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 $7\text{W/mK}$. A person was found dead today at 6 am in a room temperature of which was maintained at $20{}^{\circ }C$. The temperature of the body is measured to be $26{}^{\circ }C$. Assuming human body properties as that of water, and convective heat transfer coefficient as $8{\text{W/m}}^2\text{K}$ at what time man died ? (Take body temperature of living man as $37{}^{\circ }C$)

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

Answer 1

The correct option is A 7 : 35 pm yesterday

Given: $d_0=30\text{cm}$,
$L=170\text{cm}$,
$h=8{\text{W/m}}^2\text{K}$,
$k=7\text{W/mK}$

$s=\frac{\pi r_0^{2}L}{2\pi r_{0}L+2\pi r_0^2}$

$s=\frac{\pi \times {0.15}^2\times 1.7}{2\pi \times 0.15\times 1.7+2\pi \times {0.15}^2}$

$s=0.0689\text{m}$

$Bi=\frac{hs}{k}=\frac{8\times 0.0689}{7}=0.0787$

lumped analysis is valid,

$\frac{ht}{\rho sc}=\text{ln}\left[\frac{37-20}{26-20}\right]$

$t=\frac{1.0414\times 1000\times 0.0689\times 4180}{8}=37492\text{second}$

or $t=10.41\text{hours}=10hours25minutesbefore$

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