Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows

This study presents a detailed investigation of the temporal evolution of the Nusselt number ((Formula presented.)) in uniformly accelerated and decelerated turbulent pipe flows under a constant heat flux using direct numerical simulations. The influence of different acceleration and deceleration rates on heat transfer is systematically studied, addressing a gap in the previous research. The simulations confirm several key experimental findings, including the presence of three distinct phases in the Nusselt number temporal response—delay, recovery, and quasi-steady phases—as well as the characteristics of thermal structures in unsteady pipe flow. In accelerated flows, the delay in the turbulence response to changes in velocity results in reduced heat transfer, with average (Formula presented.) values up to (Formula presented.) lower than those for steady-flow conditions at the same mean Reynolds number. Conversely, decelerated flows exhibit enhanced heat transfer, with average (Formula presented.) exceeding steady values by up to (Formula presented.) due to the onset of secondary instabilities that amplify turbulence. To characterize the (Formula presented.) response across the full range of acceleration and deceleration rates, a new model based on a hyperbolic tangent function is proposed, which provides a more accurate description of the heat transfer response than previous models. The results suggest the potential to design unsteady periodic cycles, combining slow acceleration and rapid deceleration, to enhance heat transfer compared to steady flows.