GATE ME 2026 Set 1 — Question 35
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Heat Transfer → Conduction → Lumped Parameter System
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Question
A sphere of radius 5 mm is initially in equilibrium at 400 in a furnace. It is suddenly removed from the furnace and dipped in a well-stirred water bath at 20 , with a convection heat transfer coefficient of 500 W/(m K). For the given range of temperatures, the thermophysical properties of the material of the sphere are: density kg/m, thermal conductivity W/(mK), and specific heat J/(kgK). Neglecting radiation heat transfer, the time required for the centre of the sphere to cool from 400 to 50 is ________ seconds (rounded off to 2 decimal places).
Correct answer
24.5 to 26
Solution
First, we check if the lumped heat capacity analysis is valid by calculating the Biot number ():For a sphere, the characteristic length is:Given mm m:Since , lumped heat analysis is valid.The temperature distribution for lumped analysis is given by:Given:
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