🌬️Heat and Mass Transport Unit 14 – Chemical Engineering Applications

Key Concepts and Principles

• Understand the relationship between heat and mass transfer in chemical engineering systems
• Grasp the significance of transport phenomena, which encompasses momentum, heat, and mass transfer
• Recognize the role of thermodynamics in determining the driving forces for heat and mass transfer processes
• Differentiate between steady-state and transient transport processes
  • Steady-state processes maintain constant conditions over time
  • Transient processes involve changes in conditions over time
• Identify the key dimensionless numbers used in heat and mass transfer analysis (Reynolds number, Prandtl number, Sherwood number)
• Comprehend the concept of boundary layers and their influence on transport processes
  • Velocity boundary layer affects momentum transfer
  • Thermal boundary layer affects heat transfer
  • Concentration boundary layer affects mass transfer
• Understand the principles of conservation of mass, energy, and momentum in transport processes

Fundamental Equations

• Fourier's law describes heat conduction: $q = -k \nabla T$
  • $q$ is the heat flux, $k$ is the thermal conductivity, and $\nabla T$ is the temperature gradient
• Newton's law of cooling describes convective heat transfer: $q = h(T_s - T_\infty)$
  • $h$ is the convective heat transfer coefficient, $T_s$ is the surface temperature, and $T_\infty$ is the fluid temperature
• Fick's first law describes diffusive mass transfer: $J = -D \nabla C$
  • $J$ is the mass flux, $D$ is the diffusion coefficient, and $\nabla C$ is the concentration gradient
• The continuity equation represents conservation of mass: $\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = 0$
• The Navier-Stokes equations describe momentum transport in fluids: $\rho \frac{D\vec{v}}{Dt} = -\nabla p + \mu \nabla^2 \vec{v} + \rho \vec{g}$
• The energy equation represents conservation of energy: $\rho c_p \frac{DT}{Dt} = \nabla \cdot (k \nabla T) + \dot{q}$
• The species transport equation describes mass transfer with chemical reactions: $\frac{\partial C_i}{\partial t} + \nabla \cdot (C_i \vec{v}) = \nabla \cdot (D_i \nabla C_i) + R_i$

Heat Transfer Mechanisms

• Conduction occurs through direct contact between molecules, without bulk motion of matter
  • Governed by Fourier's law
  • Important in solid materials and stagnant fluids
• Convection involves heat transfer between a surface and a moving fluid
  • Can be natural (buoyancy-driven) or forced (externally induced flow)
  • Described by Newton's law of cooling
• Radiation is the transfer of energy through electromagnetic waves
  • Significant at high temperatures and in vacuum conditions
  • Governed by the Stefan-Boltzmann law: $q = \varepsilon \sigma (T_s^4 - T_{surr}^4)$
• Phase change processes (boiling, condensation) involve latent heat transfer
• Combined heat transfer mechanisms often occur simultaneously in chemical engineering applications (heat exchangers, reactors)
• The overall heat transfer coefficient ($U$) accounts for the combined effects of conduction, convection, and fouling resistances

Mass Transfer Processes

• Diffusion is the movement of species due to concentration gradients
  • Described by Fick's first law
  • Occurs in gases, liquids, and solids
• Convective mass transfer involves the transport of species by bulk fluid motion
  • Analogous to convective heat transfer
  • Characterized by mass transfer coefficients ($k_c$)
• Interfacial mass transfer occurs between phases (gas-liquid, liquid-liquid, solid-fluid)
  • Governed by equilibrium relationships (Henry's law, partition coefficients)
  • Mass transfer rates depend on interfacial area and driving forces
• Adsorption is the accumulation of species on a solid surface
  • Can be physical (van der Waals forces) or chemical (covalent bonding)
  • Important in catalysis, gas separation, and purification processes
• Membrane separation processes rely on selective permeation of species through a membrane
  • Examples include reverse osmosis, ultrafiltration, and gas permeation
• Mass transfer with chemical reaction is common in chemical engineering systems (reactors, absorbers)
  • Reaction kinetics and mass transfer rates can interact to control overall process performance

Transport Phenomena in Chemical Systems

• Fluid flow plays a crucial role in heat and mass transfer processes
  • Laminar flow occurs at low Reynolds numbers, with smooth streamlines
  • Turbulent flow occurs at high Reynolds numbers, with chaotic mixing
  • Flow regime affects heat and mass transfer coefficients
• Heat transfer in chemical reactors influences reaction rates and selectivity
  • Isothermal reactors maintain constant temperature
  • Adiabatic reactors operate without heat exchange with the surroundings
  • Non-isothermal reactors have spatial and temporal temperature variations
• Mass transfer in separation processes determines the efficiency of species separation
  • Distillation relies on vapor-liquid equilibrium and mass transfer between phases
  • Absorption involves mass transfer of a solute from a gas phase to a liquid phase
  • Extraction transfers a solute between two immiscible liquid phases
• Transport phenomena in porous media are relevant to catalysis, filtration, and oil recovery
  • Porosity and permeability characterize the porous structure
  • Darcy's law describes fluid flow in porous media: $\vec{v} = -\frac{K}{\mu} \nabla P$
• Multiphase transport phenomena involve interactions between phases (gas-liquid, liquid-liquid, gas-solid)
  • Interfacial transport processes and phase equilibria are important
  • Examples include bubble columns, fluidized beds, and spray dryers

