The unsteady conjugate forced convection-conduction heat transfer from a plate fin is numerically studied. The external forced flow is steady but the temperature of the fin base is an exponential change with time. Therefore, the unsteady energy equations of the fluid and the fin are solved simultaneously under the conditions of equality in heat flux and temperature at the fluid-fin interface at every instant of time. Numerical results are given for various quantities of interest including the local heat transfer coefficient, the local heat flux, the total heat transfer rate and the temperature distribution of fin under the effects of the convection-conduction parameter and the ratio of thermal diffusivities. The results of the present numerical solution have been compared with those of the conventional fin theory.