Mathematical Modelling of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surface of a Vertical Cylinder

Turbulent natural convection in cylindrical enclosures is a significant phenomenon in most engineering and industrial applications, such as thermal insulation, electronics cooling, and building climate control. An explicit understanding of the transition of flow from laminar to turbulent and its influence on heat transfer is essential in terms of optimizing system performance. The study solves two major objectives: Model the governing equations of turbulent natural convection in a cylindrical enclosure using K-Omega turbulence model, and compute the effective thermal conductivity, turbulence intensity, and streamline distribution as functions of Rayleigh number. The enclosure that has been considered is an insulated vertical sidewall enclosure with a top wall at 298 K and a bottom wall at 320 K. The mathematical formulation consists of the Reynolds-Averaged Navier–Stokes (RANS) equations, the energy equation, and transport equations for turbulence, subject to the Boussinesq approximation to model buoyancy. A low-Reynolds-number two-equation model is used to model turbulence close to the walls, and the Prandtl number is set to 0.71 to model air as the working fluid. Numerical solutions are achieved by the use of the finite difference technique and verified by simulations done in ANSYS Fluent. The simulation identifies how structures flow and mechanisms of heat transfer change with increasing Rayleigh numbers. At small Rayleigh numbers, the flow is steady, conduction-dominated, with smooth streamlines and little or no turbulence. It is noted that as the Rayleigh number increases, buoyancy-driven convection becomes more significant, leading to the formation of vortices, intensified turbulence, and enhanced mixing, which collectively improve the effective thermal conductivity. The streamline distribution becomes increasingly complex and disordered, reflecting the transition to chaotic flow. These results demonstrate that the Rayleigh number is a key parameter influencing thermal and flow characteristics in cylindrical enclosures. The study provides practical insights in designing and optimizing systems involving buoyancy-induced turbulent heat transfer.