Heat transfer mechanisms are virtually present anywhere where energy is involved; heat conduction is one of those mechanisms. Pure conduction heat transfer can be found mainly in aerospace applications especially when aircrafts are in shadows occulted from sunlight and temperatures drop to extremely low values. In these cases resistance heaters are activated in order to preserve temperatures inside the aircraft within values where circuitry does not stop working. Resistance heaters should be embedded such that appropriate thermal control is achieved. In addition conduction heat transfer is of special interest in fundamental theory for science and engineering. Typically this kind of problems are solved by means of numerical analysis or specialized software which most of the times are more time consuming and more expensive in terms of computational resources. In the other hand, traditional analytical methods such as separation of variables can be used to solve simple heat conduction problems, but do not work for problems where discrete heat generation sources are present. The purpose of this work is to present an analytical method to solve transient conduction heat transfer problems in geometries with embedded discrete heat generating sources. The Green’s Functions were used to formulate the mathematical model to find analytical solutions to transient conduction heat transfer problems for circular plates with embedded discrete heat generating sources. Two cases of embedded heat generating sources are discussed: a thin circular wire in the form of an arc, and a circular region. Results found in the present work were taken for long values of time and compared to those reported by Venkataraman et al who found results for similar problems under steady state conditions. Results were in excellent agreement. Final equations found with the technique presented here are in the form of summations series similar to those found using the separation of variables method.
Coupling the BEM/TBEM and the MFS for the numerical simulation of acoustic wave propagation and transient conduction heat transfer
