- Condensation occurs when a vapor is cooled and changes phase to a liquid. This happens in power plants, oil refineries, and desalination plants.
- Condensation can occur through either film condensation or dropwise condensation. Film condensation involves a liquid film forming on the surface, while dropwise condensation involves discrete liquid droplets.
- Dropwise condensation is more efficient with higher heat transfer rates, but is difficult to maintain as the droplet-promoting coating washes off over time. Most condensers are designed for the more conservative film condensation process.
Slides for the eLearning course Separation and purification processes in biorefineries (https://open-learn.xamk.fi) in IMPRESS project.
Section: Distillation
Subject: 1.1 Vapor Liquid Equilibrium
Shell Momentum Balances in heat transferUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process.
introduction of condensation, what is it types etc. horizontal condenser, vertical condenser, process aplications, all examples related to the process,
The Principles required to understand Distillation, Absorption, Stripping, Flashing, Gas Treating, Scrubbing and more!
Introduction:
This course covers all the theory required to understand the basic principles behind Unit Operations that are based on Mass Transfer. Most of these Unit Operations (Equipments) are used in Process Separation Technologies in the Industry.Common examples are Distillation, Absorption and Scrubbing.
This course is required for the following:
Flash Distillation
Gas Absorption & Stripping
Simple Distillation
Batch Distillation
Binary Distillation
Fractional Distillation
Scrubbers
Gas Treating
Sprayers / Spray Towers
Bubble Columns / Sparged Vessels
Agitation Vessels
Packed Towers
Tray Towers
We will cover:
Mass Transfer Basics
Diffusion, Convection
Flux & Fick's Law
The Concept of Equilibrium & Phases
Gibbs Phase Rule
Vapor Pressure
Equilibrium Vapor-Liquid Diagrams (T-xy, P-xy, XY)
Equilibrium Curves
Dew Point, Bubble Point
Volatility (Absolute & Relative)
K-Values
Ideal Cases vs. Real Cases
Henry's Law
Raoult's Law
Deviations of Ideal Cases (Positive and Negative)
Azeotropes
Solubility of Gases in Liquids
Interphase Mass Transfer and its Theories
Two Film Theory
Mass Transfer Coefficients (Overall vs Local)
Getting Vapor-Liquid and Solubility Data
Solved-Problem Approach:
All theory is backed with:
Exercises
Solved problems
Proposed problems
Homework
Case Studies
Individual Study
At the end of the course:
You will be able to understand the mass transfer concepts behind various Unit Operations involving Vapor - Liquid Interaction.
You will be able to apply this theory in further Unit Operations related to Mass Transfer Vapor - Liquid, which is one of the most common interactions found in the industry.
About your instructor:
I majored in Chemical Engineering with a minor in Industrial Engineering back in 2012.
I worked as a Process Design/Operation Engineer in INEOS Koln, mostly on the petrochemical area relating to naphtha treating. There I designed and modeled several processes relating separation of isopentane/pentane mixtures, catalytic reactors and separation processes such as distillation columns, flash separation devices and transportation of tank-trucks of product.
Mass transfer is the net movement of a component in a mixture from one location to another location where the component exists at a different concentration. Often, the transfer takes place between two phases across an interface. Thus, the absorption by a liquid of a solute from a gas involves mass transfer of the solute through the gas to the gas-liquid interface, across the interface, and into the liquid. Mass transfer models are used to describe processes such as the passage of a species through a gas to the outer surface of a porous adsorbent particle and into the pores of the adsorbent, where the species is adsorbed on the porous surface. Mass transfer is also the selective permeation through a nonporous polymeric material of a component of a gas mixture. Mass transfer is not the flow of a fluid through a pipe. However, mass transfer might be superimposed on that flow. Mass transfer is not the flow of solids on a conveyor belt.
Heat and Mass Transfer: Free Convection : Formulas and solved examples... Use of Heat and Mass transfer data book is necessary in order to obtain certain values.
This file contains slides on Transient Heat conduction: Part-II
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in the year 2010.
Contents: Semi-infinite solids with different BC’s - Problems - Product solution for multi-dimension systems -
Summary of Basic relations for transient conduction
Heat Transfer Applications
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes.
Introduction
Applications
References
conclusion
Slides for the eLearning course Separation and purification processes in biorefineries (https://open-learn.xamk.fi) in IMPRESS project.
Section: Distillation
Subject: 1.1 Vapor Liquid Equilibrium
Shell Momentum Balances in heat transferUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process.
introduction of condensation, what is it types etc. horizontal condenser, vertical condenser, process aplications, all examples related to the process,
The Principles required to understand Distillation, Absorption, Stripping, Flashing, Gas Treating, Scrubbing and more!
