Glossary

8.3 Natural convection mass transfer

4 min read•july 31, 2024

Natural convection mass transfer occurs when density differences in fluids, caused by concentration gradients, drive mass movement without external forces. This process relies on buoyancy forces and forms concentration boundary layers near surfaces where mass transfer happens.

Key dimensionless parameters like the Grashof, Sherwood, and Schmidt numbers help describe and analyze natural convection mass transfer. These numbers relate buoyancy forces, convective mass transfer, and fluid properties, enabling us to solve complex mass transfer problems using empirical correlations.

Natural convection mass transfer

Principles and driving forces

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  • Natural convection mass transfer transports mass due to density differences in a fluid caused by concentration gradients, without the aid of external forces (pumps or fans)
  • The buoyancy force, which arises from density variations in the fluid due to concentration differences, drives natural convection mass transfer
  • In natural convection mass transfer, the concentration gradient induces fluid motion, leading to the formation of boundary layers near the surface where mass transfer occurs
  • The , a region near the surface where the concentration gradient exists, has a thickness that depends on the fluid properties and the strength of the buoyancy force
  • The balance between the buoyancy force and the viscous force acting on the fluid determines the rate of mass transfer in natural convection

Dimensionless parameters

  • The (Gr) represents the ratio of buoyancy forces to viscous forces in natural convection mass transfer
    • Gr = gβ(Cs−C∞)L3ν2\frac{g \beta (C_s - C_\infty) L^3}{\nu^2}, where gg is the gravitational acceleration, β\beta is the volumetric expansion coefficient, CsC_s and C∞C_\infty are the surface and bulk concentrations, LL is the characteristic length, and ν\nu is the kinematic viscosity
  • The (Sh) represents the ratio of convective mass transfer to diffusive mass transfer
    • Sh = hmLD\frac{h_m L}{D}, where hmh_m is the mass transfer coefficient, LL is the characteristic length, and DD is the mass diffusivity
  • The (Sc) is the ratio of momentum diffusivity to mass diffusivity
    • Sc = νD\frac{\nu}{D}, where ν\nu is the kinematic viscosity and DD is the mass diffusivity

Factors affecting mass transfer rates

Concentration difference and fluid properties

  • A higher concentration difference between the surface and the bulk fluid leads to a stronger buoyancy force and enhanced mass transfer rates
  • Fluid properties (density, viscosity, and diffusivity) play a crucial role in determining the natural convection mass transfer rate
    • Lower fluid viscosity promotes faster fluid motion and increases the mass transfer rate
    • Higher diffusivity of the species being transferred facilitates faster mass transport through the boundary layer

Geometry and surface characteristics

  • The geometry of the system (shape and orientation of the surface) affects the flow patterns and the mass transfer rate
    • Vertical surfaces generally experience higher mass transfer rates compared to horizontal surfaces due to the unobstructed upward flow of the fluid
    • Rough surfaces enhance mass transfer by promoting turbulence and disrupting the boundary layer
  • The presence of external factors (vibrations or surface waves) can enhance the mass transfer rate by inducing additional fluid motion and mixing

Solving mass transfer problems

Dimensionless correlations

  • Empirical correlations based on dimensionless numbers estimate the mass transfer coefficients in natural convection
  • The most common correlation for natural convection mass transfer is the Sherwood-Rayleigh-Schmidt (Sh-Ra-Sc) correlation, which relates the Sherwood number to the (Ra) and Schmidt number
    • The Rayleigh number is the product of the Grashof number and Schmidt number (Ra = Gr × Sc)
    • The Sh-Ra-Sc correlation takes the form: Sh = C × (Ra)^n × (Sc)^m, where C, n, and m are constants that depend on the geometry and flow conditions

Problem-solving approach

  • To solve natural convection mass transfer problems, select the appropriate correlation based on the system geometry and flow regime
  • Calculate the mass transfer coefficient using the dimensionless numbers (Sh, Ra, Sc)
  • Example: For a in laminar flow, the correlation is Sh = 0.59 × (Ra)^(1/4) × (Sc)^(1/3)
  • Example: For a horizontal cylinder in turbulent flow, the correlation is Sh = 0.53 × (Ra)^(1/4) × (Sc)^(1/3)

