In this study, developing combined forced and natural convection heat transfer and fluid flow in a duct with an open cavity are numerically studied using two- and three-dimensional models of various cavity size and flow induced parameters. The left wall of the cavity is isothermal while all other walls, including duct walls, are assumed to be adiabatic. Air (Pr=0.71) flows through the duct. The geometrical parameters used in this work are the cavity width to cavity height ratio (0.5 <= W/D <= 2), and the channel height to cavity height ratio (0.25 <= H/D <= 2). The flow induced parameters consists of the Reynolds number (Re) and the Richardson number (Ri). Re=10, 100, 200 and Ri=0.01, 0.1, 1 and 10 cases are considered in the study. The effects of the geometrical parameters of the cavity as well as the flow parameters on the fluid flow patterns and the temperature distribution (isotherms) were analyzed. The mean Nusselt number over the isothermal wall of the cavity was computed, and the effects of Richardson and Reynolds numbers, cavity aspect ratio and relative duct dimensions on the heat transfer were investigated. The results show that for all Re numbers, as the Richardson number increases, the air circulation becomes stronger inside the cavity. The flow inside the cavity for Ri>1 and Re>100 becomes three-dimensional. Based on the 2D and 3D numerical simulations, using the computed mean Nusselt numbers, correlations were developed.