Anisotropic fluids (e.g. liquid crystals) offer a remarkable promise as optofluidic materials owing to the directional, tunable, and coupled interactions between the material, flow, and the optical fields. Here we present a comprehensive in silico treatment of this anisotropic interaction by performing nonequilibrium molecular dynamics simulations. We quantify the response of a nematic liquid crystal (NLC) undergoing a Poiseuille flow in the Stokes regime, while being illuminated by a laser beam incident perpendicular to the flow direction. We adopt a minimalistic model to capture the interactions, accounting for two features: first, the laser heats up the NLC locally; and second, the laser polarises the NLC and exerts an optical torque that tends to reorient molecules of the nematic phase. Because of this reorientation the liquid crystal exhibits small regions of biaxiality, where the nematic director is one symmetry axis and the axis of rotation for the reorientation of the molecules is the other one. We find that the relative strength of the viscous and the optical torques mediates the flow-induced response of the biaxial regions, thereby tuning the emergence, shape and location of the regions of enhanced biaxiality. The mechanistic framework presented here promises experimentally tractable routes toward novel optofluidic applications based on material-flow-light interactions.