1) The document discusses the development of modeling in chemical engineering over the 20th century. Prandtl's boundary layer concept and simple fluid flow models were highly influential.
2) These simple models, like the $10 models for fluid flow, heat transfer, and mass transfer, were widely adopted despite being approximations. They formed the basis of design methods in areas like heat exchangers and mass transfer equipment.
3) Other influential modeling concepts discussed include the film model for heat transfer developed by Lewis, the film model for mass transfer developed by Whitman, and Danckwerts' proposal to model chemical reactors using residence time distribution curves determined via tracer studies.
Hi All,
These are my CRE (Chemical Reaction Engineering) hand written notes when I was preparing for GATE (Graduate Aptitude Test in Engineering) in 2002 for Chemical Engineering. The current document forms the 6th chapter of book on CRE from Octave Levenspiel.
I plan to upload & share most of the stuff I prepared for the GATE exam. My best wishes to those preparing for GATE !
Hi All,
These are my CRE (Chemical Reaction Engineering) hand written notes when I was preparing for GATE (Graduate Aptitude Test in Engineering) in 2002 for Chemical Engineering. The current document forms the unsolved problems from 3rd chapter of book on CRE from Octave Levenspiel.
I plan to share most of the stuff I prepared for the GATE exam. My best wishes to those preparing !
Reflection and Transmission of Thermo-Viscoelastic Plane Waves at Liquid-Soli...IDES Editor
The present paper is aimed at to study the reflection and transmission characteristics of plane waves at liquid-solid interface. The liquid is chosen to be inviscid and the solid
half-space is homogeneous isotropic, thermally conducting viscoelastic. Both classical (coupled) and non-classical (generalized) theories of linear thermo-viscoelasticity have been employed to investigate the characteristics of reflected and transmitted waves. Reflection and transmission coefficients are obtained for quasi-longitudinal ( qP ) wave. The numerical computations of reflection and transmission coefficients are carried out for water-copper structure with the help of Gauss-elimination by using MATLAB software and the results have been presented graphically.
This tutorial covers heat transfer via convection and radiation. It discusses:
- Natural and forced convection, and how to calculate heat transfer rates using surface heat transfer coefficients.
- Combining conduction and convection to solve problems involving multi-layer surfaces.
- The basic theory of radiated heat transfer, and how emissivity and surface shape affect heat transfer rates.
- Calculating effective surface heat transfer coefficients to model radiation using similar equations as convection.
- Worked examples are provided to demonstrate calculating heat transfer rates via combined conduction, convection and radiation in practical scenarios.
The document discusses applications of differential equations. It begins by providing a brief history of differential equations, noting they were independently invented by Newton and Leibniz. It then defines ordinary and partial differential equations. Examples of applications are given for modeling phenomena like cooling, oscillations, and game development. Specific differential equations like Laplace's, heat, and wave equations are discussed along with physical applications in fields like physics, engineering, and biology. Newton's law of cooling is provided as a motivating example and its applications are outlined.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via conduction, convection and radiation. Heat flux is directly proportional to temperature gradient based on Fourier's Law. Measurements show highest heat flux at mid-ocean ridges and lowest in old ocean crust. Heat flux decreases with age of sea floor and continental crust due to cooling and decreasing radioactive elements. Conservation of energy equations relate heat flux to temperature gradient and internal heat sources.
1) A new cosmological model is proposed where the universe is spontaneously created from nothing via quantum tunneling into a de Sitter space.
2) After tunneling, the model evolves according to the inflationary scenario, avoiding the big bang singularity and not requiring initial conditions.
3) The model suggests that the universe was created via quantum tunneling from a state of literally nothing into a de Sitter space, which then evolved into the expanding universe we observe according to known physics.
This document discusses heat transfer on Earth. It notes that the main sources of heat on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Conduction and convection are most important in Earth's lithosphere. The heat flux is directly proportional to the temperature gradient according to Fourier's Law. Heat flow measurements show the highest heat loss at mid-ocean ridges and lowest at old oceanic crust. The geotherm can be determined from the conservation of energy and appropriate boundary conditions.
Hi All,
These are my CRE (Chemical Reaction Engineering) hand written notes when I was preparing for GATE (Graduate Aptitude Test in Engineering) in 2002 for Chemical Engineering. The current document forms the 6th chapter of book on CRE from Octave Levenspiel.
I plan to upload & share most of the stuff I prepared for the GATE exam. My best wishes to those preparing for GATE !
Hi All,
These are my CRE (Chemical Reaction Engineering) hand written notes when I was preparing for GATE (Graduate Aptitude Test in Engineering) in 2002 for Chemical Engineering. The current document forms the unsolved problems from 3rd chapter of book on CRE from Octave Levenspiel.
I plan to share most of the stuff I prepared for the GATE exam. My best wishes to those preparing !
Reflection and Transmission of Thermo-Viscoelastic Plane Waves at Liquid-Soli...IDES Editor
The present paper is aimed at to study the reflection and transmission characteristics of plane waves at liquid-solid interface. The liquid is chosen to be inviscid and the solid
half-space is homogeneous isotropic, thermally conducting viscoelastic. Both classical (coupled) and non-classical (generalized) theories of linear thermo-viscoelasticity have been employed to investigate the characteristics of reflected and transmitted waves. Reflection and transmission coefficients are obtained for quasi-longitudinal ( qP ) wave. The numerical computations of reflection and transmission coefficients are carried out for water-copper structure with the help of Gauss-elimination by using MATLAB software and the results have been presented graphically.
