Podcast
Questions and Answers
In heat transfer through a solid slab, what does the term '$k$' represent in Fourier's Law?
In heat transfer through a solid slab, what does the term '$k$' represent in Fourier's Law?
- The thermal conductivity of the slab (correct)
- The heat flux through the slab
- The temperature difference across the slab
- The thermal resistance of the slab
Fick's First Law describes mass transfer based on what driving force?
Fick's First Law describes mass transfer based on what driving force?
- Pressure gradient
- Concentration gradient (correct)
- Velocity gradient
- Temperature gradient
According to the principles of transport phenomena, which direction does heat flow?
According to the principles of transport phenomena, which direction does heat flow?
- From low concentration to high concentration
- From high concentration to low concentration
- From low temperature to high temperature
- From high temperature to low temperature (correct)
What best describes the fundamental processes of momentum, heat, and mass transport?
What best describes the fundamental processes of momentum, heat, and mass transport?
In the context of mass transfer, what is the significance of $D_{AB}$?
In the context of mass transfer, what is the significance of $D_{AB}$?
In which direction do heat, momentum, and mass transport typically occur in a system?
In which direction do heat, momentum, and mass transport typically occur in a system?
Which of the following analogies is correct regarding the driving force in different transport phenomena?
Which of the following analogies is correct regarding the driving force in different transport phenomena?
What is the correct relationship between flux and the transferring quantity in heat transfer?
What is the correct relationship between flux and the transferring quantity in heat transfer?
What characterizes molecular transport in the context of transport phenomena?
What characterizes molecular transport in the context of transport phenomena?
If the temperature difference across a slab is doubled and the thermal conductivity remains the same, how does the heat flux change according to Fourier's Law?
If the temperature difference across a slab is doubled and the thermal conductivity remains the same, how does the heat flux change according to Fourier's Law?
Which of the following applications is primarily concerned with the transfer of momentum in moving media?
Which of the following applications is primarily concerned with the transfer of momentum in moving media?
Heat transfer involves the movement of energy from high-energy molecules to low-energy molecules, characterized by which quantity?
Heat transfer involves the movement of energy from high-energy molecules to low-energy molecules, characterized by which quantity?
Considering Fick's First Law, if the diffusivity $D_{AB}$ increases while the concentration gradient remains constant, what happens to the molar flux $J_{Ay}$?
Considering Fick's First Law, if the diffusivity $D_{AB}$ increases while the concentration gradient remains constant, what happens to the molar flux $J_{Ay}$?
In mass transfer, what drives the movement of molecules from one phase to another?
In mass transfer, what drives the movement of molecules from one phase to another?
What differentiates turbulent transport from molecular transport?
What differentiates turbulent transport from molecular transport?
Considering an ice cube placed in warm water, which action would most effectively speed up the cooling process, utilizing principles of transport phenomena?
Considering an ice cube placed in warm water, which action would most effectively speed up the cooling process, utilizing principles of transport phenomena?
According to the Kinetic Molecular Theory, what type of collisions do gas molecules experience?
According to the Kinetic Molecular Theory, what type of collisions do gas molecules experience?
Which statement is NOT consistent with the Kinetic Molecular Theory of gases?
Which statement is NOT consistent with the Kinetic Molecular Theory of gases?
The Kinetic Theory of Gases assumes gas molecules behave as perfect spheres with diameter $d$. What is the significance of this assumption?
The Kinetic Theory of Gases assumes gas molecules behave as perfect spheres with diameter $d$. What is the significance of this assumption?
According to the Kinetic Theory of Gases, what happens to the mean free path ($l$) of a gas molecule if the number density of molecules increases at a constant temperature?
According to the Kinetic Theory of Gases, what happens to the mean free path ($l$) of a gas molecule if the number density of molecules increases at a constant temperature?
In real gases, intermolecular forces and the volume of molecules are not negligible. How does this affect the applicability of the Kinetic Theory of Gases?
In real gases, intermolecular forces and the volume of molecules are not negligible. How does this affect the applicability of the Kinetic Theory of Gases?
If the temperature of a gas is doubled, how does the average kinetic energy of the gas molecules change?
If the temperature of a gas is doubled, how does the average kinetic energy of the gas molecules change?
A gas mixture contains two types of molecules with different masses. According to the Kinetic Theory of Gases, which molecules will have the higher average speed at the same temperature?
A gas mixture contains two types of molecules with different masses. According to the Kinetic Theory of Gases, which molecules will have the higher average speed at the same temperature?
