Nusselt number, abbreviated as \(Nu\), a dimensionless number, is heat transfer analysis to characterize the convective heat transfer coefficient. It relates the rate of convective heat transfer to the rate of conductive heat transfer in a fluid flow over a solid surface.
Nusselt Number Formula |
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\( Nu \;=\; \dfrac{ h \cdot L_c }{ k }\) (Nusselt Number) \( h \;=\; \dfrac{ Nu \cdot k }{ L_c }\) \( L_c \;=\; \dfrac{ Nu \cdot k }{ h }\) \( k \;=\; \dfrac{ h \cdot L_c }{ Nu }\) |
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| Symbol | English | Metric |
| \( Nu \) = Nusselt Number | \(dimensionless\) | \(dimensionless\) |
| \( h \) = Heat Transfer Coefficient | \(Btu\;/\;hr-ft^2-F\) | \(W\;/\;m^2-K\) |
| \( L_c \) = Characteristic Length | \(ft\) | \(m\) |
| \( k \) = Thermal Conductivity | \(Btu\;/\;hr-ft-F\) | \(W\;/\;m-K\) |
The Nusselt number is widely used in engineering, particularly in the design of heat exchangers, cooling systems, and other thermal management systems. It often appears in correlations derived from experimental data or theoretical models, depending on factors like flow type (laminar or turbulent), geometry, and fluid properties (Reynolds number and Prandtl number).
Nusselt Number Interpretation
Nu > 1 - Convection is enhancing heat transfer beyond what conduction alone would achieve. The larger the value, the more effective the convective transport relative to conduction. This generally reflects thinner thermal boundary layers, higher velocities, or more vigorous mixing (e.g., turbulence).
Order of magnitude matters by context - Nu \(\approx\) 1–10 is typical of natural convection or slow laminar flows. Nu in the hundreds to thousands is common in high-velocity turbulent forced convection (e.g., inside pipes, over turbine blades). There is no universal "good" or "bad" value, it must be compared within the same geometry/flow class and characteristic length definition.
Practical/Engineering Significance
- Nu is the vehicle for calculating h, once Nu is known from an empirical or theoretical correlation, \( h = Nu \cdot k / L_c \).
- h then feeds directly into design of heat exchangers, electronics cooling, HVAC coils, boilers, condensers, and any surface where convective heat flux \(q" = h ( T_s - T_{ \infty } )\) must be estimated.
- Higher Nu (at fixed geometry and fluid) generally means smaller required heat transfer area for a given duty, or higher achievable heat flux for a given area, directly affecting equipment sizing and cost.
- Engineers select/derive Nu correlations specific to geometry (flat plate, pipe interior, cylinder in crossflow, sphere, finned surfaces, natural vs. forced convection). Correlations are not interchangeable across geometries.
Relation to other Parameters
Forced Convection - Nu = f(Re, Pr) - e.g., Dittus–Boelter, Sieder–Tate, Colburn analogy.Natural/Free Convection - Nu = f(Gr, Pr), often combined as Nu = f(Ra), where Ra = Gr·Pr.
Stanton Number (St) - St = Nu/(Re·Pr), links convective transport to heat capacity flux.
Prandtl Number (Pr) - Ratio of momentum to thermal diffusivity. Appears in nearly all Nu correlations to account for fluid property effects (how thermal vs. velocity boundary layers compare).
Biot Number (Bi) - Same algebraic form (h \cdot L/k) but uses the solid's conductivity rather than the fluid's. Governs whether internal conduction resistance in a solid is negligible (lumped system) versus significant.
