A full analytical description of a bowtie nanoantenna excited by a localized emitter is presented using the transformation electromagnetic technique. By applying the conformal mapping, the bowtie nanoantenna is transformed into a periodic multi-parallel plate transmission line problem which can be easily evaluated analytically providing physical insight of the coupling between the dipole nanoemitter and the bowtie nanoantenna. The non-radiative Purcell enhancement spectrum is evaluated both analytically and numerically for different lengths, arm angles and metals, demonstrating a good agreement between both approaches. The method here presented fills the gap of the design techniques for optical nanoantennas.