3.5 Boiling and Condensation

Boiling and condensation are crucial heat transfer processes in many engineering applications. These phenomena involve phase changes between liquid and vapor states, dramatically affecting heat transfer rates and system efficiency.

Understanding boiling regimes and condensation types is essential for designing effective heat exchange systems. From nucleate boiling's high heat transfer rates to dropwise condensation's superior performance, these concepts are key to optimizing thermal management in various industries.

Pool Boiling Regimes

Mechanisms and Characteristics

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• Pool boiling occurs when a heated surface is submerged in a large volume of stagnant liquid, and the liquid near the surface undergoes phase change to vapor
• The boiling process can be divided into different regimes based on the excess temperature (ΔT), which is the difference between the surface temperature and the saturation temperature of the liquid
• The boiling regimes, in order of increasing ΔT, are: natural convection, nucleate boiling, transition boiling, and film boiling

Regimes and Their Descriptions

• In the natural convection regime, heat transfer occurs primarily through convection currents in the liquid, without significant bubble formation
  • Example: Heating water in a pot before bubbles start to form
• Nucleate boiling is characterized by the formation and growth of vapor bubbles at nucleation sites on the heated surface, leading to high heat transfer rates
  • Example: Water boiling in a pot with bubbles forming at the bottom and rising to the surface
• Transition boiling occurs when the vapor bubbles begin to coalesce and form larger vapor patches, resulting in a decrease in heat transfer coefficient
  • Example: Large vapor patches forming on a heated surface, causing the liquid to intermittently contact the surface
• In the film boiling regime, a stable vapor film covers the heated surface, acting as an insulating layer and reducing the heat transfer rate
  • Example: Leidenfrost effect, where a droplet of liquid levitates on a cushion of its own vapor when placed on a sufficiently hot surface

Critical Heat Flux in Boiling

Factors Influencing Critical Heat Flux

• The critical heat flux (CHF) is the maximum heat flux that can be achieved during nucleate boiling before the transition to film boiling occurs
• Factors that influence the critical heat flux include:
  • Surface roughness: Rougher surfaces provide more nucleation sites, increasing the CHF
  • Surface wettability: Highly wettable surfaces promote liquid contact and delay the onset of film boiling, increasing the CHF
  • Liquid properties: Liquids with higher latent heat of vaporization, higher thermal conductivity, and lower surface tension tend to have higher CHF values
  • System pressure: Increasing the system pressure generally increases the CHF

Estimating Critical Heat Flux

• Correlations, such as the Zuber correlation, can be used to estimate the critical heat flux based on fluid properties and system parameters
  • Zuber correlation: $q_{CHF} = C\rho_v h_{fg} \left[\frac{\sigma g(\rho_l - \rho_v)}{\rho_v^2}\right]^{1/4}$
  • where $C$ is a constant, $\rho_v$ and $\rho_l$ are vapor and liquid densities, $h_{fg}$ is the latent heat of vaporization, $\sigma$ is the surface tension, and $g$ is the gravitational acceleration
• Example: Estimating the CHF for water at atmospheric pressure using the Zuber correlation with $C = 0.131$, $\rho_l = 958 \, kg/m^3$, $\rho_v = 0.6 \, kg/m^3$, $h_{fg} = 2257 \, kJ/kg$, and $\sigma = 0.0589 \, N/m$

Film vs Dropwise Condensation

Mechanisms and Characteristics

• Condensation occurs when a vapor comes into contact with a surface at a temperature below the saturation temperature of the vapor
• Film condensation is characterized by the formation of a continuous liquid film on the cooling surface, with the condensate flowing down the surface due to gravity
  • Example: Steam condensing on a cold vertical plate, forming a continuous liquid film
• Dropwise condensation occurs when the condensate forms discrete droplets on the cooling surface, which grow, coalesce, and are eventually shed from the surface
  • Example: Water vapor condensing on a non-wettable surface, such as a treated metal or a hydrophobic coating

Heat Transfer Coefficients

• The heat transfer coefficient for film condensation can be estimated using the Nusselt analysis, which accounts for the thermal resistance of the liquid film
  • Nusselt analysis: $h = 0.943\left[\frac{\rho_l(\rho_l - \rho_v)g h_{fg} k_l^3}{\mu_l(T_{sat} - T_s)L}\right]^{1/4}$
  • where $\rho_l$ and $\rho_v$ are liquid and vapor densities, $g$ is the gravitational acceleration, $h_{fg}$ is the latent heat of vaporization, $k_l$ is the liquid thermal conductivity, $\mu_l$ is the liquid dynamic viscosity, $T_{sat}$ and $T_s$ are the saturation and surface temperatures, and $L$ is the characteristic length
• Dropwise condensation typically results in higher heat transfer coefficients compared to film condensation due to the reduced thermal resistance and the continuous exposure of the surface to the vapor
• Promoting dropwise condensation requires the use of non-wettable surfaces or the application of surface treatments to prevent the formation of a continuous liquid film

Boiling and Condensation Applications

Problem-Solving Approach

• Boiling and condensation heat transfer find applications in various fields, such as power generation, refrigeration, and process industries
• In boiling heat transfer problems, the objective is often to determine the heat transfer rate, surface temperature, or critical heat flux for a given set of conditions
• In condensation heat transfer problems, the goal may be to calculate the heat transfer rate, surface temperature, or condensation rate for a given set of conditions
• When solving problems, it is essential to:
  • Identify the boiling or condensation regime
  • Select the appropriate correlations or models
  • Account for the relevant fluid properties and system parameters

Calculating Heat Transfer Rates

• The heat transfer rate in boiling can be calculated using Newton's law of cooling:
  • $q = h \times A \times \Delta T$
  • where $h$ is the boiling heat transfer coefficient, $A$ is the surface area, and $\Delta T$ is the excess temperature
• The heat transfer rate in condensation can be determined using the appropriate heat transfer coefficient correlation:
  • Nusselt analysis for film condensation
  • Empirical correlations for dropwise condensation
• Example: Calculating the heat transfer rate for film condensation of steam on a vertical tube with a surface temperature of 80°C, given the saturation temperature of 100°C, tube length of 1 m, and tube diameter of 0.02 m