Equipment and Design Considerations

• Heat exchangers transfer heat between two fluid streams
  • Shell-and-tube exchangers are common, with one fluid in tubes and the other in the shell
  • Plate heat exchangers offer high surface area and enhanced heat transfer
  • Design considerations include heat transfer area, pressure drop, and fouling
• Chemical reactors are vessels where chemical reactions occur
  • Batch reactors operate with a fixed amount of reactants
  • Continuous stirred-tank reactors (CSTRs) have continuous inflow and outflow
  • Plug flow reactors (PFRs) have no mixing in the axial direction
• Separation columns are used for distillation, absorption, and extraction processes
  • Tray columns have a series of perforated plates for vapor-liquid contact
  • Packed columns contain a bed of packing material to enhance mass transfer
  • Column design involves selecting the number of stages, feed location, and operating conditions
• Piping and pumping systems transport fluids between process units
  • Pipe sizing considers fluid velocity, pressure drop, and material compatibility
  • Pumps are selected based on flow rate, head, and fluid properties
• Instrumentation and control systems monitor and regulate process variables
  • Temperature, pressure, flow rate, and composition are commonly measured
  • Control valves, thermocouples, and sensors are used for process control
• Safety considerations are crucial in chemical engineering design
  • Pressure relief valves, rupture discs, and safety interlocks prevent equipment failure
  • Hazardous area classifications guide the selection of electrical equipment

Industrial Applications

• Petroleum refining involves separation and conversion of crude oil into valuable products
  • Distillation, cracking, and reforming processes rely on heat and mass transfer principles
  • Catalytic reactors and separation units are key equipment in refineries
• Chemical manufacturing produces a wide range of products (polymers, pharmaceuticals, fertilizers)
  • Batch and continuous processes are used depending on production scale and product requirements
  • Reactor design and optimization are critical for product quality and yield
• Food processing employs heat and mass transfer operations to ensure product safety and quality
  • Pasteurization, sterilization, and drying are common thermal processes
  • Extraction, filtration, and membrane separation are used for ingredient isolation and purification
• Environmental engineering applications mitigate pollution and protect human health
  • Wastewater treatment removes contaminants through physical, chemical, and biological processes
  • Air pollution control systems (scrubbers, filters, catalytic converters) reduce emissions
  • Soil remediation techniques (vapor extraction, bioremediation) clean up contaminated sites
• Renewable energy technologies harness heat and mass transfer principles
  • Solar thermal collectors capture and store solar energy for heating and power generation
  • Biofuel production involves fermentation, separation, and purification processes
  • Fuel cells convert chemical energy into electrical energy through electrochemical reactions

Problem-Solving Techniques

• Dimensional analysis is a powerful tool for understanding the relationships between variables
  • Buckingham Pi theorem reduces the number of variables by forming dimensionless groups
  • Dimensionless numbers (Reynolds, Nusselt, Sherwood) characterize transport phenomena
• Analogies between heat, mass, and momentum transfer simplify problem-solving
  • Reynolds analogy relates fluid friction and heat transfer in turbulent flow
  • Chilton-Colburn analogy extends the Reynolds analogy to mass transfer
  • Prandtl number (Pr) and Schmidt number (Sc) are analogous dimensionless numbers
• Conservation laws form the basis for analyzing transport processes
  • Mass balances account for the accumulation, inflow, outflow, and generation of species
  • Energy balances consider the storage, transfer, and conversion of energy
  • Momentum balances relate forces, pressure gradients, and fluid acceleration
• Boundary conditions specify the conditions at the edges of a problem domain
  • Fixed value (Dirichlet) conditions prescribe the value of a variable at a boundary
  • Fixed flux (Neumann) conditions specify the gradient of a variable at a boundary
  • Mixed (Robin) conditions involve a combination of value and flux conditions
• Numerical methods are employed when analytical solutions are not available
  • Finite difference methods discretize differential equations into algebraic equations
  • Finite element methods divide the domain into small elements and solve variational equations
  • Computational fluid dynamics (CFD) simulates fluid flow, heat transfer, and mass transfer in complex geometries
• Empirical correlations and experimental data are used to estimate transport properties and coefficients
  • Nusselt number correlations predict convective heat transfer coefficients
  • Sherwood number correlations estimate convective mass transfer coefficients
  • Friction factor correlations relate pressure drop to fluid flow conditions