1. Introduction Thermo-physical properties of any material such as thermal conductivity, specific heat, and thermal diffusivity are very important to be known. It can either be determined using steady state method or transient state method. Transient state method is often used for it can measure such properties at a shorter period oftime, higher precision, and broader measuring range in contrast to the steady state method. One simple way of doing this method is to use a flat rectangular test specimen be subjected to a heat flux in one side thereby producing heat conduction. The temperature increase of the specimen with respect to time then determines such properties. However, due to its geometry such simple transient method causes less accurate measurement since the heat applied cannot be treated as one dimensional. Modifying its geometry into a hollow cylindrical shell with heat flux applied radially outward makes it one dimensional assuming it has infinite length. In this manner a more reliable and accurate data can be generated. This study aims to develop a mathematical model representing one- dimensional transient heat conduction across a cylindrical layer of sample material. This method was originally proposed by Abdel- Wahed and co-workers which measures thermal properties of material sample contained in the annular space between two concentric, metallic cylinders with the inner cylinder being heated uniformly. This allows simultaneous measurements of specific heat, thermal conductivity, and thermal diffusivity.[1] A better solution to a mathematical modeling involves numerical approach which applies Implicit, Explicit, and Crank-Nicolson methods. Further simulation of the model using computer software may able to provide a faster, reliable, and graphical solution to the problem. 2. Modeling Mathematical models are used to predict behavior of physical systems, such as heat flow through a material, fluid flow, vibration and other engineering problems. Such models are useful in many engineering applications where cost estimates and safety considerations need be predicted to ensure the success of the project. ONE DIMENSIONAL TRANSIENT HEAT CONDUCTION MODEL USING FINITE DIFFERENCE METHOD Richard Jess Chan, Gromyko Geraldino Jr., and Joseph Mayormita Department of Mechanical Engineering University of San Carlos Cebu City, Philippines 6000 Abstract This paper presents a mathematical solution to a one dimensional transient heat conduction model representing the proposed cylindrical instrument used for measuring thermo physical properties such as thermal conductivity, specific heat, and thermal diffusivity. The model is co mposed of two cylindrical shell one being inside the other in a concentric manner while the test material being put between them. Constant heat flux is applied in the inner shell which causes heat conduction in outward radial direction to the outer insulated shell. Physical laws that govern the conduction heat transfer process were employed with the boundary conditions given. Using Finite Difference Method namely Explicit, Implicit, and Crank-Nicolson methods the model was able to give mathematical solutions. Implicit and Crank-Nichols on methods are found to be reliable solutions having an error of only 9.89% compared to 71.27% of explicit method. With the aid of computer programming the model was able to simulate and predict the characteristics of different test materials. It was found out that the lesser the difference between the inner and outer shell radius the faster the results can be achieved. The obtained mathematical model in this paper serves as a guide in the design of the proposed instrument.
