Design allowances — In heat-exchanger calculations, the fouling factor is introduced to:

Introduction:
Over time, heat-exchanger surfaces accumulate deposits (scale, biofilm, particulates) that add thermal resistance and reduce performance. Engineers include a fouling factor to ensure that the exchanger meets duty even after fouling develops.

Given Data / Assumptions:

• Fouling factor R_f has units of m²·°C/W (or hr·ft²·°F/Btu).
• It is added to clean-side resistances in series.
• Values depend on service, fluid, temperature, and maintenance schedule.

Concept / Approach:
Total overall resistance R_total = 1/U = (1/h_hot) + R_wall + (1/h_cold) + R_f,hot + R_f,cold. The fouling factors R_f,hot and R_f,cold account for expected deposit resistance, effectively lowering the allowable U for design and providing robustness against performance decay.

Step-by-Step Solution:
Start with clean U based on convection and conduction.Add fouling resistances R_f to obtain design U_d = 1 / (R_clean + R_f,total).Size area A using Q = U_d * A * ΔT_lm so duty is met despite fouling.

Verification / Alternative check:
Comparing clean and dirty performance during operation confirms that deposit buildup reduces U; fouling-factor allowances approximate this effect at design time.

Why Other Options Are Wrong:

• (a) It is not dimensionless; it has resistance units.
• (b) It explicitly provides a safety margin.
• (d) It does not eliminate cleaning needs.
• (e) It relates to thermal resistance from fouling, not corrosion allowance.

Common Pitfalls:
Using overly conservative R_f values leading to excessively large exchangers; ignoring that fouling is asymmetric between hot and cold sides.

Final Answer:
Account for additional resistances to heat flow due to deposits and fouling