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Context: White dwarf - Brown dwarf short period binaries (P$_{\rm orb}$ $\lesssim$ 2 hours) are some of the most extreme irradiated atmospheric environments known. These systems offer an opportunity to explore theoretical and modelling efforts of irradiated atmospheres different to typical hot Jupiter systems. Aims: We aim to investigate the three dimensional atmospheric structural and dynamical properties of the Brown dwarf WD0137-349B. Methods: We use the three dimensional GCM model Exo-FMS, with a dual-band grey radiative-transfer scheme to model the atmosphere of WD0137-349B. The results of the GCM model are post-processed using the three dimensional Monte Carlo radiative-transfer model \textsc{cmcrt}. Results: Our results suggest inefficient day-night energy transport and a large day-night temperature contrast for WD0137-349B. Multiple flow patterns are present, shifting energy asymmetrically eastward or westward depending on their zonal direction and latitude. Regions of overturning are produced on the western terminator. We are able to reproduce the start of the system near-IR emission excess at $\gtrsim$ 1.95 $μ$m as observed by the GNIRS instrument. Our model over predicts the IR phase curve fluxes by factors of $\approx$1-3, but generally fits the shape of the phase curves well. Chemical kinetic modelling using \textsc{vulcan} suggests a highly ionised region at high altitudes can form on the dayside of the Brown dwarf. Conclusions: We present a first attempt at simulating the atmosphere of a short period White dwarf - Brown dwarf binary in a 3D setting. Further studies into the radiative and photochemical heating from the UV irradiation is required to more accurately capture the energy balance inside the Brown dwarf atmosphere. Cloud formation may also play an important role in shaping the emission spectra of the Brown dwarf.