Introduction:
This course covers all the theory required to understand the basic principles behind Unit Operations that are based on Mass Transfer. Most of these Unit Operations (Equipments) are used in Process Separation Technologies in the Industry.Common examples are Distillation, Absorption and Scrubbing.
This course is required for the following:
Flash Distillation
Gas Absorption & Stripping
Simple Distillation
Batch Distillation
Binary Distillation
Fractional Distillation
Scrubbers
Gas Treating
Sprayers / Spray Towers
Bubble Columns / Sparged Vessels
Agitation Vessels
Packed Towers
Tray Towers
We will cover:
Mass Transfer Basics
Diffusion, Convection
Flux & Fick's Law
The Concept of Equilibrium & Phases
Gibbs Phase Rule
Vapor Pressure
Equilibrium Vapor-Liquid Diagrams (T-xy, P-xy, XY)
Equilibrium Curves
Dew Point, Bubble Point
Volatility (Absolute & Relative)
K-Values
Ideal Cases vs. Real Cases
Henry's Law
Raoult's Law
Deviations of Ideal Cases (Positive and Negative)
Azeotropes
Solubility of Gases in Liquids
Interphase Mass Transfer and its Theories
Two Film Theory
Mass Transfer Coefficients (Overall vs Local)
Getting Vapor-Liquid and Solubility Data
Solved-Problem Approach:
All theory is backed with:
Exercises
Solved problems
Proposed problems
Homework
Case Studies
Individual Study
At the end of the course:
You will be able to understand the mass transfer concepts behind various Unit Operations involving Vapor - Liquid Interaction.
You will be able to apply this theory in further Unit Operations related to Mass Transfer Vapor - Liquid, which is one of the most common interactions found in the industry.
About your instructor:
I majored in Chemical Engineering with a minor in Industrial Engineering back in 2012.
I worked as a Process Design/Operation Engineer in INEOS Koln, mostly on the petrochemical area relating to naphtha treating. There I designed and modeled several processes relating separation of isopentane/pentane mixtures, catalytic reactors and separation processes such as distillation columns, flash separation devices and transportation of tank-trucks of product.
Mass transfer is the net movement of a component in a mixture from one location to another location where the component exists at a different concentration. Often, the transfer takes place between two phases across an interface. Thus, the absorption by a liquid of a solute from a gas involves mass transfer of the solute through the gas to the gas-liquid interface, across the interface, and into the liquid. Mass transfer models are used to describe processes such as the passage of a species through a gas to the outer surface of a porous adsorbent particle and into the pores of the adsorbent, where the species is adsorbed on the porous surface. Mass transfer is also the selective permeation through a nonporous polymeric material of a component of a gas mixture. Mass transfer is not the flow of a fluid through a pipe. However, mass transfer might be superimposed on that flow. Mass transfer is not the flow of solids on a conveyor belt.
Heat and Mass Transfer: Free Convection : Formulas and solved examples... Use of Heat and Mass transfer data book is necessary in order to obtain certain values.
This file contains slides on Transient Heat conduction: Part-II
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in the year 2010.
Contents: Semi-infinite solids with different BC’s - Problems - Product solution for multi-dimension systems -
Summary of Basic relations for transient conduction
Heat Transfer Applications
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes.
Introduction
Applications
References
conclusion
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
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The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
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Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
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We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
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Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
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All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
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https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
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Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
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1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
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Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
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Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
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2. CONDENSERS
Power plant – water is boiled in boiler and condensed in condenser
Oil refinery - oil is evaporated in distillation column and condensed
into liquid fuels like gasoline and kerosene
Desalination plant – water vapor is produced by evaporation from
brine and condensed as pure water
Condensation – enthalpy of phase change to be removed by a coolant
Enthalpy of phase change is relatively large, for water (2.5 106 J/kg)
and associated heat transfer rates are also large
Heat transfer to phase interface – convective process – complicated by
an irregular surface – bubbles and drops
3. CONDENSATION HEAT TRANSFER
• Film condensation
• Dropwise condensation
FILM CONDENSATION
Condensate wets the surface and forms a liquid film
on the surface that slides down under the influence
80° C
of gravity.
