Question

Product of Reynolds number and Prandtl number is known as:

• A. Stanton number
• B. Peclet number
• C. Mach number
• D. Biot number

Hint:

Remember the product:
- Peclet = Reynolds \( \times \) Prandtl (Pe = R \( \times \) P).
This number is used to determine whether heat or mass transport is domited by conduction/diffusion or by convectiodvection.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Dimensionless groups are used in engineering to characterize the relative importance of different transport mechanisms in fluid flow and heat transfer.
Key Formula or Approach:
The Peclet number (\( Pe \)) is defined as the product of the Reynolds number (\( Re \)) and the Prandtl number (\( Pr \)):
\[ Pe = Re \times Pr \]

Step 2: Detailed Explation:
Let's alyze the physical definitions of these dimensionless numbers:
1. Reynolds Number (\( Re \)): Ratio of inertial forces to viscous forces:
\[ Re = \frac{\rho v D}{\mu} \]
2. Prandtl Number (\( Pr \)): Ratio of momentum diffusivity to thermal diffusivity:
\[ Pr = \frac{C_p \mu}{k} \]
Multiplying these two numbers yields the thermal Peclet number (\( Pe \)):
\[ Pe = Re \times Pr = \left( \frac{\rho v D}{\mu} \right) \left( \frac{C_p \mu}{k} \right) = \frac{\rho C_p v D}{k} \]
The Peclet number represents the ratio of the rate of heat transport by advection (bulk fluid motion) to the rate of heat transport by conduction.
For comparison:
- Stanton number (\( St \)) represents the ratio of heat transferred into a fluid to the thermal capacity of the fluid.
- Mach number (\( Ma \)) is the ratio of fluid velocity to the speed of sound.
- Biot number (\( Bi \)) compares interl thermal resistance of a solid to exterl convective resistance.

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