Quiz 12 MAE336

What two conditions are required for buoyancy-driven (free) convection?

A temperature difference and the presence of gravity (or a body force).

Why is gravity necessary for free convection?

It acts on density differences caused by temperature differences, creating fluid motion.

What is a quiescent fluid?

A fluid that is initially at rest (no bulk motion).

What is the velocity boundary condition at the surface in free convection?

u=0 (no-slip condition).

What is the velocity condition far from the surface in free convection?

Velocity approaches zero (u→0u \to 0u→0).

What is the thermal boundary condition at the surface?

T=Ts​ (surface temperature).

What is the thermal condition far from the surface?

T→T∞​ (ambient temperature)

For a heated horizontal plate, which surface has higher heat transfer?

The top surface.

Why does the top surface of a heated plate transfer more heat?

Warm air rises freely, enhancing convection.

Why is convection weaker on the bottom surface of a heated plate?

Warm air is trapped underneath and cannot rise easily.

What is the Grashof number (Gr)?

A dimensionless number representing the ratio of buoyancy forces to viscous forces.

What does a large Grashof number indicate?

Strong natural convection (buoyancy dominates over viscosity).

What does a small Grashof number indicate?

Weak convection; viscous forces dominate.

What is the volumetric coefficient of thermal expansion β?

The fractional change in volume with temperature.

What is the formula for β

β=1/V​*(∂T/∂V​)

What is β for an ideal gas?

β≈1/T​

Estimate β for air at 500 K.

β≈0.002K^−1

What is the Rayleigh number (Ra)?

Ra=Gr⋅Pr, combining buoyancy and thermal diffusion effects.

What does the Rayleigh number tell you?

Whether convection will be strong and whether flow is laminar or turbulent.

What drives natural convection flow physically?

Density differences caused by temperature variations in a gravitational field.