In this paper, we investigate the influence of convection heat transfer coefficient and declivity fin angle to the efficiency and effectiveness of pentagonal fins. The temperature distribution is computed using an explicit finite difference method. The area of the fin is dependent on the one-dimensional position. Our computational experiments show that: (a) the convection heat transfer coefficient influences the efficiency and effectiveness for the steady and unsteady states, that is, the larger the coefficient leads to the smaller the efficiency and effectiveness (b) the declivity fin angle also influences the efficiency and effectiveness of the fin for the steady and unsteady states, that is, the smaller the declivity fin angle leads to the larger effectiveness both for steady and unsteady states, but the efficiency is smaller for steady state.