This tutorial covers heat transfer via convection and radiation. It discusses:
- Natural and forced convection, and how to calculate heat transfer rates using surface heat transfer coefficients.
- Combining conduction and convection to solve problems involving multi-layer surfaces.
- The basic theory of radiated heat transfer, and how emissivity and surface shape affect heat transfer rates.
- Calculating effective surface heat transfer coefficients to model radiation using similar equations as convection.
- Worked examples are provided to demonstrate calculating heat transfer rates via combined conduction, convection and radiation in practical scenarios.
The document discusses applications of differential equations. It begins by providing a brief history of differential equations, noting they were independently invented by Newton and Leibniz. It then defines ordinary and partial differential equations. Examples of applications are given for modeling phenomena like cooling, oscillations, and game development. Specific differential equations like Laplace's, heat, and wave equations are discussed along with physical applications in fields like physics, engineering, and biology. Newton's law of cooling is provided as a motivating example and its applications are outlined.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via conduction, convection and radiation. Heat flux is directly proportional to temperature gradient based on Fourier's Law. Measurements show highest heat flux at mid-ocean ridges and lowest in old ocean crust. Heat flux decreases with age of sea floor and continental crust due to cooling and decreasing radioactive elements. Conservation of energy equations relate heat flux to temperature gradient and internal heat sources.
1) A new cosmological model is proposed where the universe is spontaneously created from nothing via quantum tunneling into a de Sitter space.
2) After tunneling, the model evolves according to the inflationary scenario, avoiding the big bang singularity and not requiring initial conditions.
3) The model suggests that the universe was created via quantum tunneling from a state of literally nothing into a de Sitter space, which then evolved into the expanding universe we observe according to known physics.
This document discusses heat transfer on Earth. It notes that the main sources of heat on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Conduction and convection are most important in Earth's lithosphere. The heat flux is directly proportional to the temperature gradient according to Fourier's Law. Heat flow measurements show the highest heat loss at mid-ocean ridges and lowest at old oceanic crust. The geotherm can be determined from the conservation of energy and appropriate boundary conditions.
This document provides an overview of heat transfer topics covered in a module, including objectives, topics, and introductions. The key topics are the three modes of heat transfer - conduction, convection, and radiation. Equations for calculating heat transfer via these three modes are presented, including Fourier's law of conduction, Newton's law of cooling for convection, and the Stefan-Boltzmann law for radiation. Examples of combined radiation and convection heat transfer are also discussed.
This document summarizes key concepts from Chapter 9 of a fluid mechanics textbook on flow over immersed bodies. It discusses:
1) Boundary layer flow and bluff body flow, which are characterized by high or low Reynolds numbers and possible flow separation.
2) Drag is decomposed into form and skin friction contributions, with implications for streamlining bodies.
3) The boundary layer equations, which provide a simplified description of viscous flow and can be solved using methods like the Blasius solution for laminar flat plate boundary layers.
This document discusses contact angles and the Young-Laplace equation. It begins with an introduction to wetting and motivation for studying contact angles. It then summarizes the Young relationship between contact angle and interfacial tensions. The Young-Laplace equation relating pressure jump, mean curvature, and surface tension is derived. Interfaces are described as being 3D, dynamic, and asymmetric. The document discusses measurements of contact angles and their relationship to molecular interactions.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes heat flux as proportional to the temperature gradient. Global heat flow measurements show the highest heat flux at mid-ocean ridges and lowest at old oceanic crust. Heat flow over stable continental areas decreases with crustal age due to radioactive decay, while heat flow over oceanic crust decreases with age due to cooling of the crust over time.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes heat flux as proportional to the temperature gradient. Global heat flow measurements show the highest heat flux at mid-ocean ridges and lowest at old oceanic crust. Heat flow over stable continental areas decreases with crustal age due to radioactive decay, while heat flow over oceanic crust decreases with age due to cooling of the crust over time.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes heat flux as proportional to the temperature gradient. Global heat flow measurements show the highest heat flux at mid-ocean ridges and lowest at old oceanic crust. Heat flow over stable continental areas decreases with crustal age due to radioactive decay, while heat flow over oceanic crust decreases with age due to cooling of the crust over time.
This document discusses heat transfer on Earth. It notes that the main sources of heat on Earth's surface are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes how heat flux is directly proportional to the temperature gradient. Global heat flow measurements show the highest heat loss at mid-ocean ridges and lowest at old oceanic crust. The temperature profile within Earth (the geotherm) can be derived from the conservation of energy, taking into account internal heat sources.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes heat flux as proportional to the temperature gradient. Global heat flow measurements show the highest heat flux at mid-ocean ridges and lowest at old oceanic crust. Heat flow over stable continental areas decreases with crustal age due to radioactive decay, while heat flow over oceanic crust decreases with age due to cooling of the crust over time.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes how heat flux is directly proportional to the temperature gradient. Global heat flow measurements show the highest heat loss at mid-ocean ridges and lowest at old oceanic crust. The temperature profile within Earth (the geotherm) can be derived from the conservation of energy, taking into account internal heat sources.