Mass transfer vs heat transfer

Similarities

  • Both processes involve the transport of a quantity (mass or heat) due to buoyancy-driven fluid motion
  • The driving force is the density difference in the fluid, caused by either concentration gradients (mass transfer) or temperature gradients (heat transfer)
  • The development of boundary layers (concentration boundary layer for mass transfer and for heat transfer) is a common feature

Differences

  • In mass transfer, the transported quantity is mass or species, while in heat transfer, it is thermal energy
  • The driving potential in mass transfer is the concentration difference, whereas in heat transfer, it is the temperature difference
  • The dimensionless numbers used in mass transfer (Sh, Sc) are analogous to those in heat transfer (Nu, Pr), but they represent different physical quantities
    • (Nu) represents the ratio of convective heat transfer to conductive heat transfer
    • Prandtl number (Pr) is the ratio of momentum diffusivity to thermal diffusivity

Key Terms to Review (21)

Building Ventilation: Building ventilation is the process of supplying fresh air to and removing stale air from a building to maintain indoor air quality and comfort. It plays a vital role in controlling humidity, temperature, and pollutants, ensuring a healthy living or working environment. Effective ventilation systems can rely on natural forces, like wind and thermal buoyancy, or mechanical systems to achieve optimal airflow throughout the structure.
Buoyancy-driven flow: Buoyancy-driven flow refers to the movement of fluid resulting from density differences within that fluid, which are usually caused by temperature variations. As warmer, less dense fluid rises, it creates a pressure difference that causes the cooler, denser fluid to sink, leading to a cycle of circulation. This phenomenon is crucial in natural convection processes, where heat transfer occurs without external mechanical forces, significantly affecting mass transport in various applications.
Concentration boundary layer: The concentration boundary layer is the region adjacent to a solid surface where the concentration of a diffusing species changes from its value in the bulk fluid to that at the surface. This layer plays a crucial role in mass transfer processes, influencing how substances interact at surfaces and determining the rates of reaction and diffusion in various systems.
Convection heat transfer: Convection heat transfer is the process of heat transfer through a fluid (liquid or gas) caused by the motion of the fluid itself. This motion can be induced by external forces, such as fans or pumps, or occur naturally due to density differences within the fluid, leading to natural convection. The effectiveness of convection heat transfer is influenced by factors like fluid velocity, temperature differences, and the characteristics of the surfaces involved.
Cylindrical enclosure: A cylindrical enclosure is a three-dimensional geometric structure that has a circular base and extends vertically to a certain height, forming a cylindrical shape. This type of enclosure is often analyzed in the context of heat and mass transfer, particularly when dealing with natural convection processes involving fluids surrounding or moving within the cylinder.
Diffusion: Diffusion is the process by which molecules or particles spread from areas of high concentration to areas of low concentration, driven by the random motion of particles. This phenomenon plays a crucial role in various transport processes, impacting how momentum, energy, and mass are transferred in different systems.
Fluid density variation: Fluid density variation refers to the changes in the density of a fluid due to differences in temperature, pressure, or composition. These variations can significantly affect the behavior and movement of fluids, particularly in natural convection mass transfer processes where the buoyancy effects driven by density differences lead to the circulation of fluid.
Grashof Number: The Grashof Number is a dimensionless quantity that measures the relative significance of buoyancy forces to viscous forces in a fluid. It plays a crucial role in determining the flow regime in natural convection scenarios, helping to predict how heat transfer will occur in a fluid due to density differences caused by temperature variations.
Heat Exchangers: Heat exchangers are devices designed to efficiently transfer heat from one fluid to another without mixing them. They play a critical role in many applications, including heating and cooling systems, where managing temperature and energy transfer is essential for optimal performance.
Ideal gas: An ideal gas is a theoretical gas composed of a large number of particles that are in constant random motion, where the interactions between these particles are negligible. This concept helps simplify the understanding of gas behavior, allowing scientists to derive equations like the Ideal Gas Law, which relates pressure, volume, temperature, and the number of moles of gas. Ideal gases serve as a fundamental model in thermodynamics and heat transfer, particularly in explaining natural convection mass transfer phenomena.
