6.4 Simultaneous Heat and Mass Transfer

Heat and mass transfer often happen together in engineering. Think of cooling towers or drying processes. When temperature changes, it can cause mass to move, and when concentration shifts, it affects heat flow.

These coupled processes are key in designing heat exchangers and cooling systems. They can make transfer rates faster or slower than if they happened separately. Understanding this interplay is crucial for engineers tackling thermal challenges.

Heat and Mass Transfer Coupling

Simultaneous Occurrence in Engineering Applications

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• Heat and mass transfer processes often occur simultaneously in many engineering applications (evaporative cooling, drying, condensation)
• The presence of a temperature gradient can induce mass transfer, while the presence of a concentration gradient can affect heat transfer rates
• Coupled heat and mass transfer is essential in the design and analysis of heat exchangers, cooling towers, and other thermal systems involving phase change or mass transport
• The coupling between heat and mass transfer can lead to enhanced or reduced transfer rates compared to the individual processes occurring separately

Examples of Coupled Heat and Mass Transfer

• Evaporation of water from a wet surface (cooling towers, sweat evaporation from skin)
• Condensation of moisture from humid air (dehumidification systems, fog formation)
• Drying of porous materials (food drying, wood drying, ceramic drying)
• Absorption of gases into liquids (gas scrubbing, carbonation of beverages)
• Distillation processes (separation of liquid mixtures based on boiling point differences)

Governing Equations for Coupled Transfer

Conservation Equations

• The governing equations for simultaneous heat and mass transfer include conservation of mass, momentum, energy, and species transport equations
• The mass conservation equation accounts for the transport of different species in the system, considering diffusion and convection mechanisms
• The energy conservation equation describes the heat transfer processes, including conduction, convection, and latent heat effects associated with phase change
• The species transport equation governs the diffusion and convection of individual species in the mixture, considering concentration gradients and bulk fluid motion

Boundary Conditions and Numerical Methods

• Boundary conditions for the governing equations must be specified (temperature, concentration, flux conditions at interfaces)
• Numerical methods (finite difference, finite element techniques) are often employed to solve the coupled governing equations for complex geometries and boundary conditions
• Initial conditions must be specified for transient problems, describing the initial temperature and concentration distributions in the system
• Convergence and stability of the numerical solution must be ensured through appropriate mesh refinement, time step selection, and iterative techniques

Heat Transfer Influence on Mass Transfer

Thermophoresis and Soret Effect

• The presence of a temperature gradient can enhance or reduce mass transfer rates through various mechanisms (thermophoresis, Soret effect)
• Thermophoresis refers to the movement of particles or molecules in a fluid due to a temperature gradient, affecting the mass transfer rates
• The Soret effect describes the mass transfer driven by a temperature gradient in a mixture, leading to the separation of species
• Thermophoresis can be utilized in particle separation and deposition processes (aerosol sampling, thermal precipitators)
• The Soret effect is important in the separation of isotopes and in the study of thermodiffusion in liquid mixtures

Latent Heat Effects

• Mass transfer can also influence heat transfer rates through the latent heat associated with phase change processes (evaporation, condensation)
• The evaporation of a liquid requires latent heat, which affects the overall heat transfer rate and temperature distribution in the system
• Condensation of a vapor releases latent heat, impacting the heat transfer characteristics and surface temperature
• Latent heat effects are crucial in the design of heat exchangers involving phase change (condensers, evaporators)
• The coupling of latent heat and mass transfer is essential in the analysis of multi-phase systems (boiling, condensation, sublimation)

Analogy for Coupled Transfer Coefficients

Dimensionless Numbers and Correlations

• The heat and mass transfer analogy allows for the estimation of mass transfer coefficients based on heat transfer correlations, or vice versa
• The analogy is based on the similarity between the governing equations and boundary conditions for heat and mass transfer
• Dimensionless numbers (Nusselt number (Nu) for heat transfer, Sherwood number (Sh) for mass transfer) are used to quantify the transfer coefficients
• The Chilton-Colburn analogy relates the heat and mass transfer coefficients through the Stanton number (St) and the Schmidt number (Sc)

Applicability and Empirical Correlations

• The heat and mass transfer analogy is applicable to systems with similar geometry, flow conditions, and boundary conditions
• Empirical correlations based on the heat and mass transfer analogy are available for common geometries (flat plates, cylinders, spheres) under various flow regimes (laminar, turbulent)
• The analogy allows for the estimation of mass transfer coefficients when heat transfer data is available, or vice versa, reducing the need for extensive experimental measurements
• The analogy is widely used in the design and analysis of heat and mass transfer equipment (cooling towers, humidifiers, dryers)
• Limitations of the analogy include differences in fluid properties, presence of chemical reactions, and non-uniform surface conditions