In many industrial designs, such as nuclear reactor cooling tubes or electrical equipment casings, fluid is trapped in a tight space between two cylinders. This space is called an “Annulus.” When one cylinder is hot and the other is cold, the trapped air begins to move on its own. Understanding this invisible airflow is critical for preventing machines from overheating. To see this flow, engineers perform a Natural Convection in a Narrow Annulus CFD simulation.

This project is a detailed Natural Convection in a Narrow Annulus fluent simulation tutorial. We are recreating the physical conditions described by Husain and Siddiqui [1] to study how heat moves in confined spaces. We use the powerful ANSYS Fluent software to visualize the temperature and calculate the heat transfer efficiency. By mastering this CFD Analysis of Natural Convection in a Narrow Annulus, you will understand the core principles of buoyancy-driven thermal management. For more foundational lessons on modeling thermal energy, please visit our Heat Transfer tutorials.

• Reference [1]: Husain, Shahid, and M. Altamush Siddiqui. “Experimental and numerical analyses of natural convection flow in a partially heated vertical annulus.” Numerical Heat Transfer, Part A: Applications7 (2016): 763-775.

Figure 1: The computational geometry for the Narrow Annulus CFD simulation, representing the space between two vertical cylinders. [1].

Simulation Process: Axisymmetric Setup and Boussinesq Model

To perform this Natural Convection in a Narrow Annulus ANSYS Fluent study, we do not need to draw the entire 3D pipe. Because a cylinder is perfectly round, we used a 2D Axisymmetric model. This means we only simulate a flat, rectangular slice of the gap, which saves a massive amount of computer power while keeping the results perfectly accurate. We filled this gap with a high-quality structured grid.

The core physics of this Narrow Annulus fluent simulation relies on the Boussinesq approximation. Natural convection happens because hot air expands and becomes lighter than cold air. The Boussinesq model is a special mathematical rule in ANSYS Fluent that calculates this tiny density change. It is the invisible engine that drives the flow in our simulation.

Post-processing: The Analytical Story of the Nusselt Number Drop

To truly understand this CFD Analysis of Natural Convection in a Narrow Annulus, we must connect the visual colors to the exact numbers on the graph. Let’s trace the journey of the air to understand the “Cause and Effect” of the heat transfer. Look at the Temperature Contour (Figure 2). The “Cause” of the flow is the extreme temperature difference. The inner wall is hot (Red), and the outer wall is cool (Blue). Because of the Boussinesq physics we set up, the cold, heavy air sinks down the blue outer wall. When it hits the bottom, it turns and touches the red inner wall.

This bottom corner is where the magic happens. Look at the Nusselt Number Plot (Figure 3). The Nusselt number measures how fast heat is moving. At the very bottom of the annulus, the Nusselt number spikes to its maximum value of roughly 9.3. Why? Because this is where the freshest, coldest air suddenly hits the hottest wall. The temperature gap is massive, creating a huge “thermal shock” that pulls heat away incredibly fast.

Figure 2: The temperature field from the Narrow Annulus fluent simulation, showing the hot inner wall (red) driving the upward flow, and the cool outer wall (blue) driving the downward flow.

But as we move up the cylinder, the story changes. The air is now rising along the hot inner wall. As it climbs, it absorbs heat. It becomes warmer and warmer. By the time this air reaches the top of the annulus, it is almost as hot as the inner wall itself. Because the air is already hot, it cannot absorb much more energy. The temperature gap has shrunk. This perfectly explains the “Effect” seen in Figure 3. As you trace the line from the bottom to the top, the heat transfer efficiency steadily drops. By the time the flow reaches the top, the Nusselt number has fallen from 9.3 all the way down to approximately 3.6. This Natural Convection in a Narrow Annulus fluent simulation proves a vital engineering rule: in vertical heated channels, the best cooling always happens at the entrance (the bottom), and the cooling power slowly dies out as the fluid travels upward.

Figure 3: The local Nusselt number plot, proving analytically how heat transfer drops from 9.3 at the bottom to 3.6 at the top as the air warms up.

Key Takeaways & FAQ

• Q: Why use a 2D Axisymmetric model?
  • A: It allows ANSYS Fluent to simulate a full 3D cylinder using only a 2D slice, making the Natural Convection in a Narrow Annulus CFD simulation much faster without losing accuracy.
• Q: What drives the flow inside the annulus?
  • A: Buoyancy. The temperature difference between the hot inner wall and cold outer wall causes density changes, calculated by the Boussinesq model.
• Q: Why is the Nusselt number highest at the bottom?
  • A: Because that is where the coldest, fresh air first contacts the hot wall. As the air rises, it warms up, and its cooling efficiency drops from 9.3 to 3.6.