Thermodynamics of vesicle growth and morphologyrichardgmorris
1. The document describes a theoretical model for the growth of vesicles through accretion of amphiphilic molecules.
2. The model uses linear non-equilibrium thermodynamics to describe the vesicle system and its dynamics in terms of thermodynamic forces and fluxes.
3. Stability analysis of the model predicts that spherical vesicles are unstable at small surface areas but become stable at larger surface areas due to a balance of molecular incorporation and water transport effects.
This document discusses the basics of electrostatics including frictional electricity, properties of electric charges, Coulomb's law, units of charge, and continuous charge distribution. It explains that rubbing two materials like glass and silk can cause the transfer of electrons leaving one material positively charged and the other negatively charged. Coulomb's law states that the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Continuous charge distributions can be characterized by linear, surface, and volume charge densities which describe the charge per unit length, area, or volume, respectively.
The document discusses applications of first order differential equations. It provides examples in several domains:
1) Cooling/warming laws can be modeled using differential equations, like the temperature of cooling coffee over time.
2) Population growth and decay models use differential equations, like calculating time for a population to double at a growth rate.
3) Determining geometric properties of curves can involve solving differential equations, like finding the equation of a curve based on its tangent slope.
4) Applications also include radioactive decay, electrical circuits, mixture of solutions, and modeling motion. First order differential equations have widespread uses in physics, statistics, chemistry, engineering, and other fields.
This document provides information about the course "Heat Transfer II" for the Chemical Engineering program. It includes details such as course code, credits, prerequisites, and general and specific objectives. It also outlines the main topics that will be covered, including heat exchanger design, laminar and free convection flow, process calculations, evaporation, and cooling towers. Evaluation methods are mentioned which include exams, simulations, and design projects related to evaporators and cooling towers. Recommended textbooks are also provided.
- Heat exchangers transfer heat between fluids through solid surfaces. Heat is transferred by convection between the fluid and solid surface.
- The rate of heat transfer depends on the convection heat transfer coefficient (h), which depends on fluid properties and velocities.
- Dimensionless numbers like Reynolds, Prandtl, and Nusselt relate fluid flow regime (laminar or turbulent) to heat transfer rate.
- Empirical relationships using these numbers predict heat transfer for forced and natural convection in different geometries.
- The overall heat transfer coefficient (U) accounts for resistances of conductive and convective boundaries in composite systems.
The document discusses the importance of mathematics in describing ionic solutions, which play a key role in biology. It notes that while chemists have reliable quantitative data on ionic solutions, most theories ignore interactions between ions. This represents an opportunity for new mathematical approaches that can account for these interactions. The document advocates for developing a consistent theoretical framework, like the Energetic Variational Approach, to model ionic solutions in a way that replaces trial and error with computations. This would help provide insights into important biological and chemical processes that occur in ionic solutions.
This document presents a statistical thermodynamic framework for describing the evolution of open systems undergoing chemical reactions.
The framework derives an entropy formula for such systems and uses it to obtain an equation of motion. The equation describes the system moving towards more probable states via the flow of matter and energy between chemical compounds through reaction pathways. The framework suggests that the driving forces of these reactions, known as chemical affinities, are not conserved quantities, indicating the motion is non-integrable and chaotic in nature.
Here are the key steps to solve this problem:
1. Draw a schematic of the system and define the parameters. You have a pipe with water flowing through it at a rate of 0.15 kg/s. The inlet temperature is 20°C and desired outlet temperature is 50°C.
2. Write the energy balance equation:
Rate of heat transfer into the water = Rate of increase of thermal energy of water
Q = mCpΔT
Where:
Q = Rate of heat transfer (W)
m = Mass flow rate (0.15 kg/s)
Cp = Specific heat of water (4.18 kJ/kg-K)
ΔT = Increase in
This document discusses heat transfer and conduction heat transfer principles. It defines heat transfer as energy in transit due to a temperature difference. The three modes of heat transfer are conduction, convection, and radiation. Fourier's law of conduction and Newton's law of cooling are described as the basic laws governing conduction and convection. The document also discusses concepts like the heat conduction equation, thermal resistance, boundary conditions, and classification of conduction heat transfer problems.
The document provides contact information for Statistics Homework Helper, including their website, email address, and phone number. It offers help with Statistics Homework through online tutoring services.
This document provides an overview of heat transfer topics covered in a module, including objectives, topics, and introductions. The key topics are the three modes of heat transfer - conduction, convection, and radiation. Equations for calculating heat transfer via these three modes are presented, including Fourier's law of conduction, Newton's law of cooling for convection, and the Stefan-Boltzmann law for radiation. Examples of combined radiation and convection heat transfer are also discussed.
This document summarizes key concepts from Chapter 9 of a fluid mechanics textbook on flow over immersed bodies. It discusses:
1) Boundary layer flow and bluff body flow, which are characterized by high or low Reynolds numbers and possible flow separation.
2) Drag is decomposed into form and skin friction contributions, with implications for streamlining bodies.
3) The boundary layer equations, which provide a simplified description of viscous flow and can be solved using methods like the Blasius solution for laminar flat plate boundary layers.
