Nusselt

Nusselt is a surname most associated with Wilhelm Andreas Nusselt, a German engineer who made foundational contributions to the study of heat transfer in the early 20th century. The Nusselt number, named in his honor, is a dimensionless parameter that characterizes the relative strength of convective to conductive heat transfer at a solid boundary.

Definition and meaning: The Nusselt number is defined as Nu = hL/k, where h is the convective heat transfer coefficient, L is a characteristic length, and k is the thermal conductivity of the fluid. For internal flows, Nu is often written as Nu = h Dh / k, with Dh the hydraulic diameter. Nu can refer to either a local value along a surface or an average value over an area.

Significance and use: The Nusselt number encapsulates how effectively a fluid moves heat away from or toward a surface through convection, in relation to conduction within the fluid. It is used to determine heat transfer coefficients from correlations that depend on flow regime (laminar or turbulent) and boundary conditions. Once Nu is known, the convective coefficient can be obtained via h = Nu k / L.

Typical results and correlations: In fully developed laminar flow in a circular tube with constant wall temperature, the average Nu is about 3.66; with constant wall heat flux, it is about 4.36. For turbulent pipe flow, empirical correlations such as Nu = 0.023 Re^0.8 Pr^0.4 (the Dittus–Boelter correlation) are commonly applied for a range of Reynolds and Prandtl numbers.

Applications: The concept is widely used in engineering and physics to design and analyze cooling and heating systems, including heat exchangers, electronic device cooling, and chemical processing, where convective heat transfer is a key factor.