How is the mean free path ($l$) related to the effective molecular diameter ($d$) of gas molecules according to the Kinetic Theory of Gases?
How is the mean free path ($l$) related to the effective molecular diameter ($d$) of gas molecules according to the Kinetic Theory of Gases?
In the context of molecular transport phenomena, what is the fundamental characteristic that momentum, energy, and mass transfer have in common?
In the context of molecular transport phenomena, what is the fundamental characteristic that momentum, energy, and mass transfer have in common?
Which of the following statements accurately describes Newton's Law of Viscosity?
Which of the following statements accurately describes Newton's Law of Viscosity?
What do Fourier's Law and Fick's Law have in common regarding transport processes?
What do Fourier's Law and Fick's Law have in common regarding transport processes?
In the general transport equation $\psi_z = -\delta \frac{d\Gamma}{dz}$, what does the term $\delta$ represent?
In the general transport equation $\psi_z = -\delta \frac{d\Gamma}{dz}$, what does the term $\delta$ represent?
According to the general transport equation, how is the 'rate' of transport related to the 'driving force' and 'resistance'?
According to the general transport equation, how is the 'rate' of transport related to the 'driving force' and 'resistance'?
A fluid is at rest between two parallel plates. The bottom plate is suddenly moved with a velocity V, and after some time, a linear velocity profile is attained. At steady state, what is the relationship between the force F required to maintain the movement, the area A of the plate, the fluid's viscosity $\mu$, the velocity V, and the distance Y between the plates?
A fluid is at rest between two parallel plates. The bottom plate is suddenly moved with a velocity V, and after some time, a linear velocity profile is attained. At steady state, what is the relationship between the force F required to maintain the movement, the area A of the plate, the fluid's viscosity $\mu$, the velocity V, and the distance Y between the plates?
Newton's Law of Viscosity is represented by $\tau = -\mu \frac{dv}{dy}$. In this equation, what does $\frac{dv}{dy}$ represent?
Newton's Law of Viscosity is represented by $\tau = -\mu \frac{dv}{dy}$. In this equation, what does $\frac{dv}{dy}$ represent?
In the context of flux and driving forces, how is the flux related to the gradient and the transport coefficient?
In the context of flux and driving forces, how is the flux related to the gradient and the transport coefficient?
Flashcards
Gas Composition
Gas Composition
Tiny, discrete particles (atoms or molecules) that compose gases.
Gas Molecular motion
Gas Molecular motion
Gases move randomly, colliding with each other and container walls.
Perfectly Elastic Collisions
Perfectly Elastic Collisions
Collisions where kinetic energy is conserved; no energy lost.
Temperature and Kinetic Energy
Temperature and Kinetic Energy
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Intermolecular Forces (Gases)
Intermolecular Forces (Gases)
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Gas Particle Volume
Gas Particle Volume
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Mean Free Path
Mean Free Path
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Mean Time between Collisions
Mean Time between Collisions
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Momentum Transport
Momentum Transport
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Heat Transfer
Heat Transfer
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Mass Transfer
Mass Transfer
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Molecular Transport
Molecular Transport
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Molecular Transport (Speed)
Molecular Transport (Speed)
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Turbulent Transport (Speed)
Turbulent Transport (Speed)
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Incorrect statement about transport
Incorrect statement about transport
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Direction of Transport
Direction of Transport
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Phenomenological Laws
Phenomenological Laws
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Newton's Law of Viscosity
Newton's Law of Viscosity
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Fourier's and Fick's Law Commonality
Fourier's and Fick's Law Commonality
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General Transport Equation Components
General Transport Equation Components
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General Transport Equation
General Transport Equation
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Transport Rate Equation
Transport Rate Equation
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Newton's Law of Viscosity (Equation)
Newton's Law of Viscosity (Equation)
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Temperature Gradient
Temperature Gradient
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Heat Transfer: Q/A
Heat Transfer: Q/A
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Fourier's Law
Fourier's Law
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Fick's First Law
Fick's First Law
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Momentum Transfer Flux
Momentum Transfer Flux
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Heat Transfer Flux
Heat Transfer Flux
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Mass Transfer Flux
Mass Transfer Flux
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Fourier's Law & Fick's Law
Fourier's Law & Fick's Law
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Study Notes
- ChE 407 covers momentum transfer, which is an introduction to transport processes.
