# Natural Convection

# Case study - Simulation of natural convection

Thermal transport due to natural convection problems are concerned with temperature-driven flows. These types of flows are driven due to the relationship between the temperature and the density of fluid. In many fluids, such as air, the density is decreased as the temperature is increased and vice versa. Local spatial temperature differences change the local density of the fluid and generate a buoyancy driven force in the flow. This buoyancy driven force causes the fluid-motion called natural convection. In this article we will study how simulation of natural convection can be used in an engineering application.

Fluid and thermal transport due to natural convection is critical to take into consideration in many natural phenomenon and engineering applications. Natural convection is e.g. a focal effect in all weather systems such as the formation of wind or the formation of tropical cyclones. In engineering and industrial applications, natural convection is often used to cool devices without the aid of electrically driven cooling fans.

**Case description - Simulation of natural convection**

This case study has its point of departure in a light-emitting-diode (LED) and is inspired by the work in reference [1]. LEDs convert electric energy to light with an effectiveness of approximately 25–35% [2], where the remaining part of the electric energy is converted to thermal energy. The thermal energy is generated in a relatively small volume in the LED lamp, which result in large local temperatures. Temperature control of LEDs is critical to take into consideration as too large temperatures result in a shift of emission wavelength, lower the lumen output and lower the lifetime of the lamps.

In this example we will demonstrate how CFD and engineering intuition can be used to design and simulate a passive cooler, which is capable cooling an LED by taking advantages of natural convection. A picture of a LED and the passive cooler design is shown below:

**Simulation setup**

To adequately model heat transfer due to natural convection requires the solutions to the Naiver-Stokes and energy equations in the fluid and conductive heat transfer in the solid. Thermal transport with natural convection is a strongly two-way coupled problem, as the temperature field influences the velocity field and vice versa. Natural convection problems are computationally expensive to solve numerically, due to the number of unknown fields (pressure, velocity and temperature) and the non-linear and coupled nature of the physics.

The flow in this study is assumed turbulent, compressible and time-dependent, where the compressibility of the fluid is modelled with the ideal gas equation. The heat transfer in the solid is assumed to be governed by the heat conduction equation. To reduce the computational effort, we take advantage of the symmetry of the problem and reduce the modelling to 1/4 of the full domain. The surface of the LED lamp is 400 K and the temperature of the ambient air is 300 K. The computational domain and the boundary conditions are shown to the left.

**Results **

As the thermal energy enters the passive cooler, the air in the proximity of the cooler is heated and the flow is accelerated due to the density differences of the air. The passive cooler works as a chimney where air is accelerated inside the cooler and exiting in the top. The steady state versions of the flow fields, the temperature field and the heat flux through the surface of the passive cooler are plotted on the figures below:

The passive cooler chimney design is inspired by the topology optimized design in [1]. Despite the simple design, we notice that the chimney effect results in an effective exacting of thermal energy from the LED.

The case study serves as an industrial example of a problem, in which the effects natural convection is critical to take into consideration. If your company faces problems, where the effects of natural convection are important to take into consideration, Aerotak can provide specialist and knowhow to solve and communicate the problems.

**Appendix**

The computational domain is discretized into approximately 3,000,000 elements. The surface mesh of the passive cooler and a cross section plane of the computational domain can be seen below:

**Reference**

[1] Lazarov, B. S., Sigmund, O., Meyer, K. E., & Alexandersen, J. (2018). Experimental validation of additively manufactured optimized shapes for passive cooling. *Applied Energy*, *226*(February), 330–339. https://doi.org/10.1016/j.apenergy.2018.05.106

[2] Cheng H-C, Lin J-Y, Chen W-H. On the thermal characterization of an rgb led-based white light module. Appl Therm Eng 2012;38:105–16. http://dx.doi.org/10.1016/j. applthermaleng.2012.01.014.