An important application of transient conduction in forensic sciences is to esti

Question

An important application of transient conduction in forensic sciences is to estimate the time of death. The core body temperature is measured which is generally lower than the normal human body temperature of 37 degree C due to heat loss to the surroundings. The time of death is estimated by assuming a lumped capacitance model of the human body. In this problem, you are required to validate whether the lumped capacitance model is valid in the given situation. Assume the human body to be cylindrical in shape with a height of 180 cm and a diameter of 50 cm The average thermal conductivity of the tissue can be assumed to be 1 W/m.K. The convection heat transfer coefficient can be estimated as h = 4.088 +6.92v^1.715 W/m^2.K where v (m/s) s the velocity inside the room. Assume a typical air velocity of 0.1 m/s inside the room.

Explanation / Answer

In order to check the validity of the lumped capacitance model,

Bicylinder = h. Lc / k

where Bi = Biot number

Lc = characteristic length

k = average thermal conductivity

v = air velocity in m/s

Lc can also be written as   Lc = r0 / 2

Bicylinder = (4.088 + 6.92 (0.1 m/s)1/2 W/m2.K) X (r0 / 2 m) / 1 W/m.K

Bicylinder = (4.088 + 2.188 W/m2.K) X (0.25 / 2 m) / 1 W/m.K

Please note that the radius, r0 has been converted to meters.

Bicylinder = 6.276 X 0.125

Bicylinder = 0.7845

We can see that Bicylinder > 0.1, hence the lumped capacitance model is not valid in the given situation.

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