This document discusses contact angles and the Young-Laplace equation. It begins with an introduction to wetting and motivation for studying contact angles. It then summarizes the Young relationship between contact angle and interfacial tensions. The Young-Laplace equation relating pressure jump, mean curvature, and surface tension is derived. Interfaces are described as being 3D, dynamic, and asymmetric. The document discusses measurements of contact angles and their relationship to molecular interactions.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes heat flux as proportional to the temperature gradient. Global heat flow measurements show the highest heat flux at mid-ocean ridges and lowest at old oceanic crust. Heat flow over stable continental areas decreases with crustal age due to radioactive decay, while heat flow over oceanic crust decreases with age due to cooling of the crust over time.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes heat flux as proportional to the temperature gradient. Global heat flow measurements show the highest heat flux at mid-ocean ridges and lowest at old oceanic crust. Heat flow over stable continental areas decreases with crustal age due to radioactive decay, while heat flow over oceanic crust decreases with age due to cooling of the crust over time.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes heat flux as proportional to the temperature gradient. Global heat flow measurements show the highest heat flux at mid-ocean ridges and lowest at old oceanic crust. Heat flow over stable continental areas decreases with crustal age due to radioactive decay, while heat flow over oceanic crust decreases with age due to cooling of the crust over time.
This document discusses heat transfer on Earth. It notes that the main sources of heat on Earth's surface are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes how heat flux is directly proportional to the temperature gradient. Global heat flow measurements show the highest heat loss at mid-ocean ridges and lowest at old oceanic crust. The temperature profile within Earth (the geotherm) can be derived from the conservation of energy, taking into account internal heat sources.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes heat flux as proportional to the temperature gradient. Global heat flow measurements show the highest heat flux at mid-ocean ridges and lowest at old oceanic crust. Heat flow over stable continental areas decreases with crustal age due to radioactive decay, while heat flow over oceanic crust decreases with age due to cooling of the crust over time.
This document discusses heat transfer on Earth. It notes that the main sources of heat transfer on Earth are the Sun and Earth's interior. Heat is transferred via three main mechanisms: conduction, convection, and radiation. Fourier's law of heat conduction describes how heat flux is directly proportional to the temperature gradient. Global heat flow measurements show the highest heat loss at mid-ocean ridges and lowest at old oceanic crust. The temperature profile within Earth (the geotherm) can be derived from the conservation of energy, taking into account internal heat sources.
Thermodynamics of vesicle growth and morphologyrichardgmorris
1. The document describes a theoretical model for the growth of vesicles through accretion of amphiphilic molecules.
2. The model uses linear non-equilibrium thermodynamics to describe the vesicle system and its dynamics in terms of thermodynamic forces and fluxes.
3. Stability analysis of the model predicts that spherical vesicles are unstable at small surface areas but become stable at larger surface areas due to a balance of molecular incorporation and water transport effects.
This document discusses the basics of electrostatics including frictional electricity, properties of electric charges, Coulomb's law, units of charge, and continuous charge distribution. It explains that rubbing two materials like glass and silk can cause the transfer of electrons leaving one material positively charged and the other negatively charged. Coulomb's law states that the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Continuous charge distributions can be characterized by linear, surface, and volume charge densities which describe the charge per unit length, area, or volume, respectively.
The document discusses applications of first order differential equations. It provides examples in several domains:
1) Cooling/warming laws can be modeled using differential equations, like the temperature of cooling coffee over time.
2) Population growth and decay models use differential equations, like calculating time for a population to double at a growth rate.
3) Determining geometric properties of curves can involve solving differential equations, like finding the equation of a curve based on its tangent slope.
4) Applications also include radioactive decay, electrical circuits, mixture of solutions, and modeling motion. First order differential equations have widespread uses in physics, statistics, chemistry, engineering, and other fields.
This document provides information about the course "Heat Transfer II" for the Chemical Engineering program. It includes details such as course code, credits, prerequisites, and general and specific objectives. It also outlines the main topics that will be covered, including heat exchanger design, laminar and free convection flow, process calculations, evaporation, and cooling towers. Evaluation methods are mentioned which include exams, simulations, and design projects related to evaporators and cooling towers. Recommended textbooks are also provided.
- Heat exchangers transfer heat between fluids through solid surfaces. Heat is transferred by convection between the fluid and solid surface.
- The rate of heat transfer depends on the convection heat transfer coefficient (h), which depends on fluid properties and velocities.
- Dimensionless numbers like Reynolds, Prandtl, and Nusselt relate fluid flow regime (laminar or turbulent) to heat transfer rate.
- Empirical relationships using these numbers predict heat transfer for forced and natural convection in different geometries.
- The overall heat transfer coefficient (U) accounts for resistances of conductive and convective boundaries in composite systems.
The document discusses the importance of mathematics in describing ionic solutions, which play a key role in biology. It notes that while chemists have reliable quantitative data on ionic solutions, most theories ignore interactions between ions. This represents an opportunity for new mathematical approaches that can account for these interactions. The document advocates for developing a consistent theoretical framework, like the Energetic Variational Approach, to model ionic solutions in a way that replaces trial and error with computations. This would help provide insights into important biological and chemical processes that occur in ionic solutions.
This document presents a statistical thermodynamic framework for describing the evolution of open systems undergoing chemical reactions.
The framework derives an entropy formula for such systems and uses it to obtain an equation of motion. The equation describes the system moving towards more probable states via the flow of matter and energy between chemical compounds through reaction pathways. The framework suggests that the driving forces of these reactions, known as chemical affinities, are not conserved quantities, indicating the motion is non-integrable and chaotic in nature.