Surface is blanketed by a liquid film of increasing
thickness, and this “liquid wall” between the solid
surface and the vapor serves as a resistance to heat
transfer
Liquid film
4. • Condensate film thickness are thin – heat transfer coefficients are large
• Example - steam at a saturation temperature of 305 K condenses on a 2 cm – O.D
tube with a wall temperature of 300 K
•Average film thickness - 50m (0.05 mm) and the average heat transfer coefficient –
11,700 W/m2.K
• If the condensate flow rate is small, the surface of the film will be smooth and the
flow laminar because
• Temperature difference is small
• Wall is short
• If the condensate flow rate is high, waves will form on the surface to give wavy
laminar flow
•If the condensate flow rate is yet higher, the flow becomes turbulent
5. DROPWISE CONDENSATION
80°C
Droplets
If the condensate does not wet the wall, because either it is dirty or it has been
treated with a non-wetting agent, droplets of condensate nucleate at small pits and
other imperfections on the surface, and they grow rapidly by direct vapor
condensation upon them and by coalescence
When the droplets become sufficiently large, they flow down the surface under the
action of gravity and expose bare metal in their tracks, where further droplet
nucleation is initiated
THIS IS CALLED DROPWISE CONDENSATION
6. Droplets slide down when they reach a certain size, clearing the surface and
exposing it to vapor.
There is no liquid film in this case to resist heat transfer.
Heat transfer rates that are more than 10 times larger than those associated with
film condensation can be achieved with dropwise condensation
Most of the heat transfer is through drops of less than 100m diameter
Thermal resistance of such drops is small; hence, heat transfer coefficients for
dropwise condensation are large; values of upto 30000 W/m2.K have been
measured.
Hence, dropwise condensation is preferred over filmwise condensation
Considerable efforts are put for non-wetting heat exchanger surfaces
If the surface is treated with non-wetting agent (stearic acid) to promote dropwise
condensation, the effect lasts only few days, until the promoter is washed off or
oxidised.
Continuous adding of the promoter to the vapour is expensive and contaminates the
condensate.
7. Bonding a polymer such as teflon to the surface is expensive and adds additional
thermal resistance
Gold plating is also expensive
Because of lack of sustainability of dropwise condensation, present day condensers
are designed based on filmwise condensation
Filmwise condensation – conservative estimate
8. LAMINAR FLOW CONDENSATION ON A VERTICAL WALL
Tsat g
Tw
Laminar
Vapor reservoir
Cold wall Wavy T
Tw x
T x
0
Tsat
Velocity Vapor
Turbulent Liquid Vapor Liquid
Tw
Temperature of the liquid-vapour interface is the saturation temperature that
corresponds to Tsat
Vapour in the descending jet is colder than the vapour reservoir and warmer than
the liquid in the film attached to the wall
9. LAMINAR FLOW CONDENSATION ON A VERTICAL WALL
Consider a vertical wall exposed to a saturated vapour at pressure p and saturation
temperature Tsat = Tsat(P).
The wall could be flat or could be the outside surface of a vertical tube
If the surface is maintained at a temperature Tw < Tsat, vapour will continuously
condense on the wall, and if the liquid phase wets the surface well, will flow
down the wall in a thin film
Provided the condensation rate is not too large, there will be no discernable waves
on the film surface, and the flow in the film will be laminar
• Fluid dynamics of the flow of a thin liquid film
• Heat transfer during the flow of a thin liquid film
10. 0
x
Laminar film of
condensate x
0
T
Tsat
u
Zero shear , 0
v y
u
Tw
v
x = δ(y)
Interface
T = Tsat
Tsat
Tw x
y H
y + dy From reservoir of
hg d
saturated vapor
d
T Tsat
H + dH
11. ASSUMPTIONS
• Laminar flow and constant properties are assumed for the liquid film
• Gas is assumed to be pure vapour and at a uniform temperature equal to Tsat. The
merit of this simplification is that it allows us to focus exclusively on the
