INTEGRAL-TRANSFORMS IN THE 2-DIMENSIONAL NONLINEAR FORMULATION OF LONGITUDINAL FINS WITH VARIABLE PROFILE

The integral transform method is employed for the hybrid numerical-ana lytical solution of two-dimensional, steady-state heat conduction with in extended surfaces of variable longitudinal profile and temperature dependent thermal conductivity. Numerical results are then obtainable with automatic accuracy, allowing for the establishment of benchmark r esults and for the validation of approximate solutions. Convergence ra tes are illustrated for longitudinal fins with trapezoidal and parabol ic profiles, and for different values of the governing parameters, Blo t number and aspect ratio. In addition, the classical one-dimensional approximate solutions are critically examined for these typical non-st raight profiles, and the applicability limits are investigated.