Which dimensionless number defines the ratio of convective to conductive heat transfer across a boundary?

Which dimensionless number defines the ratio of convective to conductive heat transfer across a boundary?

• A. The ratio of convection to conductive heat transfer across a boundary
• B. The ratio of radiation to conduction
• C. The ratio of diffusion to convection
• D. The ratio of turbulent to laminar flow

Answer: (A)

The key idea is comparing how heat moves across a boundary by two mechanisms: convection in the surrounding fluid and conduction through the boundary itself. The dimensionless group that captures this balance is the Nusselt number. It arises from comparing the convective heat transfer rate, Q_conv ≈ hAΔT, with the conductive transfer through the boundary, Q_cond ≈ kAΔT/L. Taking the ratio gives Nu ≈ (hAΔT) / (kAΔT/L) = hL/k, where h is the convective heat transfer coefficient, L a characteristic length, and k the thermal conductivity. A larger Nu means convection dominates the transfer across the boundary, while Nu ≈ 1 indicates conduction is the main mechanism. The other options describe different ideas (radiation vs conduction, diffusion vs convection, turbulent vs laminar flow) and do not quantify the convective-to-conductive transfer across a boundary.

The key idea is comparing how heat moves across a boundary by two mechanisms: convection in the surrounding fluid and conduction through the boundary itself. The dimensionless group that captures this balance is the Nusselt number. It arises from comparing the convective heat transfer rate, Q_conv ≈ hAΔT, with the conductive transfer through the boundary, Q_cond ≈ kAΔT/L. Taking the ratio gives Nu ≈ (hAΔT) / (kAΔT/L) = hL/k, where h is the convective heat transfer coefficient, L a characteristic length, and k the thermal conductivity. A larger Nu means convection dominates the transfer across the boundary, while Nu ≈ 1 indicates conduction is the main mechanism. The other options describe different ideas (radiation vs conduction, diffusion vs convection, turbulent vs laminar flow) and do not quantify the convective-to-conductive transfer across a boundary.