dEnclosure effects on the transition from a localized ignition to subsequent flame growth over a thermally thin solid fuel in microgravity are numerically investigated by solving the low Mach number time-dependent Navier-Stokes equations. The numerical model solves the two and three dimensional, time-dependent, convective/diffusive mass, and heat transport equations with a one-step global oxidation reaction in the gas phase coupled to a three-step global pyrolysis/oxidative reaction system in the solid phase. Cellulosic paper is used as the solid fuel and is placed in a slow imposed flow parallel to the surface. Ignition is initiated across the width of the sample or at a small circular area by an external thermal radiation source. Two cases are examined; an open configuration (i.e., without any enclosure) and the case with the test chamber used in our previous microgravity experiments. Numerical results show that the upstream centerline flame spread rate for the case with the enclosure is faster than that for the case without any enclosure. This is due to the confinement of the flow field and also thermal expansion initiated by heat and mass addition in the chamber. The confinement accelerates the flow in the chamber, which enhances oxygen transport into the flame. In the three-dimensional configuration with the spot ignition, the flame growth in the direction perpendicular to the flow is significantly enhanced by the confinement effects. The effect of the enclosure is most significant at the slowest flow condition investigated and the effect becomes less important with an increase in imposed flow velocity. The total heat release rate from the flame during a flame growth period increases significantly with the confinement and the enclosure effects should be accounted to avoid underestimating fire hazard in a spacecraft.