Boiling

Boiling is phase-change heat transfer where liquid converts to vapor at a heated surface. This process provides extremely high heat transfer coefficients and is fundamental to refrigeration cycles, evaporators, and thermal management systems.

Pool Boiling Fundamentals

Pool boiling occurs when a heated surface is submerged in a quiescent liquid pool. The heat transfer characteristics depend strongly on the degree of superheat (ΔT = T_surface - T_sat).

Pool Boiling Curve

The pool boiling curve relates heat flux to surface superheat and exhibits distinct regimes:

Free Convection Regime (ΔT < 5°C):

• Heat transfer by natural convection
• No bubble formation
• q" ∝ ΔT^(5/4) (typical)

Nucleate Boiling Regime (5°C < ΔT < 30°C):

• Vapor bubbles form at nucleation sites
• Extremely high heat transfer coefficients
• h = 2,500 to 100,000 W/(m²·K)
• Optimal regime for most HVAC applications

Transition Boiling Regime (30°C < ΔT < 120°C):

• Unstable region
• Alternating nucleate and film boiling
• Decreasing heat flux with increasing ΔT

Film Boiling Regime (ΔT > 120°C):

• Continuous vapor film blankets surface
• Poor heat transfer
• Surface temperatures can reach dangerous levels

Nucleate Boiling

Nucleate boiling provides the highest heat transfer coefficients in pool boiling.

Rohsenow Correlation

The Rohsenow correlation predicts nucleate boiling heat transfer:

q"/μ_l h_fg = [c_p,l (T_s - T_sat) / (C_sf h_fg Pr_l^n)]^3

Where:

• q" = heat flux (W/m²)
• μ_l = liquid dynamic viscosity (Pa·s)
• h_fg = latent heat of vaporization (J/kg)
• c_p,l = liquid specific heat (J/(kg·K))
• T_s = surface temperature (K)
• T_sat = saturation temperature (K)
• C_sf = surface-fluid combination constant
• Pr_l = liquid Prandtl number
• n = exponent (typically 1.0 for water, 1.7 for other fluids)

Typical C_sf Values:

Surface roughness significantly affects nucleation site density and boiling performance. Rougher surfaces generally provide better nucleate boiling heat transfer.

Bubble Dynamics

Bubble formation follows a sequence:

1. Nucleation - Vapor embryo forms at cavity
2. Growth - Bubble expands as liquid evaporates
3. Departure - Bubble detaches when buoyancy exceeds surface tension
4. Condensation - Bubble may condense in subcooled liquid

Bubble departure diameter (Fritz correlation):

D_b = 0.0208 β [σ / (g(ρ_l - ρ_v))]^(1/2)

Where:

• D_b = bubble departure diameter (m)
• β = contact angle (degrees)
• σ = surface tension (N/m)
• g = gravitational acceleration (9.81 m/s²)
• ρ_l, ρ_v = liquid and vapor densities (kg/m³)

Critical Heat Flux (CHF)

CHF represents the maximum heat flux achievable in nucleate boiling before transition to film boiling. Exceeding CHF causes rapid surface temperature increase and potential equipment damage.

Zuber Correlation (Pool Boiling)

For pool boiling on large horizontal surfaces:

q"_CHF = 0.149 h_fg ρ_v [σ g (ρ_l - ρ_v) / ρ_v²]^(1/4)

Typical CHF values:

• Water at 1 atm: 1.0 to 1.3 MW/m²
• R-134a at 5°C: 200 to 300 kW/m²
• Ammonia at -10°C: 400 to 600 kW/m²

CHF Design Considerations:

• Operate at 50-70% of CHF for safety margin
• Higher pressures increase CHF
• Surface orientation affects CHF (horizontal surfaces optimal)
• Subcooling increases CHF

Flow Boiling

Flow boiling occurs inside tubes and channels where forced convection augments boiling heat transfer.

