We have studied the behaviour of a biaxial smectic A liquid crystal based on the soft ellipsoid string-fluid in shear flow by molecular dynamics simulation using the SLLOD equation of motion. This is facilitated by the fact that the biaxial symmetry allows linear relations between the pressure and the velocity gradient. This means that linear irreversible thermodynamics can be applied independently of the simulations to obtain the torques determining the orientations of the system and that the predictions of this theory can be cross-checked by the simulations. It turns out that there is a torque turning the smectic layers to the orientation parallel to the vorticity plane if the simulation is started in another orientation. In the orientation parallel to the vorticity plane where the director formed by the long axes of the molecules, n_w, is perpendicular to the vorticity plane there is another torque keeping the director formed by the normals of the broadsides of the molecules, n_u, parallel to this plane at a constant alignment angle, ψ relative to the streamlines independently of the strain rate. Moreover, this alignment angle seems to be the one where the irreversible energy dissipation rate, ẇ, is minimal. This is in agreement with a recently proven theorem according to which ẇ is minimal in the linear regime of a nonequilibrium steady state. Finally, we studied the orientation of n_u when the smectic layers are parallel to the shear plane. In a simulation this orientation is stabilised by the periodic boundary conditions. Then we found that there was a nonlinear torque turning n_u to the orientation perpendicular to the streamlines thus minimising the value of ẇ even though this value is larger than the value of ẇ in the orientation parallel to the vorticity plane. This means that ẇ is minimized given the external boundary conditions.