GATE ME 2016 Set 1 — Question 52
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Heat Transfer → Conduction → Lumped Parameter System
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Question
A steel ball of diameter at is required to be cooled to by immersing it in a water environment at . The convective heat transfer coefficient is . Thermal conductivity of steel is . The time constant for the cooling process is . The time required (in s) to reach the final temperature is __________
Correct answer
42 to 42.5
Solution
Using the lumped heat capacity analysis for transient heat conduction, the temperature variation with time is given by:Where:
- (final temperature)
- (ambient temperature)
- (initial temperature)
- (time constant)
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