Context : White dwarf - Brown dwarf short period binaries ( P _ { 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 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 Hadley-like overturning are produced on the western terminator . We are able to reproduce the observed start of the systems near-IR emission excess at \gtrsim 1.95 \mu m. 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 . 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 .