Kinetic Molecular Theory
- Gases comprise minute discrete particles referred to as atoms or molecules
- The molecules move randomly while they collide with each other as well as the walls of their container
- Collisions between molecules do not result in energy loss due to friction, thus remain perfectly elastic
- Absolute temperature relates proportionally to average kinetic energy
- At relatively low pressures, the average intermolecular distance significantly exceeds the molecular diameters, rendering the Intermolecular Forces of Attraction, IMFA negligible
- Particle volume is minuscule compared to the entire gas
Kinetic Theory of Gases
- Gases consist of molecules, each shaped like a perfect sphere
- Gas molecules do not have attractive or repulsion forces between them
- Molecule volume is negligible relative to the space separating them
- Collisions are perfectly elastic
- Molecules move randomly at average speed in random directions
- Individual molecules travel a certain distance "l" between collisions, which relates to the mean free path
- The mean free path describes the required time it takes for each molecule to travel at average speed between collisions
- Statistical averages describe large numbers of molecules
Types of Transport
- Molecular transport relies on molecule motion for mass, heat, or momentum
- Microscopic changes influence macroscopic observation
- Momentum transfer, commonly called fluid mechanics, focuses on momentum transfer in moving media
- Momentum transfer relates to separation processes of fluid flow, sedimentation, mixing, and filtration
- Heat transfer relates to transfer energy as heat from high to low-energy molecules through drying, evaporation, or distillation
- Mass transfer transfers material or mass from one phase to another when molecules shift from high to low concentrations from processes like distillation, absorption, liquid-liquid extraction, or crystallization
- Transport phenomena take place through molecular or turbulent mechanisms
- Molecular transport is orderly but gradual
- Turbulent transport is chaotic but rapid
Molecular Transport
- Molecular transport transports momentum, energy, and mass from high to low concentrations
- Molecular transports follow similar governing equations or Phenomenological Laws
General Transport Equation
- Molecular transport mechanisms follow the general equation:
- Ψz = -δ(dΓ/dz) where:
- Ψz = property flux (flux = rate/area)
- δ = diffusivity (momentum, thermal, and mass diffusivity)
- Γ = transported property (momentum, energy, and concentration)
- z = direction of transfer
- Ψz = -δ(dΓ/dz) where:
- Rate can be described:
- rate = drivingforce/ resistance
Newton's Law of Viscosity
- A liquid at rest between two plates starts to flow upon the bottom plate's movement at velocity V, which causes laminar flow
- F/A=-μ(0-V)/(Y-0)
- τ = -μ(dv/dy)
- Ï„ is shear stress
- μ corresponds to viscosity
Flux occurs due to a driving force
- Flux = (Flow Quantity/ (Time)(Area)
- Flux = (Transport Coefficient)(Gradient)
- Expressing unidirectional temperature gradients:
- Temperature Gradient = dT/dy
Fourier's Law states heat will flow from high to low temperatures
- The temperature of one of the opposite faces of the slab increases to T2. The result is that heat flows from the higher to the lower temperature region
- Q/A = -k((T1-T2)) /Δx
- qx = -k dT/dx
- qx is heat flux in the x direction
- k signifies thermal conductivity
Fick's First Law
- Fick's First Law covers mass transfer due to concentration differences in a binary system
- JAy = -DAB dCA/dy where:
- JAy = molar flux of component A in the y direction
- DAB = the diffusivity of A in B (the other component); transport coefficient
- dCA/dy = change in concentration with respect to position
Transport Phenomena Comparisons
- Momentum:
- Flux: Ï„ = F/A
- Driving Force: dv/dy = Δv/Δy
- Diffusivity: μ
- Transferring Quantity: Molecular Velocity
- Direction: high to low velocity
- Heat:
- Flux: Q = q/A
- Driving Force: dT/dx = ΔT/Δx
- Diffusivity: k
- Transferring Quantity: Molecular energy (temperature)
- Direction: high to low temperature
- Mass:
- Flux: JA = NA/A
- Driving Force: dCA/dx = ΔCA/Δx
- Diffusivity: DAB
- Transferring Quantity: Molecules
- Direction: high to low concentration
Transport Properities
- Diffusivity relates to each molecular transport
- Momentum (μ), Heat (k), and Mass (DAB) diffusivities all have the same dimensions: L2/t
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Description
Explore fundamental concepts in transport phenomena including heat transfer, mass transfer, and momentum transfer. Understand Fourier's Law, Fick's First Law, and the driving forces behind these phenomena. Learn about molecular transport and the relationships between flux and transferring quantities.
