This paper establishes a two-dimensional axisymmetric model, and combines the dynamic contact angle model with a transient two-step moving mesh model to realize the transition from constant contact radius (CCR) mode to constant contact angle (CCA) mode. The flow and heat transfer characteristics of droplets fixed on different substrate surfaces evaporated in CCR mode under both uniform and non-uniform heating modes are studied.The results show that under the uniform heating mode at the bottom of the substrate, when droplets evaporate on a substrate with high thermal conductivity, the time to reach a stable internal flow is the shortest, and the average evaporation rate is the highest. The smaller the thickness of the substrate with low thermal conductivity, the higher the average evaporation rate.Under the non-uniform heating mode at the bottom of the substrate, when the temperature gradient ΔT is -6 K, the internal flow of the droplet in the initial stage of evaporation is counterclockwise flow, then a clockwise flow vortex is generated near the three-phase line, and the internal flow is a single clockwise flow when the flow is stable.When ΔT is -4 K, the stable internal flow of the droplet is two opposite vortices. When ΔT is 6 K, the internal flow of the droplet is always a counterclockwise flow. The average droplet evaporation rate increases with the increase of ΔT.