The present study supplies a new approach to calculate thermal performance of a singular fin with variable thermal properties. With discrete model, the singular fin can be divided into many sections. Then, each section can be combined together to obtain the whole solution of the fin by recursive numerical formulation. The recursive formulas for both conditions with and without heat transfer on fin tip are derived in the present study. Finally, several examples including composite and boiling mode of a fin have been successfully simulated to demonstrate the validity of the present approach. (c) 2005 Elsevier Ltd. All rights reserved.