Abstract: In the additive manufacturing of complex structures, the auxiliary supports put on the enclosed voids are difficult to remove after build. To solve this issue, this paper proposes a convection-diffusion equation based approach for designing self-supported enclosed voids. In the density-based topology optimization, due to the lack of explicit boundary representation, it is challenging to identify the enclosed voids and control their overhang angle. In this paper, by simulating the transport of light along the build direction, we can identify the shadowed region as the enclosed voids regions. Combined with the density-gradient, a global constraint is constructed to constrain the overhang angle of the enclosed voids. In addition, in order to exclude the external overhang boundaries from the identified enclosed voids region, the intermediate density fields are eroded through the PDE-based density filtering and the Heaviside projection. Numerical examples are presented to demonstrate the efficacy of the proposed topology optimization method in the design of self-supported enclosed voids. The proposed method would help to further combine topology optimization and additive manufacturing for the generative design and fabrication of complex structures.