Question

6. Describe the differences between Grashof and Rayleigh numbers
7. For free-convection problems, describe how the momentum and energy equations are coupled.
8. Describe the driving forces for free and forced-convection problems.
9. For the momentum dimensionless form equation, describe the modulating factor for the viscous terms.
10. For the energy dimensionless form equation, describe the modulating factor for the conduction terms.

Answer 1

6)

The Grashof number is used to characterize natural (free) convection. It gives the ratio between buoyancy forces and viscous forces. It is usually very large (billions). The convection is steady for low Grasshof number values (approx. up to 10.000) unsteady laminar till about 10 million and turbulent above 10 billion. The Grasshof number is propotional to the characteristic temperature difference.

Rayleigh number is just Prandtl number multiplied by Grashof. Some empirical formulas for estimating heat transfer coefficient are given using the Rayleigh number.

7)

The momentum equation is coupled with the energy equation through the body force. And the The energy equation is coupled with the momentum equation through the velocity field. Consequently, the solution inherently involves iterations.