10.3 Evaporation and condensation

Evaporation and condensation are crucial phase change processes in heat and mass transport. These phenomena involve the conversion of liquids to vapors and vice versa, driven by temperature and pressure differences. Understanding their principles is key to designing efficient heat transfer systems.

Heat and mass transfer mechanisms in evaporation and condensation include conduction, convection, and radiation. Factors like fluid properties, flow conditions, and surface geometry affect transfer rates. Calculating these rates involves dimensionless parameters and heat exchanger analysis methods for optimal system design.

Evaporation and Condensation Principles

Fundamental Concepts

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• Evaporation converts a liquid into a vapor or gas through the addition of heat energy, occurring at the liquid-vapor interface when the vapor pressure of the liquid exceeds the surrounding pressure
• Condensation converts a vapor or gas into a liquid through the removal of heat energy, occurring when the vapor pressure of the gas is lower than the surrounding pressure and the temperature is below the dew point
• The latent heat of vaporization is the amount of energy required to convert a unit mass of liquid into vapor at a constant temperature and pressure, which is released during condensation

Driving Forces and Factors Affecting Evaporation and Condensation

• The driving force for evaporation is the difference between the vapor pressure of the liquid and the partial pressure of the vapor in the surrounding gas; a larger difference results in a higher evaporation rate
• The driving force for condensation is the difference between the partial pressure of the vapor in the surrounding gas and the vapor pressure of the liquid at the condensation surface; a larger difference results in a higher condensation rate
• The boiling point of a liquid is the temperature at which its vapor pressure equals the surrounding pressure; evaporation can occur below the boiling point, while boiling involves the formation of vapor bubbles within the liquid
• The saturation temperature is the temperature at which the vapor pressure of a gas equals the surrounding pressure; condensation occurs when the temperature of the gas falls below the saturation temperature

Heat and Mass Transfer in Evaporation

Mechanisms of Heat and Mass Transfer

• Heat transfer during evaporation and condensation occurs through:
  • Conduction: transfer of heat through a material by molecular interaction
  • Convection: movement of fluids due to density differences
  • Radiation: transfer of energy through electromagnetic waves
• Mass transfer during evaporation and condensation occurs through:
  • Diffusion: movement of molecules from a region of high concentration to a region of low concentration
  • Convection: bulk motion of fluids
• The rate of heat transfer depends on the temperature difference between the liquid/vapor and the surrounding medium, the surface area available for heat transfer, and the heat transfer coefficient
• The rate of mass transfer depends on the concentration difference between the liquid/vapor and the surrounding medium, the surface area available for mass transfer, and the mass transfer coefficient

Factors Affecting Heat and Mass Transfer

• The heat and mass transfer coefficients are influenced by factors such as:
  • Fluid properties (viscosity, density, thermal conductivity)
  • Flow conditions (laminar or turbulent)
  • Geometry of the heat and mass transfer surfaces
• The presence of non-condensable gases can significantly impact the heat and mass transfer rates during condensation by forming a barrier layer at the condensation surface, reducing the partial pressure of the condensable vapor and hindering the condensation process
• The formation of droplets or films during condensation affects the heat and mass transfer mechanisms:
  • Dropwise condensation typically results in higher heat transfer rates compared to filmwise condensation due to the continuous exposure of fresh condensation surfaces
  • Filmwise condensation forms a continuous liquid film on the surface, which can act as a resistance to heat transfer

Calculating Transfer Rates

Dimensionless Parameters

• The Nusselt number (Nu) is a dimensionless parameter that relates the convective heat transfer coefficient to the thermal conductivity of the fluid and a characteristic length, used to quantify the heat transfer performance of evaporators and condensers
  • For laminar flow, the Nusselt number can be calculated using correlations such as the Sieder-Tate equation or the Dittus-Boelter equation, depending on the flow conditions and geometry
  • For turbulent flow, the Nusselt number can be calculated using correlations such as the Dittus-Boelter equation, the Colburn equation, or the Gnielinski equation, depending on the Reynolds number and Prandtl number ranges
• The Sherwood number (Sh) is a dimensionless parameter that relates the convective mass transfer coefficient to the diffusivity of the species and a characteristic length, used to quantify the mass transfer performance of evaporators and condensers
  • The Sherwood number can be calculated using correlations such as the Ranz-Marshall equation or the Frossling equation, depending on the flow conditions and geometry

