Heat transfer dimensionless number: write the Nusselt number definition Define Nusselt number (Nu) in terms of convection coefficient, characteristic length, and thermal conductivity for convective heat transfer. Choose the correct expression.

Concept/ApproachThe Nusselt number is a dimensionless group that compares convective to conductive heat transfer across a boundary layer: Nu = (convective heat transfer / conductive heat transfer at the same temperature gradient).

DefinitionNu = hL/kwhere h = convection coefficient (W/m²·K), L = characteristic length (m), k = thermal conductivity of the fluid (W/m·K).

Unit check(W/m²·K × m) / (W/m·K) = 1 (dimensionless).

Common pitfalls

• Inverting k and h giving kL/h, which has dimensions and is incorrect.
• Using an area instead of a length in the definition; Nu uses a length scale.

Final AnswerNu = hL/k