ABSTRACT
This chapter presents the governing equations and methods of analysis of conduction heat transfer. It analyzes one-dimensional and two-dimensional problems, as well as steady-state and transient problems. The chapter investigates fundamental transport processes. It outlines advanced solution methods such as separation of variables, conformal mapping, and solutions in orthogonal curvilinear coordinates. The chapter examines various formulations and solutions of Fourier's Law and the heat equation for a range of coordinate systems. It includes the formulation and analysis of the heat equation, thermal resistance networks, fins and extended surfaces, advanced solution methods for multidimensional problems, and transient heat conduction. The flow of heat by conduction depends on three key factors: the temperature gradient, cross-sectional area of heat flow, and thermal conductivity. The temperature gradient prescribes the rate and direction of temperature change at a particular location. Heat flows by conduction in a direction perpendicular to a local isotherm. In other words, heat flows in a direction of steepest temperature descent.
