Heat transfer with phase change: boiling

Pool boiling regimes, the boiling curve, critical heat flux and burnout, Rohsenow and Zuber correlations, and reboiler design practice.

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Why it matters

Reboilers, kettle and thermosiphon vaporisers, evaporators, steam boilers and cryogenic equipment all rely on boiling, which gives the highest heat transfer coefficients in process equipment. The same process has a dangerous limit: if the heat flux exceeds the critical heat flux, the surface blankets with vapour and its temperature can jump by hundreds of degrees, burning out tubes or heating elements.

Key ideas

What boiling is. Evaporation at a solid–liquid interface when the surface temperature T_s exceeds the saturation temperature T_sat of the liquid at the system pressure. The driving force is the excess temperature ΔT_e = T_s − T_sat. Heat goes mainly into latent heat, carried away by bubbles, and into intense agitation of the liquid near the wall.

Pool and flow boiling; saturated and subcooled. Pool boiling: liquid is stagnant and moves only by buoyancy and bubbles (kettle reboiler). Flow (convective) boiling: liquid is pumped through a tube (thermosiphon reboiler, boiler tubes). Subcooled boiling: bulk liquid below T_sat, bubbles collapse in the liquid; saturated boiling: bulk at T_sat, bubbles rise and escape.

The pool boiling curve (Nukiyama), heat flux versus ΔT_e on log axes, for water at 1 atm (approximate values):

  1. Natural convection (ΔT_e below about 5 K): no bubbles; heat removed by free convection and evaporation at the free surface.
  2. Nucleate boiling (about 5–30 K): bubbles form at nucleation sites (cavities, scratches). First isolated bubbles, then jets and columns. Very high h (often 10⁴–10⁵ W/m²·K) and q″ rises steeply, roughly as ΔT_e³. This is the design region.
  3. Critical heat flux (CHF), q″_max: the peak of the curve (about 1 MW/m² for water at 1 atm, at ΔT_e ≈ 30 K). Vapour leaving the surface becomes so abundant that liquid can no longer reach it.
  4. Transition boiling (about 30–120 K): unstable, partial vapour film; q″ actually falls as ΔT_e rises.
  5. Leidenfrost point, q″_min: minimum heat flux, where a stable vapour film first covers the surface (the effect that makes water drops dance on a very hot pan).
  6. Film boiling (beyond about 120 K): continuous vapour blanket; heat crosses the vapour by conduction and, at high temperature, radiation. h is low.

Burnout. If the heat flux is imposed (electric heater, nuclear fuel, fired tube) and is raised beyond q″_max, the surface cannot stay on the nucleate branch. It jumps at the same heat flux across to the film-boiling branch, at a ΔT_e near 1000 K — often above the metal's melting point. If instead the surface temperature is controlled (condensing steam heating), the operating point simply moves along the curve, including into transition boiling.

What affects nucleate boiling. Surface condition (roughness, number of active sites, surface–fluid combination through C_sf in Rohsenow's correlation), pressure (raising pressure generally increases h and, up to about one third of critical pressure, the CHF), fouling and dissolved gases. CHF depends on fluid properties, pressure, gravity and heater geometry but not on the surface material to first order.

Design practice. Keep the design flux well below CHF (often half or less), avoid very large ΔT_e from too-hot steam (which can push a reboiler into film boiling — reducing steam temperature can increase duty), and use data-book correlations for the fluid.

Formulas

q″ = h·(T_s − T_sat) = h·ΔT_e Heat flux (W/m²); ΔT_e excess temperature (K).

q″ = μ_l·h_fg·[g·(ρ_l − ρ_v)/σ]^(1/2)·[c_pl·ΔT_e/(C_sf·h_fg·Pr_lⁿ)]³ Rohsenow nucleate pool boiling. μ_l liquid viscosity (Pa·s), h_fg latent heat (J/kg), ρ_l, ρ_v densities (kg/m³), σ surface tension (N/m), c_pl liquid specific heat (J/kg·K), Pr_l liquid Prandtl number, C_sf surface–fluid constant (about 0.013 for water on polished copper or stainless steel) and n = 1 for water, 1.7 for other fluids — take C_sf from your data book.

q″_max = 0.149·h_fg·ρ_v·[σ·g·(ρ_l − ρ_v)/ρ_v²]^(1/4) Critical heat flux (Zuber/Lienhard, large horizontal heater); some texts use 0.131 or π/24 ≈ 0.131.

