Precipitation nowcasting, key for early warning of disasters, currently relies on computationally expensive and restrictive methods that limit access to many countries. To overcome this challenge, we propose precipitation nowcasting using satellite imagery with physics constraints for improved accuracy and physical consistency. We use a novel physics-informed dual neural operator (PIANO) structure to enforce the fundamental equation of advection-diffusion during training to predict satellite imagery using a PINN loss. Then, we use a generative model to convert satellite images to radar images, which are used for precipitation nowcasting. Compared to baseline models, our proposed model shows a notable improvement in moderate (4mm/h) precipitation event prediction alongside short-term heavy (8mm/h) precipitation event prediction. It also demonstrates low seasonal variability in predictions, indicating robustness for generalization. This study suggests the potential of the PIANO and serves as a good baseline for physics-informed precipitation nowcasting.