Glossary term
Nusselt Number
A dimensionless number comparing convective heat transfer to conductive heat transfer.
Definition
quantityA dimensionless number comparing convective heat transfer to conductive heat transfer.
The Nusselt number relates convective heat transfer at a surface to conductive heat transfer through a fluid layer of characteristic length. It is used to estimate heat-transfer coefficients for pipes, plates, heat exchangers, electronics cooling, natural convection, and forced convection.
The Nusselt number is a dimensionless heat-transfer quantity:
where h is the convective heat-transfer coefficient, L_c is the characteristic length, and k is the thermal conductivity of the fluid. It compares actual convection at a boundary with pure conduction across the same characteristic scale. Higher Nusselt number generally means stronger convective transport.
Role in heat-transfer design
In many engineering calculations, the Nusselt number is obtained from a correlation and then rearranged to estimate h:
This coefficient is then used in heat-flux calculations, thermal resistance networks, heat-exchanger sizing, cooling-fin design, electronics thermal analysis, and process-equipment models. A wrong Nusselt correlation can therefore produce a wrong surface temperature, heat duty, or safety margin even if the arithmetic is correct.
Regime dependence
Nusselt correlations depend on geometry, flow regime, boundary condition, fluid properties, and characteristic length. Internal pipe flow, external flow over a flat plate, cross-flow over a cylinder, natural convection on a vertical wall, and boiling all use different relationships. Reynolds number captures forced-flow inertia relative to viscosity, while Grashof number captures buoyancy-driven natural convection.
Thermal boundary conditions matter. Constant wall temperature and constant heat flux can produce different Nusselt numbers for the same geometry. Property evaluation temperature also matters because viscosity, conductivity, density, and specific heat may change significantly across the thermal boundary layer.
Engineering interpretation
A Nusselt number is not a universal performance rating. It is tied to a specific definition of L_c, a surface, a fluid, and an operating state. In CFD or experiments, local Nusselt number may vary over a surface, while average Nusselt number is used for system-level heat balance. The distinction must be clear when comparing data or validating a thermal model.
Common mistakes
A common mistake is to use a correlation outside its Reynolds-number, geometry, roughness, or property range. Another is to mix hydraulic diameter, plate length, tube diameter, and fin spacing as if they were interchangeable characteristic lengths. A good thermal review states the selected correlation, validity range, property temperature, boundary condition, surface roughness assumptions, and whether the reported value is local or averaged.