A complex variable boundary element method for two-dimensional steady heat conduction

Abstract

Engineers are responsible for understanding scientific ideologies while turning them into reality. For example, to invent a vacuum flask, engineers need to model the prototype and do different engineering analysis such as thermal, stress and strain analysis on the flask. Engineers now have a variety of methods and software to pick, which require engineers to understand the basis of the methods and differences among them so that the engineer can make a wise choice. Also, many common analytical methods can be used together with software in order to decrease computational time and to reduce errors, especially when the structure is too complicated and effortdemanding to solve entirely manually. Additionally, many kinds of software are able to simulate with given conditions by the engineers which would not have been possible physically. In the report, the author will discuss the different method and software available and how they are used together. These include numerical method such as boundary element method (BEM) and its extension, complex variable boundary element method (CVBEM) in which emphasis is placed on the development of CVBEM. Theories and examples to prove for the accuracy of the CVBEM software will be reviewed and demonstrated. In addition, the report deals with the study of heat transfer, in which methods discussed must be able to solve partial differential equations (PDEs) effectively. In particular, where the CVBEM software is proven to be reliable in solving specific twodimensional heat conduction scenarios in the form of Laplace equation.