Anterior eye diseases are commonly treated by topically applied drugs in the form of eye drops or ointment. In order to assess the effectiveness of topical drug administration, it is crucial to understand temporal evolution and spatial distribution of the drug in the anterior eye. In this paper, a numerical model of topical drug transport in the anterior human eye is developed, which is coupled with heat transfer and fluid flow in the anterior eye. Spatio-temporal evolution of drug concentration is then investigated numerically, with an emphasis on the drug concentration at three targets: the trabecular meshwork (TM), iris and lens. The results show that after the drug diffuses across the cornea, convection by the aqueous humor (AI-I) flow is the dominant mechanism of transport of topically applied drugs in the anterior human eye, which is due to temperature difference across the eye. Effects of eye orientation and ambient temperature are also analyzed. Ambient temperature is found to play an important role in the transport of topically applied drugs to various target tissues in the anterior eye. With the increase of ambient temperature, the peak concentration at the target first decreases, and then increases, and the minimum value is reached when ambient temperature is close to the body core temperature. Eye orientation is found to influence the maximum drug concentration at different targets, as well as the time it takes to reach the maximum. The results may help to understand the drug transport process in the anterior human eye, and provide guidelines of drug administration in order to improve the delivery efficacy. (C) 2015 Elsevier Ltd. All rights reserved.