Non-iterative control volume aproach to one-dimensional steady conduction with convection - Applications to extended surfaces

A numerical method based upon the integral formulation of the conduction equation has been applied to extended surfaces of arbitrary profile, with nonuniform heat transfer coefficient, end cooling and imperfect base contact. The method utilizes temperature excess coefficients which relate local and adjacent upstream temperature excesses. General expressions of the temperature excess coefficients, local temperature excess, total fin heat loss rate and fin efficiency are developed for longitudinal fins, spines and pins, and circular annular fins. Several examples discussed in Kern and Kraus are considered to demonstrate the simplicity, directness and accuracy of the method which can be easily adapted to programmable calculators or microcomputers.