Annular fin

In thermal engineering, an annular fin is a specific type of fin used in heat transfer that varies, radially, in cross-sectional area. Adding an annular fin to an object increases the amount of surface area in contact with the surrounding fluid, which increases the convective heat transfer between the object and surrounding fluid. Because surface area increases as length from the object increases, an annular fin transfers more heat than a similar pin fin at any given length. Annular fins are often used to increase the heat exchange in liquid–gas heat exchanger systems. In thermal engineering, an annular fin is a specific type of fin used in heat transfer that varies, radially, in cross-sectional area. Adding an annular fin to an object increases the amount of surface area in contact with the surrounding fluid, which increases the convective heat transfer between the object and surrounding fluid. Because surface area increases as length from the object increases, an annular fin transfers more heat than a similar pin fin at any given length. Annular fins are often used to increase the heat exchange in liquid–gas heat exchanger systems. To derive the governing equation of an annular fin, certain assumptions must be made. The fin must have constant thermal conductivity and other material properties, there must be no internal heat generation, there must be only one-dimensional conduction, and the fin must be at steady state. Applying the energy conservation principle to a differential element between radii r and r + Δr yields where the first two terms are heat transferred through conduction, while the third is heat lost due to convection with the surrounding fluid. T represents the temperature at r and Te represents the temperature of the surrounding fluid. Next, applying Fourier's law and dividing by 4πΔr, letting Δr → 0, yields Assigning new variables z and θ, where Tb is the temperature at the base of the fin,