Definitions of Constants

Question 1

What is the Biot Number?

Answer 1

Ratio of internal conduction resistance to external convection resistance.

Small Bi (< 0.1): Conduction is much faster than convection → Uniform temperature inside.
Large Bi (> 0.1): Significant temperature gradients inside the object.

Bi = h*Lc/k (solid)

Question 2

What is the Fourier Number?

Answer 2

Ratio of heat conduction to heat storage.

➡ High Fo: Heat diffuses quickly.
➡ Low Fo: Heat takes longer to spread.

Fo= alphat / Lc^2
alpha = k/rhoc

Question 3

What is the Reynolds Number?

Answer 3

✅ Ratio of inertial forces to viscous forces.

➡ Low Re (< 2000): Laminar flow (smooth, orderly).
➡ High Re (> 4000): Turbulent flow (chaotic, mixing).
➡ 2000 - 4000: Transitional flow.

Re= U*Lc / v (kin visc.)

Question 4

What is the Prandtl Number?

Answer 4

✅ Ratio of momentum diffusivity to thermal diffusivity.

➡ Low Pr → Heat diffuses faster than momentum (e.g., liquid metals).
➡ High Pr → Momentum diffuses faster than heat (e.g., oils).

Pr = v/alpha

Question 5

What is the Nusselt Number?

Answer 5

✅ Ratio of convective to conductive heat transfer.

➡ Nu = 1: Pure conduction (no convection).
➡ Nu > 1: Convection enhances heat transfer.

Nu= h*Lc / k (fluid)

Question 6

What us the Rayleigh Number?

Answer 6

✅ Ratio of buoyancy forces to viscous forces in natural convection.

➡ Ra < 1708: Laminar flow in natural convection.
➡ Ra > 1708: Turbulent flow.
Ra = Gr*Pr

Question 7

What is the Grashof Number?

Answer 7

✅ Ratio of buoyancy forces to viscous forces in fluid flow due to temperature differences.

➡ Gr > 10⁹: Significant natural convection.
➡ Gr < 10⁹: Flow is dominated by viscous forces.