A numerical study is pursued to investigate the aerodynamics and thermal interactions between a spreading flame and the surrounding walls as well as their effects on fire behaviors. This is done in support of upcoming microgravity experiments aboard the International Space Station. For the numerical study, a three-dimensional transient Computational Fluid Dynamics combustion model is used to simulate concurrent-flow flame spread over a thin solid sample in a narrow flow duct. The height of the flow duct is the main parameter. The numerical results predict a quenching height for the flow duct below which the flame fails to spread. For duct heights sufficiently larger than the quenching height, the flame reaches a steady spreading state before the sample is fully consumed. The flame spread rate and the pyrolysis length at steady state first increase and then decrease when the flow duct height decreases. The detailed gas and solid profiles show that flow confinement has competing effects on the flame spread process. On one hand, it accelerates flow during thermal expansion from combustion, intensifying the flame. On the other hand, increasing flow confinement reduces the oxygen supply to the flame and increases conductive heat loss to the walls, both of which weaken the flame. These competing effects result in the aforementioned non-monotonic trend of flame spread rate as duct height varies. This work relates to upcoming microgravity experiments, in which flat thin samples will be burned in a low-speed concurrent flow using a small flow duct aboard the International Space Station. Two baffles will be installed parallel to the fuel sample (one on each side of the sample) to create an effective reduction in the height of the flow duct. The concept and setup of the experiments are presented in this work.