Question

A product of Grashof Number and Prandtl Number is ............... number.

• A. Reynold
• B. Nusselt
• C. Rayleigh
• D. Graetz

Hint:

A simple mnemonic for this relationship:
- Rayleigh = Grashof \( \times \) Prandtl (Ra = Gp).
This number is the primary indicator of the transition from lamir to turbulent flow in tural convection.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Dimensionless numbers are mathematical ratios used in fluid mechanics and heat transfer to simplify the alysis of complex transport phenome.
Key Formula or Approach:
The Rayleigh number (\( Ra \)) is defined as the product of the Grashof number (\( Gr \)) and the Prandtl number (\( Pr \)):
\[ Ra = Gr \times Pr \]

Step 2: Detailed Explation:
Let's define the individual dimensionless numbers:
1. Grashof Number (\( Gr \)): Represents the ratio of buoyant forces to viscous forces acting on a fluid. It is used to alyze tural convection.
2. Prandtl Number (\( Pr \)): Represents the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It describes the relative thickness of the velocity and thermal boundary layers.
The product of these two numbers is the Rayleigh Number (\( Ra \)).
The Rayleigh number is used to characterize tural (free) convection heat transfer.
When the Rayleigh number is below a critical value for a given geometry, heat transfer occurs primarily by conduction.
When it exceeds the critical value, tural convection becomes the domint mode of heat transfer.
For comparison:
- Reynolds number (\( Re \)) is the ratio of inertial to viscous forces.
- Nusselt number (\( Nu \)) represents convective to conductive heat transfer across a boundary.
- Graetz number (\( Gz \)) characterizes lamir flow in conduits.

Step 3: Fil Answer
The product of the Grashof number and the Prandtl number is defined as the Rayleigh number.