Understanding how air moves around a hot pipe or cylinder is important for many everyday applications like cooling systems and heaters. This study looks at natural convection from a heated cylinder – the way air flows naturally when warmed without using fans or pumps. Our CFD simulation recreates the exact conditions from a research paper called “Natural convection from horizontal heated cylinder with and without horizontal confinement [1]” to make sure our computer model works correctly. This VALIDATION study focuses specifically on comparing Nusselt number values – which tell us how efficiently heat transfers from the cylinder surface to the surrounding air – at a Rayleigh number of 40,000 and a confinement ratio (H/D) of 0.3.

• Reference [1]: Sebastian, Geo, and S. R. Shine. “Natural convection from horizontal heated cylinder with and without horizontal confinement.” International Journal of Heat and Mass Transfer82 (2015): 325-334.

Figure 1: Model geometry showing boundary condition [1]

Simulation Process

Model geometry is erected by Design Modeler. A proper division of the zones eases the production of a structured grid. The Boussinesq model is used to consider density as a variable in the momentum equation’s buoyancy part. Sutherland’s equation is used to connect viscosity and air. As given in relations 3 & 4 in the paper, density and specific heat are variable and dependent on temperature. A user-defined function (UDF) is written to apply so.

Post-processing

The most important part of this study was checking if our simulation matches real experimental results from the research paper. Looking at the plot comparing local Nusselt number values around the cylinder, our simulation results line up almost perfectly with the published data. The Nusselt number basically tells us how efficiently heat transfers from the cylinder surface to the surrounding air at different positions. The good match proves our CFD simulation using the Boussinesq approximation and temperature-dependent properties through our custom user-defined function (UDF) correctly captures the physics of natural convection. This validation is really important because it means engineers can trust this simulation approach to predict heating patterns in similar real-world situations like hot water pipes, electronics cooling systems, or heating elements.

Figure 2: Local Nusselt number variation around the cylinder

Looking at the images together tells an interesting story about natural convection around our heated cylinder. In the velocity contour, we can see how air moves fastest (yellow-green areas showing about 0.015 m/s) along the sides of the cylinder as it gets heated. This creates what engineers call a thermal plume – basically a column of rising hot air – that forms right above the cylinder. The air near the top and bottom of the cylinder moves much slower (blue regions), which is exactly what happens in real life when you have horizontal confinement limiting the flow. In the temperature contour (bottom image), the warmest air (25.5°C, shown in red) hugs the cylinder surface and forms a thin thermal boundary layer. As this warm air rises, it creates the distinctive mushroom-shaped pattern above the cylinder with temperatures gradually cooling from red to yellow to green as the buoyancy-driven flow mixes with the surrounding cooler air. Both images show perfectly symmetrical patterns because the laminar flow conditions at this relatively low Rayleigh number (40,000) create very stable and predictable flow patterns.

Figure 3: Temperature & Velocity pattern around the hot cylinder regarding natural convection