# The Thermal Resistance of Convection

### Key Takeaways

• Heat transfer through convective heat transfer occurs in electronics cooling when the device is hotter than the surrounding fluid.

• Electronics cooling utilizes natural air convection as well as forced air convection for heat removal from the circuit.

• Forced air convection heat transfer offers less thermal resistance than natural air convection. The heat transfer rate of electronic circuits can be varied by employing forced convection rather than natural convection

The total system efficiency of semiconductor-based high-efficiency converter circuits is influenced by their cooling system. The cooling system or thermal management system of electronic circuits heavily relies on conduction, convection, and radiation. The heat transfer rate of electronic circuits can be varied by employing forced convection rather than natural convection. The thermal resistance analogy can be used to distinguish the effect of natural and forced convection on electronics cooling. The thermal resistance of convection changes with the air flow rate, which is why the analogy also differs for natural and forced air convection. In this article, we will explore convection and its thermal resistance.

## Convection

Heat transfer through convection occurs in electronics cooling when the device is hotter than the surrounding fluid. Convection heat transfer is possible only in the presence of a moving liquid or gas.

According to Newton’s law of cooling, the rate of convection heat transfer can be given by the equation: Where Qconv is the convection heat transfer rate, h is the convective heat transfer coefficient, A is the surface area of the electronic device to be cooled, T is the temperature of the surrounding fluid, and Ts is the temperature on the surface of the electronic device.

Depending on how the surrounding fluid flow is maintained in electronic cooling, convection can be classified into natural convection and forced convection.

### Natural Convection

Natural convection is dependent on the fluid density differences produced by the temperature differences in the fluid. In electronics using natural convection-based cooling, air is usually the natural surrounding fluid. The air in the vicinity of the electronic device absorbs heat from its surface. As the air gets hotter, it rises due to density differences. The cooler air displaces the hotter air, developing natural convection. The atmospheric air circulation and local weather aid natural convection-based cooling.

### Forced Convection

When forced convection is used for electronics cooling, the surrounding fluid is in motion. By forced convective heat transfer, large amounts of heat energy can be transferred to fluid efficiently. The fluid in motion can be air movement created by employing cooling fans in the circuit. Devices can also be liquid cooled using a cold base plate.

## Natural Air Convection vs. Forced Air Convection

Electronics cooling utilizes natural air convection as well as forced air convection for heat removal from a circuit. The airflow rate in convective heat transfers depend on the geometry of the electronic device, heat flux on the surface, and the buoyancy characteristics of the surrounding fluid. Factors such as cost, noise, vibration, and reliability determine whether forced air convection should be used instead of natural air convection. Forced air convection cooling adds to the total weight of electronics.

When the geometry of an electronic device or thermal management system changes, the convective heat transfer characteristics also change. Similarly, the failing of a fan transforms forced air convection to natural air convection and the cooling rate changes.

With the help of a thermal equivalent circuit, one can investigate the characteristics of natural and forced air convective heat transfer. A thermal equivalent circuit utilizes a quantity called thermal resistance to model the thermal circuit. From thermal resistance-based models, it is possible to distinguish whether forced air convection or natural air convection is more effective.

## The Thermal Resistance of Convection

The thermal resistance of electronic components is the resistance offered to the flow of heat through its boundaries. For a given temperature difference, the thermal resistance is the quantity that influences the rate of heat transfer. The thermal resistance is dependent on the geometry of the system and thermal properties such as the thermal conductivity of the surrounding fluid. The thermal resistance varies with heat transfer mechanisms such as conduction, convection, and radiation.

Forced air convection heat transfers offer less thermal resistance than natural air convection. As the airflow rate increases, the thermal resistance value varies. The higher the forced air velocity in a convective heat transfer, the less the thermal resistance is and the higher the heat transfer coefficient is. A thermal resistance concept-based electrical circuit model is best suited to choose between natural air convection and forced air convection in electronics cooling.

## The Biot Number and the Thermal Resistance of Convection

The convection heat transfer process seldom occurs individually. It coexists with conduction and makes combined conduction and convection heat transfer a common phenomenon in any thermal management system.

### Combined Conduction and Convection Heat Transfer

Combined conduction and convection heat transfer can be natural air, forced air, or liquid convection. For combined conduction and convection transient heat transfer processes, a dimensionless quantity called the Biot number is used for solving heat transfer problems.

### Biot Number

The Biot number is the ratio of thermal resistance of conduction to the thermal resistance of convection. The Biot number approaches zero when the thermal resistance of convection is large. For a large amount of heat transfer via convection, the Biot number needs to approach infinity. The thermal resistance to convection is much less as the Biot number approaches infinity. The Biot number indicates which heat transfer mechanism is predominant in the combined conduction and convection heat transfer process.