Question

The Grashof number is the ratio of

• A. thermal diffusivity and mass diffusivity
• B. inertial force and surface tension force
• C. sensible heat and latent heat
• D. buoyancy force and viscous force

Hint:

In natural convection, the Grashof number is crucial for determining the flow behavior, especially for buoyancy-driven flows.

Answer 1

The Correct Option is D

Step 1: Understanding the Grashof number.
The Grashof number (Gr) is used in fluid dynamics and heat transfer to characterize the ratio of buoyancy forces to viscous forces in a fluid. It is an important dimensionless number in natural convection and helps determine the flow regime (laminar or turbulent). It is defined as: \[ Gr = \frac{g \beta \Delta T L^3}{\nu^2} \] Where: - \( g \) is the acceleration due to gravity
- \( \beta \) is the thermal expansion coefficient
- \( \Delta T \) is the temperature difference
- \( L \) is the characteristic length
- \( \nu \) is the kinematic viscosity
Step 2: Conclusion.
The Grashof number compares buoyancy forces (due to temperature difference) and viscous forces. Thus, the correct answer is (4).

Answer 2

The Grashof number is a dimensionless group used in natural (free) convection heat transfer to compare the relative importance of two competing forces acting on a fluid parcel near a heated or cooled surface. Let's check each option against its actual definition, \( Gr = \dfrac{g \beta \Delta T L^3}{\nu^2} \).

1. Thermal diffusivity and mass diffusivity: A ratio of these two quantities is actually the Lewis number, not the Grashof number.
2. Inertial force and surface tension force: This ratio describes the Weber number, used in droplet or bubble formation, not natural convection.
3. Sensible heat and latent heat: This kind of ratio appears in phase-change heat transfer problems (like the Jakob number), not in the Grashof number's definition.
4. Buoyancy force and viscous force: The numerator \( g \beta \Delta T L^3 \) in the Grashof number represents the buoyancy force driving fluid motion due to density differences from temperature variation, while \( \nu^2 \) in the denominator represents the retarding effect of viscous forces, exactly matching the Grashof number's physical meaning.

The Grashof number is specifically the ratio that quantifies buoyancy-driven motion against viscous resistance in natural convection.

Therefore, the correct answer is buoyancy force and viscous force.