Laser Doppler Anemometry: Laser Doppler Anemometry (LDA) is a non-intrusive optical technique used to measure the velocity of fluid flow by analyzing the frequency shift of laser light scattered by particles within the flow. This method allows for precise measurements of flow characteristics, such as velocity and turbulence, making it particularly valuable in studying natural convection mass transfer phenomena.
Navier-Stokes Equations: The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of fluid substances. They express the conservation of momentum and mass within a fluid and are fundamental in understanding various phenomena such as turbulence, flow patterns, and transport processes.
Nusselt Number: The Nusselt Number is a dimensionless quantity used in heat transfer that relates the convective heat transfer to the conductive heat transfer across a boundary. It helps in understanding the efficiency of heat transfer mechanisms, indicating how effectively a fluid transfers heat compared to conduction alone. This number is crucial for analyzing convection processes, influencing the design and optimization of thermal systems.
Particle Image Velocimetry: Particle Image Velocimetry (PIV) is an optical method used to measure the velocity field of a fluid flow by tracking the movement of seeded particles within the fluid. This technique is particularly valuable in studying natural and mixed convection, as it provides detailed insight into the flow patterns and interactions of heat and mass transport phenomena. PIV utilizes high-speed cameras to capture images of the particles, allowing for the calculation of their displacement over time, which translates into velocity vectors.
Rayleigh Number: The Rayleigh number is a dimensionless quantity that helps predict the onset of natural convection in a fluid. It represents the ratio of buoyancy forces to viscous forces and is crucial in determining the flow regime of fluid motion. A higher Rayleigh number indicates that buoyancy effects are more significant than viscous effects, leading to more vigorous convection currents, which plays a key role in heat and mass transfer processes.
Schmidt Number: The Schmidt number is a dimensionless quantity that represents the ratio of momentum diffusivity (kinematic viscosity) to mass diffusivity. It helps characterize the relative importance of momentum and mass transport in fluid flow, linking closely with concepts like boundary layers and transport phenomena.
Sherwood Number: The Sherwood number is a dimensionless number that characterizes mass transfer in fluid systems, defined as the ratio of convective mass transfer to diffusive mass transfer. It provides insights into how effectively mass is transported across a boundary layer compared to molecular diffusion, making it crucial for understanding mass transfer in various applications such as chemical engineering, environmental engineering, and biological processes.
Temperature Gradient: A temperature gradient is the rate of change of temperature in a specific direction, typically measured in degrees per unit distance. This concept is crucial in understanding how heat transfers through different materials, affecting the efficiency of processes like convective heat transfer, mass transfer, and coupled heat and mass transfer.
Thermal boundary layer: The thermal boundary layer is a region adjacent to a solid surface where the temperature gradient exists due to heat transfer, primarily in the context of convection. This layer forms as fluid moves over a surface, creating a thermal gradient that results in temperature differences between the fluid and the solid. Understanding the thermal boundary layer is crucial for analyzing heat transfer processes, as it directly impacts heat transfer coefficients and can influence both natural and forced convection scenarios.
Vertical Plate: A vertical plate refers to a flat surface oriented perpendicular to the direction of gravity, commonly used to study natural convection heat and mass transfer. These plates are significant in understanding how fluid motion and thermal gradients influence convective heat transfer, especially in systems where fluids are subject to buoyancy forces. The characteristics of vertical plates, such as their height and orientation, can greatly affect the convection currents and mass transfer processes occurring in the surrounding fluid.
Viscous Fluids: Viscous fluids are substances that exhibit resistance to flow due to their internal friction, which is a result of the interactions between their molecules. This property is crucial in understanding how fluids behave when they are in motion or under the influence of external forces, especially when examining the mechanisms behind natural convection mass transfer. The viscosity of a fluid plays a key role in determining the rate at which heat and mass are transferred within it, impacting processes like thermal conduction and buoyancy-driven flow.
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