Numerical modeling of temperature distribution in 2d model using transmission line modeling / N.N Abdul Razak and S.M Wah

This paper introduces the application of the Transmission Line Modeling (TLM) method for simulating heat flow or thermal distribution in 2-dimensional model comprising of conducting materials. The developed model is able to predict the temperature distribution in a material device and the first geometry considered was a 2D slab with a square heat generation region of 100°C in the center of the slab. The other edges of the slab were assumed to have a zero heat flow condition. The slab is assumed to be of Aluminum 2702 kg/m3, 903 J/kg.K. 237 W/m.k with a 50x50 mesh size. Coding and simulation are done by using the Salford Plato Software. A high degree of certainty is offered by numerical modeling and the numerical method which is adopted by this paper is the TLM method. TLM has become a powerful numerical tool ill solving problems of heat and mass diffusion through a medium. It is based on using transmission line elements to describe all energy storage elements. It is systematic, simple, explicit and unconditional stability has been established. The basic approach of the TLM method is to obtain a discrete model which is then solved exactly by numerical means. The method works in term of incident and scattered voltages and is different from conventional methods. In a 2D TLM model, waves propagate on a mesh of transmission lines interconnected at nodes. A voltage pulse will be incident at the node and this pulse will be partially reflected and transmitted according to transmission line theory. Energy is thus conserved and spreads isotropically from the excited node. The results prove that TLM is a perfectly compatible method to employ and can be used to solve real engineering problems, involving complex geometries, boundary conditions and material properties. Furthermore, the method is expressed in terms of circuit concept which is familiar to engineers and accuracy can be increased by reason of meshing.