Introduction to heat transfer and extended surfaces (Fins): Pioneering work of Harper and Brown /Gardner/Jacob; Fundamentals of heat transfer; Mathematical representation of heat flow across interfaces; Concept of thermal resistances and controlling resistance leading to why the use of fins; Common fin performance indicators: fin effectiveness, efficiency, surface enhancement and fin assembly augmentation; The process heat transfer design problem. One-dimensional fins and assemblies: Derivation of governing equations, boundary conditions and assumptions, Isolated single fins; Single fin attached to the primary surface and the introduction of the surface enhancement and the augmentation of the surface; Assembly augmentation; Non-uniform heat transfer coefficient; Free and mixed convection from a downward facing fin; Radiation from the surfaces of fins, Further consideration of the assumption with respect to one-dimensional heat flow through the assembly and fins. Two-dimensional fins and assemblies: Derivation of governing equations, boundary conditions and assumptions; Various geometries; The conjugate problem; Mathematical methods; Augmentation of assemblies. Important physical effects associated with two-dimensional fins and assemblies: Rectangular and cylindrical fins; Convection - uniform and non-uniform coefficients, Radiation from the surfaces of the fins and primary surface; Convection and radiation; Perfect contact; Temperature dependent physical properties, conductivity, heat transfer coefficient; Application of augmentation factors to specific fin assemblies; Axial conduction in longitudinal finned tubes. Transient heat transfer in one-dimensional fins and assemblies: Equations, boundary conditions and assumptions; Augmentation; The isolated fin; The fin assembly; General periodic heating and cooling of fin assemblies. Two-dimensional transient heat transfer in two-dimensional fins and assemblies: Equation boundary conditions and assumptions; Methods of solution; Augmentation; Isolated fins with various periodic heating and cooling, The fin assembly, General periodic heating and cooling of the system. Aspects of design using the one-dimensional and two-dimensional analysis of fin assemblies: Optimisation of fin assemblies; Discussion of augmentation devices for both sides of a primary surface; What to do next.