:A safe and economic waxy crude oil melting scheme is an important issue in oil tank storage, and thus a better understanding of the melting mechanism of waxy crude oil in the tank is necessary to develop a scientific scheme for melting. With the consideration of wax precipitation and non-Newtonian behavior, this paper establishes physical and mathematical models for melting process of waxy crude oil in the tank, and then develops an integrative numerical procedure for the coupling of physical process within wax crystal porous media, solid-liquid dispersion system and pure liquid waxy crude oil. In this research, the non-Newtonian behavior is described by the power-law equation. The melting process is simulated by the enthalpy-porous media theory. The melting characteristics of waxy crude oil in the tank with Pr=354.3, Ra=1.0×10 6 and Ste=0.371 is investigated. Particularly, the effects of wax precipitation and non-Newtonian behavior are analyzed in detail. The results show that, during melting, the heat flux varies at different stages under different wax precipitation scenarios. At the initial melting stage, heat flux decreases with the increase of the wax precipitation, and in the natural convection melting stage, heat flux increases with the increase of wax precipitation. The effect of non-Newtonian behavior on melting process is influenced by the permeability constant of wax crystal porous media. When the permeability constant is small, non-Newtonian behavior has little effect on the melting process. Conversely, when the permeability constant is large, strengthening the non-Newtonian behavior will slow down the melting process.