Here are the key steps to solve this problem:
1. Draw a schematic of the system and define the parameters. You have a pipe with water flowing through it at a rate of 0.15 kg/s. The inlet temperature is 20°C and desired outlet temperature is 50°C.
2. Write the energy balance equation:
Rate of heat transfer into the water = Rate of increase of thermal energy of water
Q = mCpΔT
Where:
Q = Rate of heat transfer (W)
m = Mass flow rate (0.15 kg/s)
Cp = Specific heat of water (4.18 kJ/kg-K)
ΔT = Increase in
This document discusses heat transfer and conduction heat transfer principles. It defines heat transfer as energy in transit due to a temperature difference. The three modes of heat transfer are conduction, convection, and radiation. Fourier's law of conduction and Newton's law of cooling are described as the basic laws governing conduction and convection. The document also discusses concepts like the heat conduction equation, thermal resistance, boundary conditions, and classification of conduction heat transfer problems.
The document provides contact information for Statistics Homework Helper, including their website, email address, and phone number. It offers help with Statistics Homework through online tutoring services.
1. Chemical Engineering Science 57 (2002) 4691 – 4696
www.elsevier.com/locate/ces
Modeling in chemical engineering
Octave Levenspiel∗
Department of Chemical Engineering, Oregon State University, Corvallis, OR 97331, USA
Abstract
In its 90 year life what has chemical engineering (ChE) contributed to society? Firstly, we have invented and developed processes to
create new materials, more gently and more e ciently, so as to make life easier for all.
Secondly, ChE has changed our accepted concepts and our ways of thinking in science and technology. Here modeling stands out as
the primary development. Let us consider this.
? 2002 Elsevier Science Ltd. All rights reserved.
1. Chemical engineering’s $10 and $100 ow models 2. The boundary layer concept
I suspect that most authors put especial thought into the How is the velocity of a uid a ected as it ows close
ÿrst sentence of a book because it sets the tone for what is to to a solid surface? Throughout the years many scientists
follow. In this light Denbigh’s monograph (Denbigh, 1951) considered this phenomenon. These studies culminated in
starts with the following sentence: the Karman–Prandtl u vs. y relationship, see von Karman
(1934),
In science it is always necessary to abstract from the com- u y 0=
= 5:75 log + 5:56;
plexity of the real world, and in its place to substitute a 0=
more or less idealized situation that is more amenable to
analysis. where
y 0 0
u= when u ¡ 11:84
This statement applies directly to chemical engineering, be-
cause each advancing step in its concepts frequently starts which is shown in Fig. 1a.
with an idealization which involves the creation of a new However, Prandtl (1904) proposed a simpler model for
and simpliÿed model of the world around us. The accep- the velocity proÿle: thus a linear velocity change with dis-
tance of such a model changes our world view. tance from the surface, or
Often a number of models vie for acceptance. Should we du
= constant and u = 0 at y = 0
favor rigor or simplicity, exactness or usefulness, the $10 or dy
$100 model? We will look at: meeting nonviscous ow further away from the surface; in
e ect, two di erent types of uid patched together. This is
• boundary layer theory,
shown in Fig. 1b.
• heat transfer and ‘h’,
This combination of viscous and nonviscous uid seemed
• mass transfer and ‘kg ’ and ‘k‘ ’,
absurd at that time, but as we shall see, it has been found to
• chemical reactors, RTD, tracer technology, and
be fabulously e cient and useful for aeronautics, chemical
• the troublesome uidized bed.
and other branches of engineering.
We may call the 20th century chemical engineering’s mod- Let me repeat a few words about the creator of the laminar
eling century. This talk considers this whole development. layer model, words written by his most illustrious student,
Theodore von Karman, director of the Guggenheim Aero-
∗ Tel.: +1-541-737-3618; fax: +1-541-737-46-00. nautical Laboratory at the California Institute of Technology
E-mail address: octave@che.orst.edu (O. Levenspiel). (von Karman, 1954).
0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 0 9 - 2 5 0 9 ( 0 2 ) 0 0 2 8 0 - 4
2. 4692 O. Levenspiel / Chemical Engineering Science 57 (2002) 4691 – 4696
change beyond, as shown in Fig. 2b. Thus, close to the cold
surface he said
replace the dT by T
−→
changing : : : dy close to y across
the surface the ÿlm
in which case the Fourier heat transfer equation becomes
T k
q = kA
˙ = A T:
y across the y
whole ÿlm
Calling k= y = h he ÿnally got
Fig. 1. Velocity proÿle near a wall: (a) actual proÿle, and (b) simpliÿed
proÿle.
q = hA T;
˙
where ‘h’ is called the heat transfer coe cient.
The acceptance and use of this concept led to explosive
research. Thousands of research studies were reported, and
are still being reported today, on ‘h’ for
• ow inside and outside of pipes,
• condensing uids,
• boiling uids,
• natural convection and
• two phase systems of all types of gases, liquids, and solids.
The resulting correlations were all made in terms of dimen-
Fig. 2. Temperature by a wall: (a) actual proÿle, and (b) simpliÿed proÿle.
sionless groups, examples of which are shown below.
