This article studies a class of fin problems with two nonlinear terms arising from thermal conductivity and convection heat transfer coefficient. A one-dimensional convective straight fin is analysed for exponentially temperature-dependent thermal conductivity and exponentially temperature-dependent heat transfer coefficient. The exact fin temperature excess, heat transfer rate and fin efficiency are obtained and presented graphically. The obtained results show the strong influences of exponent indexes of thermal conductivity and convection transfer coefficient as well as thermogeometric fin parameter on the fin efficiency and heat flow.