The concept of discrete fuels provides a good representation of the real fire scenario. Many efforts on this issue have been conducted with the aid of heat transfer analyses, while little work has focused on the mass transfer analyses, nor considering the orientation effect. In this work, four PMMA (Polymethyl methacrylate) panels (8 cm × 10 cm × 1 cm) as a discrete fuel array are burned on the fireproof board at various angles (60°, 75°, 90°, 105°, and 120° based on the horizontal plane). The mass-transfer number, serving as a flammability index, is estimated and discussed based on the analyses of the flame morphology, pyrolysis length and mass loss rate. It is found that the mass-transfer number for discrete fuel presents a wave pattern including surges at the gaps. The increase in inclination angle can raise the average level of the mass-transfer number. The present work suggests that the exposed surface of flame bulk to the ambient may cause this defamation, since its increase can induce an enhanced radiation loss fraction . This conclusion is supported by the observed changes in the flame morphology, such as the monotonous decrease in flame width with inclination angle. Furthermore, the higher mass transfer numbers at the large inclination angles are observed, accompanied by a low flame height and a low pyrolysis spread rate, which indicate that the building façade with a proper large inclination angle may be a potential solution to tackle façade fires from the perspective of architectural design. The limitations of this paper are also identified for further considerations on the application of mass-transfer number.