Heat Exchanger Analysis Methods

• The overall heat transfer coefficient (U) accounts for the resistances to heat transfer on both the hot and cold sides of a heat exchanger, as well as the resistance of the separating wall, used to calculate the overall heat transfer rate in evaporators and condensers
  • The overall heat transfer coefficient can be determined using the resistances-in-series approach, considering the convective heat transfer coefficients on the hot and cold sides, the thermal conductivity and thickness of the separating wall, and any fouling resistances
• The effectiveness-NTU (Number of Transfer Units) method is a widely used approach for designing and analyzing heat exchangers, including evaporators and condensers, relating the actual heat transfer rate to the maximum possible heat transfer rate
  • The effectiveness of a heat exchanger can be calculated based on the NTU and the heat capacity rate ratio, using correlations specific to the heat exchanger configuration (parallel flow, counter flow, cross flow)
• The log-mean temperature difference (LMTD) method is another approach for analyzing heat exchangers, particularly when the inlet and outlet temperatures of the hot and cold fluids are known, accounting for the non-linear temperature profile along the heat exchanger length
  • The LMTD is calculated based on the inlet and outlet temperatures of the hot and cold fluids, and a correction factor is applied to account for the heat exchanger configuration (parallel flow, counter flow, cross flow with one fluid mixed)

Design and Optimization of Evaporators and Condensers

Selection and Design Considerations

• The design of evaporators and condensers involves selecting the appropriate type of heat exchanger based on factors such as:
  • Phase change process (evaporation or condensation)
  • Fluid properties (viscosity, thermal conductivity, corrosivity)
  • Operating conditions (temperature, pressure, flow rates)
  • Desired performance (heat transfer rate, efficiency)
• Common types of evaporators include:
  • Falling film evaporators: liquid flows downward as a thin film on the inside or outside of tubes, with vapor generated on the surface
  • Rising film evaporators: liquid flows upward as a thin film on the inside of tubes, with vapor generated on the surface
  • Forced circulation evaporators: liquid is pumped through tubes at high velocities to promote heat transfer and minimize fouling
  • Plate evaporators: liquid and heating medium flow in alternate channels between thin plates, promoting high heat transfer rates
• Common types of condensers include:
  • Shell-and-tube condensers: vapor condenses on the outside or inside of tubes, with cooling medium flowing on the opposite side
  • Plate heat exchangers: vapor and cooling medium flow in alternate channels between thin plates, promoting high heat transfer rates
  • Air-cooled condensers: vapor condenses inside tubes, with air flowing over the outside of the tubes to remove heat
  • Direct-contact condensers: vapor is directly mixed with a cooling liquid, resulting in condensation and heat transfer
• The design process for evaporators and condensers involves:
  • Determining the required heat transfer area based on the desired heat transfer rate, the overall heat transfer coefficient, and the LMTD or effectiveness-NTU method
  • Selecting the appropriate materials of construction based on factors such as corrosion resistance, thermal conductivity, and compatibility with the fluids involved
  • Specifying the operating parameters such as flow rates, temperatures, and pressures to achieve the desired performance

Optimization Strategies

• Optimization of evaporators and condensers aims to maximize the heat and mass transfer performance while minimizing the capital and operating costs, considering factors such as:
  • Heat exchanger geometry: selecting the appropriate tube diameter, tube length, tube pitch, and baffle spacing to enhance heat transfer and minimize pressure drop
  • Flow configuration: choosing between parallel flow, counter flow, or cross flow arrangements to maximize the temperature driving force and heat transfer effectiveness
  • Operating conditions: adjusting the flow rates, temperatures, and pressures to achieve the desired evaporation or condensation rates while minimizing energy consumption and maximizing efficiency
• Fouling mitigation is an important consideration in the design and operation of evaporators and condensers, as fouling can reduce the heat transfer efficiency and increase pressure drop
  • Strategies for fouling mitigation include:
    • Selecting appropriate materials of construction to minimize fouling propensity
    • Implementing proper pretreatment of the fluids to remove fouling precursors
    • Optimizing the flow velocities to minimize stagnant zones and promote turbulence
    • Incorporating cleaning mechanisms such as mechanical or chemical cleaning to remove fouling deposits
• Process integration and energy efficiency are key aspects of designing and optimizing evaporators and condensers in industrial applications, involving:
  • Considering the overall process flowsheet and identifying opportunities for heat integration and energy recovery
  • Using heat integration techniques, such as pinch analysis, to identify the optimal placement of evaporators and condensers within the process to maximize energy efficiency and minimize utility consumption
  • Utilizing waste heat recovery from high-temperature streams to provide the necessary heat input for evaporation
  • Using the latent heat of condensation to preheat other process streams or generate useful energy (steam or electricity)