GATE ME 2020 Set 1 — Question 44
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Heat Transfer → Conduction → Lumped Parameter System
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Question
A small metal bead (radius 0.5 mm), initially at , when placed in a stream of fluid at , attains a temperature of in 4.35 seconds. The density and specific heat of the metal are and , respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in ) between the metal bead and the fluid stream is
Correct answer
(B) 299.8
Solution
For a lumped heat analysis, the temperature variation with time is given by:Given:
, , at
,
For a spherical bead, the volume-to-surface area ratio is:Substituting the values:Taking natural log on both sides:Thus, the correct option is (B).
, , at
,
For a spherical bead, the volume-to-surface area ratio is:Substituting the values:Taking natural log on both sides:Thus, the correct option is (B).
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