This work proposes the application of the Adomian decomposition method (ADM) in conjunction with the differential evolution (DE) for simultaneously estimating the dimensions of a rectangular and hyperbolic profile annular fin in order to satisfy a prescribed temperature requirement. The thermal conductivity and the surface heat transfer are assumed to be temperature-dependent. The required temperature field has been obtained using ADM for cases, involving insulated and convective boundary conditions at the tip. Then, using an inverse scheme based on DE, required fins dimensions satisfying a prescribed temperature field are estimated. Owing to the correlated nature of the unknowns, many feasible solutions have been found to lie within a given range satisfying the given temperature field. This temperature field can offer the flexibility in selecting the designing parameters. The present study is expected to be useful for selecting the dimensions of a rectangular and hyperbolic profile annular fin which can satisfy the given temperature field. (C) 2013 Elsevier Ltd. All rights reserved.