Transient thermal analysis of brake disc in c++

Abstract

Abstract This work examines the development of a C++ program to analyze one dimensional thermal conduction for asymmetrical domain using Finite Element Method in C++ environment. Finite Element Library has been used to incorporate various pre-defined Finite Element classes. The various classes have been further grouped into several modules which serve as the fundamental units of any program that encapsulated Finite Element Method. The work strives to illuminate the abstraction behind the computation of the desired unknown solution to a complex real-world problem by capturing the physics of heat conduction and highlights the mathematics required to arrive at an understandable transient solution, which adheres to the conditions of stability, and thus can be relied upon to be implemented in various automotive engineering applications. It also identifies the underlying mechanism through which simple one-dimensional and multi-dimensional partial differential equation problem are generally solved. The elliptic, classic form of partial differential equation has been developed in the form of C++ code. The development begins with elliptic partial differential equations in multi-dimension dimension for steady state heat conduction and then is expanded to included time discretization, which is requirement of a time-dependent problem. Then output of the code is compared to the solution is validated iteratively so as to find the critical time step size for stability, which also validates whether the code actually works for different numerical techniques such as Forward Difference, Backward Difference and the Crank-Nicholson Method, all three distinguished by certain value of a common parameter. The C++ code is both flexible as well as expandable and can be thought of as a mathematical model to solve time-dependent heat conduction problem.