ABSTRACT: Our present research falls into two parts regarding Heat Equations.
Part one (Time Dependency, Unsteady Case): In lieu of experimentally determining the heat transfer in a two body system on a cold and snowy Ohio night, we shall direct our attention to the more scientifically expedient investigation of determining the heat transfer of heated water in a cup as it cools to the ambient temperature in order to show that cups of different materials affect the rate of heat transfer. The experiment will consist of three cups of the same size and shape but made of different materials. Then we will perform a non-linear regression of the experimental data.
Part Two (Spatial Dependency, Steady Case): The Adomian decomposition method has been applied to evaluate the conduction-convection heat transfer through a straight fin, property distribution due to convection-diffusion, and conduction heat transfer through a slab with temperature dependent thermal conductivity. The Adomian decomposition method (ADM) provides the closed form solution for non-linear problems without applying any non-realistic simplifications and/or approximations. The obtained analytical solutions are compared with exact and numerical solutions, using the finite difference/R-K method. It is shown that the numerical simulation has some limitations and may not always produce correct results. However, the Adomian decomposition method follows the correct trend of the exact solution by applying only a few terms.
Dr. Mahmoud Najafi
Mr. Greg Putman
Donald began his pursuit of higher education, after being out of high school for fourteen years, by participating in massive open online courses known as MOOCs which gave him the necessary preparation for the rigors of college. Now in his sophomore year, he not only maintained a 4.0 GPA, but he traveled to Los Angeles, CA to present a paper at the Conference on Decision and Control, a transaction of IEEE and he traveled to San Antonio to present a paper at the Joint Mathematics Meetings, with Dr. Najafi as his advisor for both events. He is the founder of the Humanist Society of Kent State University, where he serves as President, and he serves as Treasurer of the Philosophy Club. His interests include chess, playing guitar, and discovering the deep insights of mathematics. As a mathematician, he hopes to find solutions to problems that will improve the human condition. He is profoundly concerned about convincing the next generation of students of the fundamental importance of learning mathematics and programming as gateways to their participation in the global information society.