Based on the concept of single-phase fluid, the abnormal heat transfer behavior of supercritical fluid has been investigated for many years. However, there is no unified understanding of the mechanism of its flow and heat transfer. In this paper, we first review the reported effects of buoyancy and acceleration on supercritical fluids, and then study the effects of buoyancy and acceleration on the flow structure and heat transfer for the upward vertically flowing of supercritical CO₂ fluid in a tube theoretically and experimentally. The results show that there is no conclusive experimental evidence that the abnormal heat transfer behavior of supercritical fluid is directly related to buoyancy and flow acceleration, and the existing criteria for estimating buoyancy and acceleration effect are based on the constant physical fluid and a lot of assumptions, as a result, different conclusions are obtained, though the same prediction method is used. Finally, we investigate the heat transfer deterioration of supercritical fluids based on the pseudo-boiling theory, and the proposed supercritical-boiling-number distinguishes the normal heat transfer deterioration from heat transfer deterioration of supercritical fluid. Our work paves a new way to understanding the supercritical fluid flow and heat transfer mechanism. The supercritical-boiling-number is important for establishing the optimum operating conditions for the supercritical fluid power cycle used in different technologies.