Hybrid differential transform - finite difference solution of 2 D transient nonlinear annular fin equation

One of the primary ways to enhance heat transfer rate is to use extended surfaces or fins. The heat transfer mechanism of fin is to conduct heat from the heat source to fin surface by its thermal conduction, and then dissipates it to surrounding medium by convection. Most common application areas of fins are in combustion engines, heat exchangers and cooling of electronic equipments. Early studies about thermal analysis of fins could be found in [1]. Hsiung and Wu [2] used the Laplace transformation and the integral method to study the transient heat transfer in straight fins of various shapes. Cheng and Chen [3] used a hybrid method to study the transient response of annular fins of various shapes subject to constant base temperatures. Arslantruk [4] investigated the optimum dimension of an annular fin with uniform thickness under thermally non-symmetric convective boundary condition. Recently Iborra and Campo [5] studied the temperature distribution and fin efficiency for annular fins of uniform thickness analytically. Lai et al. [6] introduced a discrete