For the inside pipe wall (turbulent ow):
0:7
Prandtl (1875 –1953) was an engineer in training. His hd d
= 0:023 1+
control of mathematical methods and tricks was limited; k L
many of his collaborators and followers surpassed him − − −− −−−−−
in solving di cult mathematical problems. However he Nusselt entrance
had a unique ability to describe physical phenomena in
relatively simple terms, to distill the essence of a situation d
0:14
and to drop the unessentials. His greatest contribution is 1 + 3:5 Re0:8 Pr 1=3
dcoil w
in boundary layer theory.
× − − − − −− −−−−−−−
coiled pipe temperature
So here we have two models for ow close to a surface, dependency
the more precise $100 Karman–Prandtl equation and the
simple $10 laminar layer or ÿlm model. We will see that Single particle : hD = 2 + 0:6 Re1=2 Pr 1=3 ,
k
chemical engineering embraced the $10 model and made it Natural convection : hL=k = A[Gr Pr]B ,
a cornerstone for its developments in the 20th century.
Condensation hundreds of studies
Boiling : : : etc:
Radiation hundreds of correlations:
3. Film model for heat transfer
Twelve years after Prandtl charted the path with his sim-
ple ow model, W. K. Lewis of M.I.T. (Lewis, 1916), fol- 4. Film model for mass transfer
lowing the ideas of Newton, Fourier, and other early work-
ers, adopted the simple ÿlm model to represent the rate of It took another 7 years before Whitman (1923) considered
heat transfer from a hot uid owing past a cold surface. applying the ÿlm model to mass transfer from a uid to its
This means that instead of considering a changing temper- bounding surface. With an approach similar to that used by
ature gradient away from the cold surface, Fig. 2a, he took Lewis he replaced the changing concentration proÿle of a
a straight line gradient in the ÿlm, but with no additional component A, Fig. 3a, by a linear concentration proÿle as
3. O. Levenspiel / Chemical Engineering Science 57 (2002) 4691 – 4696 4693
Fig. 4. Counter ow heat interchange, plug ow idealization.
Fig. 3. Mass transfer: (a) actual proÿle, and (b) simpliÿed proÿle.
shown in Fig. 3b. In symbols the absorption rate by the solid,
or removal rate of A from the uid is
˙ dCA
N A = DA (mol A removed=s):
dy at surface
With the linear model
˙ CA D Fig. 5. Countercurrent ow mass transfer: (a) plug ow model, and (b)
N A = DA = A CA = kg A( CA ) across the axial dispersion model.
y y whole ÿlm
where kg (or k‘ ) is called the mass transfer coe cient.
patterns—plug ow, mixed ow, laminar ow, crosscurrent
Again, dimensionless groups are involved in the correla-
ow, etc. However, we should be aware that the logarithmic
tions for the various mass transfer situations, as shown be-
mean is only correct and should only be used to represent
low (Perry & Green, 1984).
cocurrent and countercurrent plug ow. For all other ow
For gas absorption in columns ÿlled with Raschig rings,
patterns it is incorrect, often very incorrect to use it.
and Berl saddles.
For mass transfer of a component A from a gas to a liquid
−2=3
kg Gg dp −0:36 we have a similar development, an overall mass transfer
For the gas phase : =1:195( ) .
Gg g (1 − ) D g coe cient Kg , which is deÿned as
0:45 0:5 1 1 HA Henry s law constant
k‘ dp G ‘ dp = + ; HA = :
For the liquid phase : =25:1 . Kg kg k‘ for A
D‘ ‘ (1 − ) D ‘
In a packed bed tower, with countercurrent ow of gas and
liquid, the design method, universally used today, is based
5. Design consequences
on the crude $10 model for the ow of gas and of liquid,
the plug ow model, Fig. 5a. To be more realistic, to as-
These concepts of ‘h’ for heat transfer and ‘k’ for mass
sume dispersed plug ow, the operating line would look
transfer became the heart of design methods for heat ex-
di erent. This model is illustrated in Fig. 5b. This more re-
changers and for absorption and extraction equipment.
alistic approach, this $100 ow model, was championed by
For heat transfer from one uid through a wall to a second
Vermeulen et al. (1966), but it had problems:
uid this leads to the overall heat transfer coe cient U given
as • It required a complex computer solution.
1 1 1 • We did not have reliable values for the extent of disper-
= +
U h1 h2 sion, or deviation from plug ow for gas and for liquid.
and for a heat exchanger for counter (or parallel)- ow of • Every time you pack a column you get a di erent ow
two uids a $10 ow model assumes plug ow of the two behavior.
uids, as shown in Fig. 4. For this model the performance
expression is So this $100 approach has been lost in history.
For heat exchanger design we get similar ow complica-
q = UA( T )‘m ;
˙ where T = T i − ti ; tions if we try to account for deviations from plug ow.
with the logarithmic mean T is
T 1 − T2
T‘m = : 6. Re ections on the ÿrst 50 years of chemical engineering
ln( T1 = T2 )
It should be noted that the logarithmic mean driving force Prandtl’s simple model was taken up by Lewis for heat
is often used to represent design of all sorts of contacting transfer, and by Whitman for mass transfer, and it led
4. 4694 O. Levenspiel / Chemical Engineering Science 57 (2002) 4691 – 4696
ultimately to the core of the unit operations. Our profession
has really blossomed as a consequence of this simple con-
cept. Can you imagine what heat and mass transfer studies
would be like without ‘h’ and ‘k’? A desert.
7. Chemical reactors
In the ÿrst half of this century two ow models domi-
nated the design of ow reactors, plug ow and mixed ow.
