This paper presents a method which may be used to determine the temperature distribution within a convective-radiative longitudinal fin of variable thermal conductivity, subject to convection heat transfer from a fluid of known temperature $Tf$ through the inside face of the primary surface, and which experiences convection-radiation heat dissipation into the environment at its tip. The paper demonstrates the use of the Adomian decomposition method in generating an analytical solution of the resulting nonlinear energy balance equation with nonlinear boundary conditions.

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