Browsing by Author "Ongati, Naftali O."

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Derivation and solution of the heat equation in 1-D
(International journal of engineering, science and mathematics, 2013) Kwach, O.; Ongati, Naftali O.; Alambo, David O.; Okaka, Colleta A.
Heat flows in the direction of decreasing temperature, that is, from hot to cool. In this paper we derive the heat equation and consider the flow of heat along a metal rod. The rod allows us to consider the temperature, u(x,t), as one dimensional in x but changing in time, t.
Forensic estimation of time of death: A mathematical model
(International journal of management, IT and engineering, 2013) Kwach, O.; Ongati, Naftali O.; Nyakinda, JO.; Nyang’inja, Rachael.
In this paper we establish the exact time of death of a murdered person. This leads to an ordinary differential equations whose solution has been analyzed to provide the approximate time of death. Forensic expert will try to estimate this time from body’s current temperature and calculating how long it would have taken to lose heat to reach this point. This provides an accurate approach to establish the approximate time when crime is committed.
Mathematical model for nutrient exchange across the placenta
(International journal of engineering & mathematical sciences, 2015) Odongo, Joel Olielo.; Ongati, Naftali O.
This study presents a new mathematical model for nutrient exchange across the placenta which include nutrient exchange from foetus to mother to provide a system of equations in the form, Y ሶ ൌ AY ൅ rԦሺtሻ and whose solution was analyzed for equilibrium and stability. This model introduces another parameter that takes care of waste elimination from foetus to mother. It was established that the final model is stable compared to the existing models, that is, the eigenvalues of the coefficient matrix are negative real number and complex numbers with negative real parts. This shows that the new model provides one straight line of solutions tending to the origin and a plane of solutions which spiral towards the origin. This gives a more accurate mathematical model for nutrient exchange in the placenta. This model would create a lot of insight into nutrient exchange in the placenta, the elimination of waste from the foetus and open room for further research from the mathematical concept developed.