Improving the understanding and prediction of mixed convection under strong heating

The Apparent Reynolds Number (ARN) theory has been previously developed to explain the laminarisation of isothermal turbulent flows subjected to non-uniform body forces, and has since been extended to buoyancy-influenced heated flows, such as upward pipe flows of air and supercritical CO2. In these cases, the ARN framework has proven effective in characterizing turbulence suppression and the associated heat transfer deterioration.
This thesis extends the Apparent Reynolds Number (ARN) theory, originally developed to describe turbulence modulation under non-uniform body forces, to the prediction of heat transfer in mixed convection pipe flows. The work covers three flow conditions of increasing complexity: fully developed air flow, developing air flow, and supercritical CO2 flow. In the fully developed case, a reference flow based on the apparent Reynolds number is used to estimate eddy viscosity, enabling the model to accurately predict heat transfer deterioration caused by buoyancy, as validated against direct numerical simulation (DNS) data. For developing flows, where both buoyancy and inertial forces influence turbulence, it is observed that inertia can either suppress or enhance turbulence depending on flow conditions, similar to the effect of buoyancy. To capture this behavior, a pseudo-body force is introduced into the ARN framework, and two ARN-based models are accordingly developed based on the air-flow case presented in Chapter 4: the mixing-length model and the correlation model. Both models show strong agreement with DNS results. The same modelling strategy is then applied to upward supercritical CO2 flow, where strong property variations further complicate the flow behaviour. Despite these additional challenges, the ARN-based model remains effective in capturing both heat transfer deterioration and recovery. Overall, this research demonstrates that the ARN approach offers a unified, physically consistent, and computationally efficient framework for modeling mixed convection heat transfer across a wide range of flow conditions.