Numerical modeling and analysis of heat transfer in semitransparent media with combined radiation and conduction

The governing equation of heat transfer in semitransparent media by coupled conduction and radiation is a very complicated integro-differential equation. This equation is a function of geometry (three variables), wavelength, and direction (two variables). It is a highly nonlinear equation. It becomes more complex if the thermal and radiative properties are temperature dependent. Most difficulties encountered while solving these problems are how to handle the complex integro-differential equation and complex geometries. Except for very special situations, numerical methods have to be used to solve problems involving radiative heat transfer, especially for semitransparent media with coupled radiation and conduction.;Many numerical methods have been used to analyze combined-mode heat transfer in participating media. After reviewing state-of-the-art methods and analyzing the attributes of the combined-mode heat transfer governing equations, a new methodology is presented in this dissertation. This methodology is applied to expedite the efficiency of finite element calculations. This methodology seeks to effectively handle the topics of efficiency, accuracy, and compatibility. By using the finite element method and the proposed Effective Optical Depth (EOD), it is easy to simulate complex geometries and other complexities with reasonable accuracy and high efficiency. The incorporation of the EOD makes the computing time decrease greatly with little sacrifice of accuracy under certain conditions. Furthermore, this methodology can be extended to multi-dimensional problems. A computational code is developed based on this methodology, and a one-dimensional plain parallel plates benchmark problem is used to demonstrate the validity of the code. The results of the code show great agreement with that obtained by other numerical methods published by other investigators. After the verification of the code, several parametric studies were conducted. The results of these studies verify that the EOD approach offers solutions with reasonable accuracy and high efficiency.;The main contribution of this research is the development of a methodology for the numerical analysis of heat transfer in semitransparent media by employing an effective optical depth approximation and incorporating the EOD into a FEM formulation capable of treating integro-differential equations efficiently and accurately.