Lesson A10 calculated what the process demands. This lesson is about whether the equipment can deliver it — the physics of getting heat across a metal wall, and why a whisper of air can quietly take five hundred rupees of heat-transfer surface and make it perform like ninety.

The rate equation

Every steam heater on earth obeys Q = U · A · ΔT: heat flow equals a transfer coefficient, times surface area, times the temperature difference driving it. A is bought in stainless steel. ΔT is bought at the boiler (higher pressure, hotter steam). U — kcal per hour, per m², per °C — is where the engineering lives, because U is not a property of the metal: it is the sum of every obstacle the heat must cross.

The obstacle course

Heat leaving condensing steam for the product crosses, in order: the condensate film on the steam side (fast — condensing films run in the thousands of kcal/h·m²·°C), the metal wall (faster still — millimetres of steel barely register), any fouling (scale, product bake-on — slow), and the product-side film (usually the honest bottleneck: a few hundred for stirred liquids, less for viscous ones). Resistances add like resistors in series, and the biggest resistance rules the total. This is why polishing an already-good steam side gains nothing while a stirrer upgrade or a descale transforms performance — improve the largest resistance or you have improved nothing.

The resistance stack, to scale (jacket of the practice-plant vessel) clean: U ≈ 500 + air film (0.2 mm): still air — 0.2 mm → U collapses to ≈ 92. Same jacket, same steam, one-fifth the heat. steam film steel wall fouling product film air film segment lengths ∝ thermal resistance · steel k ≈ 37, still air k ≈ 0.022 kcal/h·m·°C — the air strip is ~40 steel walls wide
Why lesson A9 called air the U-value's enemy: the film's resistance is drawn to the same scale as everything else. It is not a subtle effect.

ΔT with steam: mercifully simple

Because saturated steam condenses at one temperature (lesson A3), the driving force calculation loses half its complexity — the hot side is a flat line. Against a product warming from 30 °C to 90 °C under 3.5 kg/cm²g steam (148 °C), the difference starts at 118 °C and shrinks to 58 °C, and the honest average is the log-mean:

LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁/ΔT₂) = (118 − 58) ÷ ln(118/58) ≈ 84 °C

(The arithmetic mean says 88 — close here, badly wrong when the ratio widens. Use the log-mean; it costs one extra key on the calculator.)

Closing the loop on the practice plant

The vessel's jacket offers 9.5 m² and a clean-service U of about 500. Capacity: Q = 500 × 9.5 × 84 ≈ 400,000 kcal/h — against the 387,000 kcal/h warm-up duty from lesson A10. The jacket makes its 45-minute batch with barely 4% to spare. Now re-read the figure above: with the air film, capacity is ~74,000 kcal/h and the batch takes over four hours. When operators say "the vessel has gone slow", this — not the boiler — is usually the arithmetic behind it. The ₹2,000 air vent from lesson A9 is protecting a 400,000 kcal/h asset.

At site
  • Diagnose slow heating in order: air first (thermometer-vs-gauge test, A9), then condensate flooding (is the trap passing? — D5), then fouling (when did it last hold schedule?), and only then blame U or the boiler.
  • Improve the biggest resistance. Stirring/circulation on the product side often buys more than any steam-side change.
  • Descaling is heat-transfer maintenance, not housekeeping. Log batch times; a creeping trend is fouling talking.
  • Quoting or checking an exchanger: ask what U was assumed, clean and fouled, and at what fouling factor. A vendor U without a fouling basis is a brochure number.
Pin this
  • Q = U·A·LMTD. Area is capital, ΔT is boiler pressure, U is engineering.
  • Resistances add in series; the largest one governs. Improve that one.
  • With steam the hot side is isothermal — LMTD = (ΔT₁−ΔT₂)/ln(ΔT₁/ΔT₂), one line.
  • A 0.2 mm still-air film ≈ forty steel walls. Venting is heat-transfer engineering.
  • The practice plant's jacket: 400,000 kcal/h clean, ~74,000 air-blanketed. Same steel, same steam.
Steam stories

The overall-coefficient method — treating a wall and its films as resistances in series — was standardised into engineering by Wilhelm Nusselt's 1916 analysis of film condensation, still the starting point of every condenser textbook. Nusselt worked the problem with pencil, paper and a controversial assumption (a smooth, undisturbed condensate film); a century of measurement later, his "ideal" numbers remain within shouting distance of real vertical-surface condensers — one of engineering's better returns on a simplifying assumption.