Flow Boiling Regimes

As vapor quality increases along evaporator length:

Subcooled Boiling (x < 0):

• Liquid temperature below saturation
• Bubbles form at wall, condense in bulk liquid
• High heat transfer coefficients

Saturated Nucleate Boiling (0 < x < 0.1):

• Bulk liquid at saturation
• Bubbles form and grow at wall
• Heat transfer dominated by nucleate boiling

Convective Boiling (0.1 < x < 0.8):

• Annular flow regime
• Thin liquid film on wall with vapor core
• Heat transfer by convection through liquid film

Dry-Out Region (x > 0.8):

• Liquid film breaks down
• Wall contacts vapor
• Sharp decrease in heat transfer coefficient
• Must be avoided in evaporator design

Flow Boiling Heat Transfer

The Chen correlation combines nucleate and convective contributions:

h = h_nucleate · S + h_convective · F

Where:

• S = suppression factor (0 to 1)
• F = Reynolds number enhancement factor

For convective component:

h_convective = 0.023 (k_l/D) Re_l^0.8 Pr_l^0.4

Where Re_l is based on liquid-only flow.

Evaporator Design Applications

Superheat Requirements

Superheat (vapor temperature above saturation) ensures complete evaporation and prevents liquid carryover to compressor.

Typical Superheat Values:

Heat Flux Design Guidelines

Maximum Design Heat Flux:

Design Considerations

Mass Flux Effects:

• Low mass flux (G < 100 kg/(m²·s)): Nucleate boiling dominant
• Medium mass flux (100 < G < 500 kg/(m²·s)): Mixed regime
• High mass flux (G > 500 kg/(m²·s)): Convective boiling dominant

Pressure Drop Concerns:

• Two-phase pressure drop reduces evaporating temperature
• ΔT_sat = (dT/dP)·ΔP_friction
• Limits evaporator length and refrigerant velocity
• Use larger diameter tubes for low pressure drop

Oil Return:

• Minimum vapor velocity required to entrain oil
• V_min ≈ 3-5 m/s for horizontal lines
• V_min ≈ 5-8 m/s for vertical risers
• Critical at low load conditions

Film Boiling and Leidenfrost Point

Film boiling occurs when surface superheat exceeds CHF condition, forming a stable vapor blanket.

Leidenfrost Temperature:

• Minimum surface temperature for stable film boiling
• Typically 200-300°C above saturation for water
• Minimum in pool boiling curve
• Must be avoided in refrigeration equipment

Film Boiling Heat Transfer:

h_film = 0.62 [k_v³ ρ_v (ρ_l - ρ_v) g h’_fg / (μ_v D (T_s - T_sat))]^(1/4)

Where:

• h’_fg = modified latent heat = h_fg + 0.4 c_p,v (T_s - T_sat)
• k_v, μ_v, ρ_v = vapor properties
• D = characteristic length

Film boiling provides poor heat transfer (h ≈ 100-400 W/(m²·K)) compared to nucleate boiling.

Practical HVAC Applications

Refrigeration Evaporators:

• Operate in nucleate to convective boiling regimes
• Design for complete evaporation plus superheat
• Monitor for dry-out at partial loads

Chiller Evaporators:

• Flooded shell design maintains nucleate boiling
• Refrigerant recirculation rates of 2-4× evaporation rate
• High heat transfer coefficients (3,000-8,000 W/(m²·K))

Heat Pump Evaporators:

• Outdoor coils experience frost formation
• Defrost cycles critical for maintaining performance
• Refrigerant distribution affects coil utilization

DX Expansion Devices:

• Control superheat to optimize evaporator utilization
• Balance between full coil usage and compressor protection
• Electronic valves provide superior control

Performance Factors

Enhancement Techniques:

• Micro-fin tubes increase nucleation sites
• Enhanced surfaces improve h by 100-300%
• Surface treatments modify wettability
• Nanofluid refrigerants under research

Degradation Factors:

• Fouling reduces heat transfer
• Oil accumulation blankets surfaces
• Non-condensable gases reduce performance
• Inadequate refrigerant charge