Question

The ratio of the energy transferred by convection to that by conduction is represented by

• A. Nusselt Number
• B. Prandtl Number
• C. Froude Number
• D. Reynolds Number

Hint:

The Nusselt number (\( \text{Nu} = \frac{hL}{k} \)) quantifies the enhancement of heat transfer by convection over conduction across a boundary.

Answer 1

The Correct Option is A

Step 1: Understand the ratio of energy transfer.
The problem asks for the dimensionless number representing the ratio of energy transferred by convection to that by conduction. This typically applies to heat transfer at a surface, where convection occurs between the surface and the fluid, and conduction occurs within the fluid or solid. Step 2: Define the relevant dimensionless numbers.
Nusselt Number (Nu): \( \text{Nu} = \frac{hL}{k} \), where \( h \) is the convective heat transfer coefficient, \( L \) is the characteristic length, and \( k \) is the thermal conductivity of the fluid. It represents the ratio of convective heat transfer to conductive heat transfer across a boundary:
Convective heat transfer: \( q_{\text{conv}} = h A \Delta T \),
Conductive heat transfer (over length \( L \)): \( q_{\text{cond}} = k A \frac{\Delta T}{L} \),
Ratio: \( \frac{q_{\text{conv}}}{q_{\text{cond}}} = \frac{h A \Delta T}{k A \frac{\Delta T}{L}} = \frac{hL}{k} = \text{Nu} \).
Prandtl Number (Pr): \( \text{Pr} = \frac{\nu}{\alpha} \), compares momentum diffusivity to thermal diffusivity, not directly related to convection vs. conduction.
Froude Number (Fr): \( \text{Fr} = \frac{v}{\sqrt{gL}} \), compares inertial forces to gravitational forces, relevant in fluid dynamics, not heat transfer.
Reynolds Number (Re): \( \text{Re} = \frac{vL}{\nu} \), compares inertial forces to viscous forces, not directly related to convection vs. conduction.
Step 3: Identify the correct dimensionless number.
The Nusselt number directly represents the ratio of convective to conductive heat transfer, making it the appropriate choice. Step 4: Evaluate the options.
(1) Nusselt Number: Correct, as it is the ratio of convective to conductive heat transfer. Correct.
(2) Prandtl Number: Relates to fluid properties, not the convection-to-conduction ratio. Incorrect.
(3) Froude Number: Relates to fluid dynamics, not heat transfer. Incorrect.
(4) Reynolds Number: Relates to flow regime, not directly to heat transfer modes. Incorrect. Step 5: Select the correct answer.
The ratio of energy transferred by convection to that by conduction is represented by the Nusselt Number, matching option (1).