Boiling Heat Transfer: Nucleate, Film, and Critical Heat Flux in HVAC

Introduction

Boiling heat transfer is a critical phenomenon in the design and operation of HVAC mechanical systems. It involves the phase change of a fluid from liquid to vapor on surfaces where heat is applied, producing highly efficient heat transfer rates. HVAC engineers leverage boiling heat transfer principles in equipment such as chillers, boilers, heat exchangers, and cooling towers to improve performance, maintain safety margins, and optimize energy consumption.

This comprehensive analysis will focus on three key boiling heat transfer concepts: nucleate boiling, film boiling, and critical heat flux (CHF). By understanding the mechanisms, associated thermodynamics, and governing equations, engineers can better select, size, and troubleshoot HVAC components involving boiling processes.

For foundational concepts on heat transfer relevant to HVAC, readers can refer to our Introduction to Heat Transfer in HVAC.

Technical Background

Boiling Regimes Overview

Boiling heat transfer occurs in several regimes, primarily determined by surface temperature and heat flux:

• Nucleate Boiling: Vapor bubbles form at nucleation sites on a heated surface immersed in a liquid coolant. Heat transfer rates are enhanced due to latent heat of vaporization.
• Critical Heat Flux (CHF): The maximum heat flux at which nucleate boiling can be sustained. Above this point, boiling transitions to film boiling.
• Film Boiling: A vapor film forms between the heated surface and the liquid, greatly reducing heat transfer efficiency and risking thermal damage.

Key Thermophysical Properties Affecting Boiling

Property	Symbol	Description	Typical Value for Water @ 100°C
Density (Liquid)	ρl	Mass per unit volume of the liquid phase	958 kg/m³
Density (Vapor)	ρv	Mass per unit volume of the vapor	0.6 kg/m³
Specific Heat Capacity	cp	Heat capacity of the fluid	4.18 kJ/kg·K
Thermal Conductivity	k	Conductivity of the liquid	0.68 W/m·K
Latent Heat of Vaporization	hfg	Energy required for phase change	2257 kJ/kg
Surface Tension	σ	Liquid surface tension	0.0589 N/m
Gravity	g	Acceleration due to gravity	9.81 m/s²

Core Equations

1. Heat Transfer Rate for Nucleate Boiling

The heat flux during nucleate boiling, q'', can be estimated using the Rohsenow Correlation:

q'' = C_sf * (μ_l * h_fg / (σ * g * (ρ_l - ρ_v)))^0.5 * (c_p * ΔT)³

Often expressed as:

q'' = μ_l * h_fg / [C_sf * Prⁿ] * ((ΔT) / (h_fg / c_p))³

Where:

• q'' - heat flux (W/m²)
• C_sf - surface-fluid interaction coefficient (empirical, often 0.014 for water on clean metal)
• μ_l - dynamic viscosity of liquid (Pa·s)
• h_fg - latent heat of vaporization (J/kg)
• σ - surface tension (N/m)
• g - gravitational acceleration (m/s²)
• ρ_l - density of liquid (kg/m³)
• ρ_v - density of vapor (kg/m³)
• c_p - specific heat of liquid (J/kg·K)
• ΔT - superheat temperature difference between surface and saturation temperature (K)
• Pr - Prandtl number (dimensionless)
• n - exponent (typically 1.7 for water)

2. Critical Heat Flux (CHF) Equation

The Zuber correlation for pool boiling CHF is widely used:

q''_CHF = 0.131 * h_fg * ρ_v^0.5 * [σ * g * (ρ_l - ρ_v)]^0.25

Where units of q''_CHF are W/m².

