Protective slag is coated on the surface of molten steel during continuous casting, the flow and heat transfer state of the protective slag is a decisive factor affecting the inflow and consumption of liquid slag and is also an important prerequisite for stabilizing and improving the quality of continuous casting billets. Based on the Navier Stokes fluid momentum conservation equation and energy equation, a two-dimensional longitudinal numerical model describing the flow/heat transfer of liquid protective slag on the surface of steel is established. The data comes from the equipment parameters and casting process of an arc shaped slab continuous casting machine in a domestic steel plant. The flow field and temperature field distribution of protective slag are calculated and analyzed, and the effects of factors such as slag layer thickness and shear speed on the flow and heat transfer status of the liquid slag layer are discussed. When the bottom shear velocity increases from 0.005 m/s to 0.2 m/s, the maximum flow velocity of liquid slag from the nozzle to the narrow surface in the center area of the model increases from 0.0012 m/s to 0.0617 m/s, and the average longitudinal flow velocity of liquid slag near the nozzle increases from 0.0012 m/s to 0.0627 m/s. The research results provide reference for investigating the complex metallurgical behavior of protective slag.