# What Is the Nusselt Number?

A Nusselt number is the product of a ratio comparison for heat transfer between two fluids where convection heat transfer is divided by the thermal conductivity of the material at rest. It is a unit-less number that essentially provides a comparison rate for how fast heat is transferred between materials where convection is taking place, or a flow of a gas or liquid, as compared to basic heat transfer by conduction where little internal movement of matter is occurring. Though the Nusselt number is often used to measure heat transfer in fluids, it can also be used to compare convection to conduction heat transfer rates between solids by gas flow. The foundation for comparisons of heat transfer in materials was established by Ernst Wilhelm Nusselt, a German mechanical engineer who taught at Dresden during the early 20^{th} century. His pioneering work in fluid mechanics at the time resulted in the Nusselt number being named after him.

A typical convection Nusselt number equation is Nu = hL/λ. *Nu* represents the Nusselt number, *h* is the heat transfer coefficient that can be measured in watts per square meter times the temperature Kelvin (W/m^{2}K). *L* equals the length of the boundary layer in meters of a material where heat is being transferred, and *lambda *(λ) represents the established thermal conductivity of the material in watts per meter Kelvin or W/mK. The measurement of Nusselt number heat is a measurement across surface boundaries only, and is directly related to Newton's Law of Cooling from which the number can also be derived.

When Nusselt correlation is close to a value of one, this indicates a type of heat transfer flow known as laminar flow or slug flow, which indicates that very little fluid motion is taking place and conductive heat loss is important. As flow rates increase, they are described as being turbulent, and can often result in Nusselt number values that range from 100 on up to 1,000. Any value for a Nusselt number between 100 to 1,000 is indicative of the fact that the dominant form of heat transfer taking place is by convection, and conduction only plays a minor role. Such numbers are important values to know in various aspects of engineering, where heat transfer may be either a desirable or undesirable trait. A high Nusselt number cylinder transfer rate is considered to be turbulent and an efficient method of heat transfer, such as in fluid flow through piping where little heat energy in the material is lost through conduction to the outside environment.

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