ṁ_v = q/h_fg Rate of vapour generation (kg/s) in saturated boiling; q duty (W).

T_sat = f(p) Saturation temperature from steam tables (water: 100 °C at 101.3 kPa, 120.2 °C at 200 kPa).

Worked examples

Example 1 (standard). Water boils at 1 atm on a polished stainless-steel surface held at 110 °C. Find the heat flux and h using Rohsenow's correlation with C_sf = 0.013, n = 1. Saturated water at 100 °C: μ_l = 2.79 × 10⁻⁴ Pa·s, h_fg = 2257 kJ/kg, ρ_l = 957.9 kg/m³, ρ_v = 0.596 kg/m³, σ = 0.0589 N/m, c_pl = 4217 J/kg·K, Pr_l = 1.76.

  1. ΔT_e = 110 − 100 = 10 K (nucleate regime).
  2. [g·(ρ_l − ρ_v)/σ]^(1/2) = [9.81 × 957.3/0.0589]^(1/2) = 399.3 m⁻¹.
  3. c_pl·ΔT_e/(C_sf·h_fg·Pr_l) = 4217 × 10/(0.013 × 2.257 × 10⁶ × 1.76) = 0.8165; cubed = 0.5444.
  4. q″ = 2.79 × 10⁻⁴ × 2.257 × 10⁶ × 399.3 × 0.5444 = 1.37 × 10⁵ W/m².
  5. h = q″/ΔT_e = 1.37 × 10⁵/10 = 1.37 × 10⁴ W/m²·K.

Answer: q″ ≈ 137 kW/m², h ≈ 13.7 kW/m²·K. Because q″ ∝ ΔT_e³, doubling ΔT_e to 20 K would raise q″ about eight times.

Example 2 (GATE level). A kettle reboiler boils water at 1 atm with a duty of 500 kW. The design heat flux is to be 60 % of the critical heat flux. Using the properties of Example 1, find (a) q″_max, (b) the heat transfer area, (c) the steam generation rate, and (d) the surface excess temperature at the design flux from Rohsenow.

  1. q″_max = 0.149·h_fg·ρ_v·[σ·g·(ρ_l − ρ_v)/ρ_v²]^(1/4). Inside the bracket: 0.0589 × 9.81 × 957.3/0.596² = 1557; fourth root = 6.282.
  2. q″_max = 0.149 × 2.257 × 10⁶ × 0.596 × 6.282 = 1.26 × 10⁶ W/m².
  3. Design flux q″ = 0.6 × 1.26 × 10⁶ = 7.55 × 10⁵ W/m²; area A = 500 000/7.55 × 10⁵ = 0.662 m².
  4. Steam rate ṁ = q/h_fg = 500 000/2.257 × 10⁶ = 0.2215 kg/s = 797 kg/h.
  5. From Example 1, q″ = 1.37 × 10⁵ W/m² at 10 K and q″ ∝ ΔT_e³: ΔT_e = 10 × (7.55 × 10⁵/1.37 × 10⁵)^(1/3) = 17.7 K.

Answer: (a) ≈ 1.26 MW/m²; (b) ≈ 0.66 m²; (c) ≈ 0.22 kg/s (≈ 800 kg/h); (d) ΔT_e ≈ 18 K, so the surface runs near 118 °C.

Common mistakes

  • Using T_s − T_bulk with a subcooled bulk; the boiling driving force is T_s − T_sat.
  • Calling the Leidenfrost point the CHF; CHF is the maximum flux, Leidenfrost the minimum flux.
  • Assuming more steam superheat or higher steam temperature always increases reboiler duty — beyond CHF it decreases.
  • Forgetting that q″ is very sensitive to ΔT_e (cubic), so small errors in temperature give large errors in flux.
  • Reading T_sat at the wrong pressure (vacuum operation lowers T_sat considerably).

For GATE CH

Typical questions: identify regimes on the boiling curve, explain burnout under flux control, compute q″ from h and ΔT_e, compute vapour generation from a duty, and evaluate Rohsenow or Zuber with given properties. Conceptual questions test the shape of the curve, the effect of pressure and surface finish, and why reboilers are kept in nucleate boiling. Practise the boiling curve sketch with the regime boundaries labelled.

