The advancement of computational technology has helped the modeling of controlled drug delivery into the biological tissues. One example is the modeling of the drug release into the human eye. Due to natural protective barriers of the eye, ocular drug delivery is considered as a major challenge in the development of treatments for diseases affecting different segments of the eye. In this work, the drug release from a current-mediated drug delivery device into the human eye is mathematically modeled and numerically simulated. The heat conduction, the flow of the aqueous humor in the anterior and posterior cavities are considered in the modeling. The heat distribution in different segments of the eye in the standing and supine positions is considered to study the thermal safety of the device. The effect of the voltage strength on the heat elevation of the eye segments is investigated. Numerical experiments highlight that ocular iontophoresis drug delivery system does not produce significant thermal damage and it is thermally safe for the eye. The mechanism of the drug release from the drug reservoir into different segments of the human eye is also studied. The observations show that the drug distribution in the standing position is asymmetric while the drug distribution in the supine position is symmetric. (C) 2018 Elsevier Ltd. All rights reserved.