Physical layer security (PLS) is critically important for emerging wireless communication networks to maintain the confidentiality of the information of legitimate users. In this paper, we investigate enhancing PLS in an unmanned aerial vehicle (UAV) based communication network where a UAV acting as an aerial base station (BS) provides coverage in a densely packed user area (such as a stadium or a concert area). In particular, non-orthogonal multiple access (NOMA) together with highly-directional multi-antenna transmission techniques in mmWave frequency bands are utilized for improving spectral efficiency. In order to achieve PLS against potential eavesdropper attacks, we introduce a protected zone around the user region. However, limited resource availability refrain protected zone being extended to cover the entire eavesdropper region. Hence, we propose an approach to optimize the protected zone shape (for fixed area) at each UAV-BS hovering altitude. The associated secrecy performance is evaluated considering the secrecy outage and sum secrecy rates. Numerical results reveal the importance of protected zone shape optimization at each altitude to maximize NOMA secrecy rates.