
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