Question

Which of the following non-dimensional terms is an estimate of Nusselt number?

• A. Ratio of internal thermal resistance of a solid to the boundary layer thermal resistance
• B. Ratio of the rate at which internal energy is advected to the rate of conduction heat transfer
• C. Non-dimensional temperature gradient
• D. Non-dimensional velocity gradient multiplied by Prandtl number

Hint:

Nusselt number represents how strongly convection enhances heat transfer compared to pure conduction and is directly related to the dimensionless temperature gradient at a surface.

Answer 1

The Correct Option is C

The Nusselt number is defined as a measure of the enhancement of convective heat transfer relative to conduction across a fluid boundary. Mathematically, it is given by: \[ Nu = \frac{hL}{k} = \frac{\text{Convective heat transfer}}{\text{Conductive heat transfer}} \] and it can also be expressed as a non-dimensional temperature gradient at the wall: \[ Nu = -\left. \frac{\partial \theta}{\partial n} \right|_{\text{wall}}. \] This representation directly links Nusselt number to the dimensionless temperature gradient. The other options refer to ratios of resistances, energy advection, or velocity gradients, which correspond to different dimensionless groups (Biot, Peclet, and Prandtl-related terms). Therefore, the only correct representation of an estimate of the Nusselt number is the non-dimensional temperature gradient. Final Answer: Non-dimensional temperature gradient