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Question

An average human body is modeled as a 30 cm diameter, 170 cm long cylinder having 72% water by mass taking thermal conductivity of body as 7 W/mK. A person was found dead today at 6 am in a room temperature of which was maintained at 20 C. The temperature of the body is measured to be 26 C. Assuming human body properties as that of water, and convective heat transfer coefficient as 8 W/m2K at what time man died ? (Take body temperature of living man as 37 C)

A
7 : 35 pm yesterday
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B
8 : 00 pm yesterday
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C
10 : 24 pm yesterday
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D
10 : 40 pm yesterday
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Solution

The correct option is A 7 : 35 pm yesterday
Given: d0=30 cm,
L=170 cm,
h=8 W/m2K,
k=7 W/mK

s=πr20L2πr0L+2πr20

s=π×0.152×1.72π×0.15×1.7+2π×0.152

s=0.0689 m

Bi=hsk=8×0.06897=0.0787

lumped analysis is valid,

htρsc=ln[37202620]

t=1.0414×1000×0.0689×41808=37492 second

or t=10.41 hours=10 hours 25 minutes before

i.e. died at 12:00 -(10:25 - 6:00) PM = 7 : 35 pm yesterday

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