8.2 Heat Transfer Coefficients and Overall U

8.2 Heat Transfer Coefficients and Overall U

Quick Answer: Each film has resistance 1/(hA); a wall has L/(kA). Sum series resistances to get 1/(UA). Then Q̇ = U A ΔT. Fouling factors add more resistance as deposits grow—cleaning and good fluid quality protect U.

Section 8.1 defined h and k. Equipment design almost never uses a single film alone: heat crosses two fluids and a wall (plus dirt). The overall heat transfer coefficient U packages that stack so duty calculations stay compact. On UPDA/MMUP Chemical Domain C, expect conceptual questions about controlling resistance, dirty vs clean U, and what happens when one film coefficient changes.

Film Coefficient h in Equipment Language

For one convective surface:

Q̇ = h A (T_surface − T_bulk)

Rule of thumb: The side with the smallest h (largest film resistance) often dominates the overall resistance unless the wall is thick insulation or heavy fouling intervenes.

What Raises h?

• Higher velocity / turbulence (higher Re) for single-phase forced flow
• Higher fluid thermal conductivity (helps Nu and the fluid k in h = Nu k/L)
• Phase change (boiling/condensation) when properly designed
• Inserts, fins, or enhanced surfaces (raise effective A or disrupt films)

What Lowers h?

• Laminar flow, low velocity, high viscosity
• Gas instead of liquid on that side
• Maldistribution, bypassing, or stratified two-phase regimes (advanced plant issues)

Resistances in Series

For steady heat flow through layers with no accumulation, the heat rate Q̇ is the same through each layer. Temperature drops add:

ΔT_total = Q̇ (R₁ + R₂ + R₃ + …)

Plane-Wall Composite (Same Area A)

Imagine process fluid | fouling | metal wall | fouling | utility fluid:

Then:

1 / (U A) = 1/(h_h A) + R_f,h/A + L/(k_w A) + R_f,c/A + 1/(h_c A)

Cancel A (same area basis):

1/U = 1/h_h + R_f,h + L/k_w + R_f,c + 1/h_c

U then satisfies:

Q̇ = U A ΔT

where ΔT is the overall driving force between the two bulk fluids (or a suitable mean such as LMTD in Section 8.3).

Cylindrical Walls (Pipes and Tubes)

Inner and outer areas differ. Engineers define U on inside or outside area:

Q̇ = U_i A_i ΔT = U_o A_o ΔT

Wall resistance becomes a logarithmic form, e.g. ln(r_o/r_i)/(2π k L) for length L. For UPDA MCQs, remember:

• State the area basis when comparing U values
• Thin metal tubes: wall resistance is often small vs films and fouling
• Thick insulation on pipe OD: conduction resistance can dominate

Overall Heat Transfer Coefficient U

Typical order-of-magnitude U values (very approximate; depend strongly on fluids):

Do not memorize a single “correct” U for all exchangers; use the table as relative intuition: gas films and viscous oils pull U down; condensing steam pulls U up.

Worked Numerical: Clean Plane Composite

A flat heat-transfer surface has:

• h_hot = 800 W/(m²·K)
• Wall: L = 0.005 m, k_w = 40 W/(m·K)
• h_cold = 400 W/(m²·K)
• No fouling

1/U = 1/800 + 0.005/40 + 1/400 = 0.00125 + 0.000125 + 0.0025 = 0.003875 m²·K/W

U ≈ 258 W/(m²·K)

Interpretation: The cold film is the largest resistance (~64% of 1/U). Improving cold-side turbulence raises U more than polishing an already conductive thin metal wall. The wall term is almost negligible—classic for thin steel.

If cold-side h doubles to 800 W/(m²·K):

1/U = 0.00125 + 0.000125 + 0.00125 = 0.002625 → U ≈ 381 W/(m²·K)

A large gain from fixing the controlling film.

Fouling Factors and Why Plants Care

Fouling is unwanted deposit on heat-transfer surfaces: scale, sludge, corrosion products, biological growth, coke, polymer, or sand/silt.

Fouling factor R_f (m²·K/W) is an extra series resistance. Designers often take values from standards or company practice for water, crude, etc.

1/U_dirty = 1/U_clean + R_f,total

(with R_f,total the sum of side-specific factors on the chosen area basis).

Worked Numerical: Add Fouling

Using the previous clean U ≈ 258 W/(m²·K), add total fouling R_f = 0.0004 m²·K/W:

1/U_dirty = 1/258 + 0.0004 ≈ 0.003876 + 0.0004 = 0.004276

U_dirty ≈ 234 W/(m²·K) (~9% drop)

If fouling is severe, R_f = 0.002 m²·K/W:

1/U = 0.003876 + 0.002 = 0.005876 → U ≈ 170 W/(m²·K) (~34% drop)

Maintenance and Operations Implications (Qatar Plant Context)

Process facilities in Qatar—gas processing, LNG, refining, petrochemicals, desalination-related utilities—run exchangers hard in hot, sometimes dusty or saline environments. Exam-relevant links:

• Cooling water systems: scale and biofouling; treatment programs protect U and reduce cleaning frequency
• Crude / heavy hydrocarbon services: fouling factors are large by design; plan turnaround cleaning
• Air coolers: fin-side fouling (dust, sand) cuts air-side h and effective U
• Velocity selection: higher velocity can reduce deposition but raises pressure drop and erosion risk—an engineering tradeoff
• Monitoring: rising approach temperatures or falling duty at fixed flows signals fouling or lost area

Design practice: Size on dirty U so the exchanger still meets duty at end of run; clean U is higher at start-up (overperformance until fouling builds).

Controlling Resistance Diagnosis

Fins are added on the low-h side (usually gas) to increase area where resistance is high—conceptual point for equipment awareness.

Coupling to Energy Balances

From Chapter 4, a single-stream cooler needs Q̇ = ṁ C_p ΔT_fluid (approx.). That duty must also equal U A ΔT_overall (with proper mean ΔT). If fouling drops U, either outlet temperatures move (less cooling/heating) or operators raise utility flow/temperature difference—until limits are hit.

Common Traps

• Adding conductivities instead of resistances
• Comparing U values defined on different area bases (ID vs OD)
• Ignoring fouling on water or crude services when the stem emphasizes “after six months online”
• Assuming metal wall always dominates (usually false for thin tubes)
• Confusing h (one film) with U (overall)

Exam Workflow

1. Sketch layers: film | foul | wall | foul | film.
2. Write each R; sum for 1/(UA).
3. Identify the largest R (controlling).
4. Predict effect of changing h, L, k, or R_f on U and Q̇.
5. Connect dirty U to cleaning and end-of-run design.

Section 8.3 applies U and A with LMTD (and F corrections) for real exchangers—the temperature difference is no longer a single flat ΔT when both streams change temperature along the unit.