Theory - Past Papers

Question 1

Explain how the Reynolds analogy follows from the normalized boundary layer equations (see below), and for which conditions this is valid.

Answer 1

• Derived by comparing normalized momentum and energy equations in turbulent boundary layers
• Valid when Pr ≈ 1, ensuring similar turbulent diffusivities for momentum and heat
• Allows direct relation between friction (Cf) and heat transfer (St) via St ≈ Cf/2

Question 2

Explain the concept of critical radius of insulation for heat conduction in radial systems.

Answer 2

• Point at which adding insulation increases rather than decreases heat loss
• Balances conductive resistance and increased surface area for convection
• Defined as r_c = k/h

Question 3

Explain how to calculate a thermal resistance [K/W] for radiation.

Answer 3

• Linearize radiative heat transfer using an effective radiative heat transfer coefficient h_rad
• h_rad = εσ(T_s² + T_sur²)(T_s + T_sur)
• Then R_rad = 1/h_rad

Question 4

Explain how the LMTD method differs from the 𝜀-NTU approach.

Answer 4

• LMTD: Uses known inlet/outlet temps, applies a log-mean temperature difference
• ε-NTU: Uses effectiveness and NTU when outlet temps are unknown
• LMTD = straightforward if all temps known, ε-NTU = flexible for unknown conditions

Question 5

Explain with the aid of equations what is meant by the ‘critical radius of insulation’ for heat conduction in radial systems?

Answer 5

• Critical radius: r_c = k/h
• At r_c, increasing insulation thickness no longer reduces heat loss
• Balances increased conduction resistance with larger convective surface area