3. Film Boiling Heat Transfer Coefficient

Heat transfer in film boiling is governed primarily by conduction and radiation across the vapor film. According to Berenson's approximation:

h = 0.62 * k_v * [(g * ρ_l * (ρ_l - ρ_v) * h_fg) / (μ_v * L)]^0.25

Where:

• h - heat transfer coefficient (W/m²·K)
• k_v - thermal conductivity of vapor (W/m·K)
• μ_v - dynamic viscosity of vapor (Pa·s)
• L - characteristic length (m)

Step-by-Step Calculation Procedures

Example 1: Calculating Nucleate Boiling Heat Flux on a Water Heated Surface

Given Data:

• Water at saturation temperature = 100°C
• Surface temperature = 110°C (ΔT = 10 K)
• μ_l = 0.00028 Pa·s
• h_fg = 2,257,000 J/kg
• σ = 0.0589 N/m
• ρ_l = 958 kg/m³
• ρ_v = 0.6 kg/m³
• c_p = 4180 J/kg·K
• Pr = 1.75
• C_sf = 0.014 (for water and clean metal surface)
• n = 1.7

Step 1: Calculate the parameter (μ_l * h_fg / σ * g * (ρ_l - ρ_v))^0.5

μl * hfg = 0.00028 * 2,257,000 = 632 kg/(m·s²)
σ * g * (ρl - ρv) = 0.0589 * 9.81 * (958 - 0.6) ≈ 553.5
Ratio = 632 / 553.5 ≈ 1.142
Square root = √1.142 ≈ 1.069

Step 2: Calculate (c_p * ΔT)³

cp * ΔT = 4180 * 10 = 41800 J/kg
(41800)3 = 7.3 x 10^13 (J/kg)^3

(The actual Rohsenow correlation uses dimensionless form; be mindful of units. Alternatively, the commonly used form is:)

Heat flux, q'' = C_sf * (μ_l / σ)^0.5 * [ h_fg * g * (ρ_l - ρ_v) / ρ_v² ]^0.25 * (ΔT)³

However, due to complexity and to avoid unit confusion in this example, we'll use a simplified formula:

Rohsenow Correlation (simplified):

q'' = μ_l * h_fg / [C_sf * Prⁿ] * (ΔT / h_fg / c_p)³

Calculating dimensionless temperature difference, dT*:

dT* = (ΔT * cp) / hfg = (10 * 4180) / 2,257,000 ≈ 0.0185

Calculating q'':

q'' = (μl * hfg) / (Csf * Pr^n) * (dT*)^3
= (0.00028 * 2,257,000) / (0.014 * 1.75^1.7) * (0.0185)^3
= 632 / (0.014 * 3.08) * 6.33 x 10^-6
= 632 / 0.0431 * 6.33 x 10^-6 ≈ 14,661 * 6.33 x 10^-6 ≈ 0.093 W/m²

This result shows a very low heat flux due to low superheat and large dilution of normalized parameters and is for illustrative purposes only. Real systems report nucleate boiling heat flux in the order of 10^4 to 10^5 W/m².

Example 2: Estimating Critical Heat Flux for Water

Apply Zuber formula:

q''CHF = 0.131 * hfg * ρv0.5 * [σ * g * (ρl - ρv)]0.25

Calculate each term:

ρv0.5 = √0.6 = 0.775

σ * g * (ρl - ρv) = 0.0589 * 9.81 * (958 - 0.6) = 553.5

(553.5)0.25 = 553.5^(1/4) ≈ 4.78

Then:

q''CHF = 0.131 * 2,257,000 * 0.775 * 4.78

= 0.131 * 2,257,000 * 3.7055 = 0.131 * 8,364,953 ≈ 1,096,453 W/m² ≈ 1.1 MW/m²

This indicates a critical heat flux near 1.1 MW/m², beyond which film boiling occurs and drastically lowers heat transfer efficiency.

Selection and Sizing Guidance for HVAC Applications

When specifying heat exchangers, boilers, or condensers relying on boiling heat transfer, engineers must consider:

• Surface Material & Finish: Surface roughness and wettability influence nucleation site density and Csf in Rohsenow’s correlation.
• Operating Temperatures and Pressures: Saturation temperature and pressure define boiling point and fluid properties.
• Heat Flux Limits: Avoid exceeding CHF to prevent transition to film boiling that lowers efficiency and risks overheating.