Fig. 6 shows, for the reaction given, if a plug ow reactor
would need a length of 1 m, then for mixed ow you would
need a length of 1000 m to produce the same product.
It would be unwise to only use these ow models, since
real reactors behave somewhere between these two ex-
Fig. 6. Volumes needed for the two ideal ow patterns: (a) plug ow
tremes. How do we deal with this? The $100 approach says model, and (b) mixed ow model.
evaluate the velocity ÿeld within the reactor, or better still,
the $1000 approach says evaluate the three-dimensional
uctuating velocity ÿeld, and then use your computer to
tell you what would happen; in essence, use computational
uid dynamics. What an ugly procedure!
In so complicated a world what should we do? It was
the genius of Danckwerts (1953) who proposed a ridicu-
lously simple ow model to tell how a vessel would act as
a chemical reactor. He said, introduce a pulse of tracer into
the uid entering the reactor and see when it leaves. This
exit concentration–time curve is called the residence time
distribution curve, or RTD curve, see Fig. 7. Fig. 7. Key to the tracer method for determining the ow pattern in
This information tells how the reactor would behave— vessels and reactors.
exactly for linear reaction kinetics, and as a close approx-
imation for more complex reaction kinetics. How wonder- the ideal frictionless uid (that imaginary stu ). This was
fully little information is needed! No need to measure what a highly mathematical exercise dealing with what is called
is happening within the reactor. irrotational ow, velocity potentials and stream functions.
This proposal of Danckwerts led to an explosion of re- On the other hand, you had hydraulics developed by civil
search, and to the development of all sorts of models to rep- engineers, who amassed mountains of tables, all obtained
resent these response curves. Fig. 8 shows one class of these from experiments on pressure drop and head loss of uids
models, the one to represent the ow in pipes and in other owing in all sorts of open and closed channels—made of
long narrow vessels. Lots of research, lots of publications concrete, fresh wood, slimy old wood, etc.
and lots of Ph.D. theses resulted from this concept, mainly Re ecting on the situation at the beginning of the 20th
in the late 1950s, the 1960s and the 1970s. century, Prandtl (see Tietjens, 1934) said
The study of the RTD of owing uids, and its conse-
quences is called tracer technology. Chemical engineers and Hydrodynamics has little signiÿcance for the engineer be-
medical researchers are those who are most interested in this cause of the great mathematical knowledge required for
subject, to the chemical engineer to represent the behavior an understanding of it and the negligible possibility of ap-
of reactors, to the medical doctor to represent the movement plying its results. Therefore engineers put their trust in the
and distribution of uids and drugs in the body, to diagnose mass of empirical data collectively known as the “science
disease, etc. of hydraulics”.
Prandtl (1904) was the genius who patched together these
8. Fluid sciences completely di erent disciplines with his simple boundary
layer model. The result is modern uid mechanics. The left
Let us brie y summarize the science and technology of side of Fig. 9 shows the pioneers in this development, the
uid ow. types of problems solved, the terms used, and so on. I call
In the 19th century two completely di erent approaches this Type 1 problem of uid ow.
were used to study the ow of uids. First there was the Then in 1952 Danckwerts introduced a completely di er-
theoretical study called hydrodynamics, which dealt with ent type of study of uids which I call tracer technology.
5. O. Levenspiel / Chemical Engineering Science 57 (2002) 4691 – 4696 4695
9.1. The LHHW models
Since the beginning of the century chemists have used
the Langmuir–Hinshelwood models to represent the rates
of chemical reactions. The chemical engineer, following
the lead of Hougen and Watson’s 1947 book (Hougen &
Watson, 1947a), built on this approach developing what
is called the Langmuir–Hinshelwood–Hougen–Watson
(LHHW) models.
These models were cumbersome to use, but were based
on the mechanism of action of molecules, such as:
• adsorption of reactants onto active sites on the solid sur-
face,
• reactions of attached molecules
◦ with adjacent attached molecules (dual site)
Fig. 8. The dispersed plug ow model is used to represent many reactors ◦ with free molecules (single site)
and vessel types.
◦ by decomposition alone
• desorption of product molecules from the surface.
For a typical equation, say for a ÿrst-order reversible reac-
tion, A → R, dual-site mechanism, surface reaction control-
ling, no product in the feed, the performance equation for
plug ow of gas through the packed bed catalytic reactor is:
C W (1= + KA nA0 + KI nI 0 )2
=
F (1 + 1=K)
2(1= + KA nA0 + KI nI 0 )(KR − KA )nA0
+
(1 + 1=K)2
Fig. 9. The two distinctly di erent types of uid mechanics problems. (KR − KA )n2
A0 nA0
+ 3
ln
(1 + 1=K) nA0 − (1 + 1=K)x
The right side of Fig. 9 shows the names of the pioneers and (KR − KA )2 x2
−
the terms used in this type of study. I call this Type 2 prob- 2(1 + 1=K)
lem of uid ow. Both these types of problems started with a 2(1= + KA nA0 + KI nI 0 )(KR − KA )x
simple approximation of the complex real world. Note how −
(1 + 1=K)
completely di erent are these two branches of uid ow. It
is interesting to note that there are dozens upon dozens of (KR − KA )2 nA0 x
books on Type 1 problem, as well as courses in every aca- − : (1)
(1 + 1=K)2
demic institution in the world on this type of problem. How-
ever, there is not a single book in print today devoted to the This is a rather awkward complicated equation.
