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Application of Heat and Mass Transfer Analogies in the Undergraduate Engineering Laboratory to Estimate Time of Death

Jimmy L. Smart, Chemical & Materials Engineering, University of Kentucky, 4810 Alben Barkley Drive, Paducah, KY 42001

Historically, estimation of time of death has always been a valuable forensic tool. In England, 925 AD, St. John of Beverly was appointed “keeper of the pleaser of the crown”, later to be shortened to “crowner”, then finally to “coroner”. At that time, only crude “forensic” tools of rigor mortis and corpse warmth were used to gage time of death. It was not until 1600, that the first criminal autopsy was conducted by Ambrose Pare (French physician) [1,2].

By 1811, an English physician named John Davey had formulated his famous law based upon the principle of algor mortis (slow cooling of a warm-blooded corpse). Davey's Law states that 1.5 oF is lost per hour as measured in the armpit. Therefore, at least in theory, it should be possible to record the temperature of a corpse and having knowledge of the heat loss rate curve, be able to estimate time of death. In reality, the rate curve is complicated by many factors and it is often difficult to pinpoint time of death.

The rate of heat loss from the human body can be calculated from the fundamental equation of heat transfer: Q = UA ΔT, where Q is energy lost per area, U is the overall heat transfer coefficient, A is the area of the body, and ΔT is the temperature difference between the body and its surroundings. It is difficult to estimate a reliable value for the heat transfer coefficient because of the complicated surface area geometry of the human body. In this laboratory exercise, a heat - mass transfer analogy: the Chilton-Colburn Analogy, is used to estimate the heat transfer coefficient governing loss of heat from the human body. The naphthalene sublimation technique [3] is used to relate mass transfer coefficients to analogous heat transfer coefficients.

Initially, simple geometries of a sphere and cylinder are cast in naphthalene and suspended in a heated duct. Following procedures of earlier investigators [4], loss of weight of these simple shapes over time is monitored and used to calculate an average mass transfer coefficient. Using the Chilton-Colburn Analogy, an average heat transfer coefficient can be determined. These results are compared to existing classical correlations to give students confidence in their technique.

Similarly, a small doll in the shape of a human body is cast from naphthalene and its mass loss monitored over time at a variety of temperatures. An average heat transfer coefficient for the doll can be determined. The surface area of the human body is estimated by modeling the body as a combination of simple geometries of a sphere and various size cylinders.

1. Sachs, Jessica S., Corpse: Nature, Forensics, and the Struggle to Pinpoint Time of Death, Perseus Books Group: Basic Books, NY, October 2002.

2. Miller, Hugh, What the Corpse Revealed: Murder and the Science of Forensic Detection, St. Martin's Press, NY, June 1999.

3. Goldstein, Leonardo and E.M. Sparrow, Heat/Mass Transfer Characteristics for Flow in a Corrugated Wall Channel, J. Heat Transfer (99), May 1977, 187 - 195.

4. Perez, J.S., and E.M. Sparrow, Determination of Shell-Side Heat Transfer Coefficients by the Naphthalene Sublimation Technique, Heat Transfer Engineering (vol 6, no. 2), 1985, 19 - 29.