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).