Type 2 problem even though it is important in the study of One of the two major problems with this approach is that
chemical reactors, in physiology, in oceanography, in deal- many possible mechanisms can and do ÿt any set of data. For
ing with the ow of ground waters, rivers, and oceans. How example, Hougen and Watson (1947b) show that 18 di erent
curious. mechanisms can be proposed by the simple reaction:
Also note that the Type 2 branch of the subject was devel-
oped as a $10 approximation of what is a very complicated C8 H16 + H2 = C8 H18 :
codimer
mathematical model, one which involves stochastic compu-
tational uid dynamics. Sad to say, not even with the most detailed experimental
program has anyone been able to choose among these mod-
els.
9. Models for chemical reactions Since these models extrapolate di erently, this means that
one cannot predict what to expect in new conditions so your
There are two broad classes of models for chemical reac- choice of this or that mechanism is arbitrary and may not
tions, the LHHW and the CRE. Let us discuss these. represent reality.
6. 4696 O. Levenspiel / Chemical Engineering Science 57 (2002) 4691 – 4696
The second problem with the LHHW models is that they So it is with the ÿlm model and the boundary layer idea.
completely ignore possible heat and mass transfer resis- Certainly, earlier works were reported in this area, for exam-
tances such as: ple: Newton (1701), Biot (1809), Peclet (1844), Reynolds
(1874), Stanton (1877), and Nernst (1904).
• ÿlm mass transfer from gas to particle surface, But Prandtl’s 1904 article (Prandtl, 1904) changed our
• pore di usion in the particle, thinking in engineering. He was our Columbus.
• ÿlm heat transfer, Let me give you a picture of what engineering was like
• nonisothermal particles. early in the century. Until 1912, ASME had only recorded
eight papers in all areas of heat transfer in the previous 32
Now the chemist deliberately chooses conditions where he years of its history, not one of which was on ÿlms, boundary
can study chemical kinetics free from physical resistances. layers or “h” (Layton & Leinhard, 1988). The very ÿrst
However, the chemical engineer, dealing with reactor de- book on engineering heat transfer was the well known 1933
sign, has to consider these contributions. volume by McAdams (1933). Thus, these concepts are all
relatively recent and all part of this century’s creations.
9.2. The CRE models May I end up by suggesting the following modeling strat-
egy: always start by trying the simplest model and then only
In 1956 a new approach was introduced, called chemical add complexity to the extent needed. This is the $10 ap-
reaction engineering (1958). This approach used a simple proach, or as Einstein said,
nonmechanistic based kinetic form (often nth order) com-
bined with heat and mass transfer e ects (Thiele modulus,
Prater–Weisz nonisothermal criteria). “Keep things as simple as possible, but not simpler”.
As an example, for the reaction leading to Eq. (1) the
CRE approach gives References
rA = k CA ;
Chemical Reaction Engineering (1958). The ÿrst symposium of the
where , the e ectiveness factor, depends on the nonisother- European federation of chemical engineers. Chemical Engineering
mal Thiele modulus. This relationship is based on values for Science, 8, 1–200.
Danckwerts, P. V. (1953). Chemical Engineering Science, 2, 1.
Denbigh, K. (1951). The thermodynamics of the steady state. Methuen’s
• the particle size, L; monographs on chemical subjects. London.
• the e ective di usion coe cient of gas in catalyst pores, Hougen, O. A., & Watson, K. M. (1947a). Chemical process principles,
D; Part III (pp. 929) (Eq. (b)). New York: Wiley.
• the thermal di usivity of the solid, k; Hougen, O. A., & Watson, K. M. (1947b). Chemical process principles,
Part III (pp. 943–958). New York: Wiley.
• the heat of reaction, Hr . Layton, E. T., & Leinhard, J. H. (Eds). (1988). History of heat transfer.
New York: ASME.
The CRE approach was found to be simpler and more gen- Lewis, W. K. (1916). Industrial and Engineering Chemistry, 8, 825.
eral, and so found favor and was widely accepted by the McAdams, W. H. (1933). Heat transfer. New York: McGraw-Hill.
profession. It is the class of model used today. Perry, J. H., & Green, D. W. (1984). Chemical engineers’ handbook (6th
ed) (pp. 11–14). New York: McGraw-Hill.
Prandtl, L. (1904). On uid motions with very small friction (in German).
Third International Mathematical Congress. Heidelberg (pp. 484 –
10. Creators of models 491).
Tietjens, O. G. (1934). Fundamentals of hydro- and aeromechanics
Who discovered America? The Egyptian reed boat ex- (p. 3). New York: Dover Publications.
plorers, the Mongol wanderers, Lief Ericsson and his Viking Vermeulen, T., et al. (1966). Chemical Engineering Progress, 62, 95.
bands or Christopher Columbus? The earlier discoveries von Karman, T. (1934). Journal of Aeronautical Science, 1, 1–20.
von Karman, T. (1954). Aerodynamics, topics in light of their historical
were isolated events which were not followed up on and development. Ithaca, NY: Cornell University Press.
were forgotten by history. But Columbus’ was di erent. It Whitman, W. G. (1923). Chemical and Metallurgical Engineering,
was used, it changed society’s thinking and action, so we 24, 147.
credit him with the discovery.