Application of Newton’s Law of Cooling case Study: Estimation of Time of Death in Mu

Abstract

Determining the time of death of a person is a major responsibility of forensic investigation. This study presents a mathematical model based on Newton’s law of cooling to determine the time of death of a person. Emphasis is put on the development of the method and computer software taking advantage of the decrease in body temperature. The model is based on four parameters: temperature of the body at time t, temperature of the surrounding area at time t, the weight of the body and the condition of the body. Computer software using Microsoft visual C sharp that allows first calculation of the time of death and graphical representation of the cooling of dead bodies is presented. The algorithms are based on a first-order linear differential equation formulated by Newton and modified with a two-exponential-model by Marshall and Hoare (1962). Several calculations are run by the program and the results are presented to allow comparism so that different parameters may be assumed and their effect on the length of the cooling period be assessed. Data from the following sources: Handbuch Gerichtliche Medizin, Volume 1 by Bernd Brinkmann and Burkhand Madea and ACTAMORPHOLOGIC, 2006; vol 3(2):51-54 Medical journal of Macedonian Association of Anatomists and Morphologists (MAAM) are used to test the computer solution. We conclude that the cooling model which includes the post mortem plateau gave good results and therefore the model can be applied to all cases.

A Thesis Submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology, in partial fulfillment of the requirement for the degree of Master of Science: Industrial Mathematics College of Science/ Institute of Distance Learning.2013

KNUST