Quick check

  1. What is ΔT_e for water at 1 atm on a surface at 112 °C?
  2. On the boiling curve, does q″ rise or fall with ΔT_e in transition boiling?
  3. Name the minimum point of the boiling curve.
  4. Duty 1.128 MW, h_fg = 2256 kJ/kg: how much vapour is produced?
  5. Why is an electrically heated element at risk when q″ exceeds CHF?

Answers: 1. 12 K. 2. It falls. 3. Leidenfrost point. 4. 0.5 kg/s. 5. It jumps at fixed flux to film boiling at a much higher temperature, possibly melting (burnout).

Interview questions

All Heat Transfer interview questions

Try answering each one aloud before you open it.

  1. 1.What is boiling in the context of heat transfer?Concept

    Boiling is evaporation at a solid–liquid interface that occurs when the surface temperature exceeds the saturation temperature of the liquid at the system pressure. The driving force is the excess temperature ΔT_e = T_s − T_sat, and the heat flux is written q″ = h·ΔT_e. Heat is absorbed as latent heat by vapour bubbles that form at nucleation sites, and the bubble growth and departure agitate the liquid near the wall, which is why boiling coefficients are so high.

  2. 2.Explain the difference between nucleate boiling and film boiling.Concept

    Nucleate boiling occurs when small vapor bubbles form at discrete points on a heated surface and then detach into the liquid. It is characterized by high heat transfer rates. Film boiling, on the other hand, occurs when a continuous layer of vapor forms between the heating surface and the liquid, leading to lower heat transfer rates due to the insulating effect of the vapor layer.

  3. 3.Why is nucleate boiling preferred in industrial heat exchangers?Application

    Nucleate boiling gives very high heat transfer coefficients (often 10⁴–10⁵ W/m²·K for water) at small excess temperatures of roughly 5–30 K, because bubble growth and departure strongly agitate the liquid at the wall and carry latent heat away. It is also stable: under temperature control the operating point stays on a well-defined branch of the boiling curve. Beyond the critical heat flux the surface vapour-blankets, h falls sharply and, under flux control, the wall temperature can jump to damaging levels, so designs stay safely below CHF.

  4. 4.What happens if the surface temperature exceeds the Leidenfrost point during boiling?Application

    If the surface temperature exceeds the Leidenfrost point, film boiling occurs. A stable vapor layer forms between the surface and the liquid, significantly reducing the heat transfer rate. This can lead to overheating and potential damage to the heating surface.

  5. 5.How does pressure affect the boiling point of a liquid?Concept

    The boiling point of a liquid increases with an increase in pressure. This is because higher pressure requires more energy (higher temperature) for the liquid molecules to escape into the vapor phase. Conversely, reducing the pressure lowers the boiling point.

  6. 6.Why is boiling used in desalination processes?Application

    Boiling is used in desalination to separate pure water from dissolved salts. When seawater is boiled, the water vaporizes, leaving the salts behind. The vapor is then condensed to obtain fresh water. This process is effective because it exploits the phase change to separate components based on their boiling points.

  7. 7.What is the critical heat flux in boiling, and why is it important?Concept

    Critical heat flux (CHF) is the maximum heat flux at which nucleate boiling can occur before transitioning to film boiling. It is important because exceeding CHF can lead to a dramatic drop in heat transfer efficiency and potential damage to the heating surface due to overheating.

  8. 8.How much heat is needed to boil off 2 kg of saturated water at atmospheric pressure? Take h_fg = 2260 kJ/kg.Numerical

    For saturated liquid only latent heat is needed: Q = m·h_fg = 2 kg × 2260 kJ/kg = 4520 kJ (4.52 MJ). This is an amount of energy, not a rate; if it were supplied over 10 minutes the average rate would be 4520/600 ≈ 7.5 kW.

  9. 9.What are the safety concerns associated with boiling in industrial settings?Application

    Safety concerns include the risk of overheating and pressure build-up, which can lead to equipment failure or explosions. Proper control of temperature and pressure, as well as regular maintenance and monitoring, are essential to prevent such hazards.

  10. 10.What is the boiling point of water at 200 kPa, and why does it differ from 100 °C?Numerical

    From steam tables the saturation temperature at 200 kPa is about 120.2 °C. Boiling occurs when the vapour pressure of the liquid equals the system pressure; since vapour pressure rises with temperature (Clausius–Clapeyron), a higher system pressure needs a higher temperature. This is why pressurised reboilers and boilers operate at higher T_sat, and vacuum evaporators boil at lower temperatures.

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