flow of the liquid film and to neglect the movement of the nearest layers of
vapour
• Shear stress at the liquid-vapour interface is assumed to be negligible
• With no temperature gradient in the vapour, heat transfer to the liquid-vapour
interface can occur only by condensation at the interface and not by
conduction from the vapour
12. Steady state two dimensional incompressible flow
u u P 2u 2u
L u v
x L 2 2
y x x y
v v P 2v 2v
L u v
x L 2 2 L g
y y x y
x ~ ;y ~ L
u v , Hence , x momentum equation vanishes
Neglected, y<<x
v v dP v v
2 2
L u v
x L 2 2 L g
y dy x y
dP
pressure imposed from the inviscid potion v g Hydrostatic pressure
dy
v v 2v
L u v L v g L 2
x
y
x
13. v v 2v
L u v
x L v g L 2
y
x
SINKING EFFECT
FRICTION
INERTIA
Assuming inertia is negligible
2v
L 2 L v g 0
x
Boundary conditions x0 v0
v
x 0
x
Integrating v
L g L v x C1
x
x2
L v g L v C1 x C 2
2
x 0 v 0 C2 0
v v
x 0 L g L v x C1 g L v C1
x x
14. x2
L v g L v C1 x C 2
2
C2 0
C1 g L v
x2
L v g L v g L v x
2
g L v x2
v x
L 2
g L v 2
x 1 x 2
vx , y
L 2
Film thickness is unknown function of (y)
15. Local mass flow rate per unit width (y)
y
y Lv dx
0
g L v x 1 x 2
y L 2 dx
L 2
0
g L v 2 x 2 1 x 3
y L 3
L 2 6
0
L g L v 2
y
L 2 6
L g L v 2
y
L 3
L g L v 3
y
L 3
16. L g L v 3
y
L 3
b L g L v 3
m b y
L 3
B – width of the plate perpendicular to the plane of paper
Flow rate is proportional to the sinking effect - g(L-v)
Flow rate is inversely proportional to the liquid viscosity (Friction)
HEAT TRANSFER PROBLEM
Film velocity is low
Temperature gradients in the y-direction are negligible since both wall and film
surface are isothermal
d 2T
0
dx 2
dT
C1 ; T C1 x C 2
dx
17. T C1 x C 2
x T Tsat
x 0 T Tw C 2 Tw
Tsat Tw
T C1 x Tw Tsat C1 Tw C1
T Tsat Tw
x
Tw
This is a linear temperature profile similar to the conduction in a plane
wall
18. Heat flux into the wall = Heat flux across the film
Q k l Tsat Tw
hTsat Tw
dT
kl
dx w A
kl
dT k l Tsat Tw
h
dx w
k
l
Tsat Tw Tsat Tw
kl
h
Determination of film thickness
L g L v b L g L v 3
m b y
3
y ;
L 3
L 3
b L g L v 3 2 d Rate of condensation of
b y
dm
dy L 3 dy vapour over a vertical
distance dy
19. Rate of heat transfer from the vapour = Heat releasead as vapour is condensed
to the plate through the liquid film
dmh k b dy Tsat Tw
dQ fg l
dm k l b Tsat Tw
dy h fg
b L g L v 3 2 d k l b Tsat Tw
b y
dm
dy L 3 dy h fg
L g L v 3 2 d k T Tw
l sat
L 3 dy h fg
L k l Tsat Tw
3 d dy
L g L v h fg
4 L k l Tsat Tw
yC y 0, 0C 0
4 L g L v h fg
20. 4 L k l Tsat Tw
y
4 L g L v h fg
1
4 k 4 T T 4
y L l sat w
y
L g L v h fg
1
g L v h fg k l4 4
h L
kl
4 L k l Tsat Tw y
1 1
L g
L L v h fg k l3 4
g L L v h fg k l3 4 L 1
1
hL
dy 1
L
y 4 dy
L 0 4 L Tsat Tw y 4 L Tsat Tw
0
21. 1
g L L v h fg k l3 4
hL 0.943
4 T T L
L sat w
1
b L g L v 3 4 k 4 T T 4
m b y
y L l sat w
y
L 3 L g L v h fg
3
b L g L v 4 L k l4 Tsat Tw 4
m
y
3 L L g L v h fg
All liquid properties evaluated at
Tsat Tw
Tf
2
22. Effect of subcooling
Rohsenow refined
• avoided linear temperature profile
• Integral analysis of temperature distribution across the film
Temperature profile whose curvature increases with the degree of subcooling
Cp,L(Tsat-Tw)
h'fg h fg 0.68C p ,L Tsat Tw
Replace in previous equations h fg by h'fg
All liquid properties evaluated at Tsat Tw
Tf
2
hfg and v are evaluated at the saturation temperature Tsat
23. JAKOB NUMBER
Is a measure of degree of subcooling experienced by the liquid film
C p ,L Tsat Tw
Ja
h fg
hfg h fg 0.68C p ,L Tsat Tw
hfg h fg 1 0.68 Ja
24. Reynolds Number
L um Dh 4 Ac 4b
Re ; um ; Dh 4
L L P b
4 4
Re L
L L L
4
Re
L
L g L v 3
y
L 3
4 4 L g L v 3
Re
L 3 L L
4 L g 3
2
4 g 3
L v Re
3 L
2
3 L
2
25. 4 L g 3
2
L v Re
3 L
2
x L l
kl k
h hx L
3
hx L havg
4
3
2
kL
3
4 g L k L
2
4 g L
Re 2
3 L hx L 3 L 3
2
havg
4
1
1
g 3
havg 1.47 k l Re 3
2
l
26. Hydraulic diameter
D
P 2L
PL P D Ac 2 L
Ac L Ac D 4 Ac
Dh 4
4 Ac P
4A
Dh c 4 Dh 4
P P
27. Wavy Laminar flow over vertical plates
At Reynolds number greater than about 30, it is observed that waves form at the
liquid vapour interface although the flow in liquid film remains laminar. The flow in
this case is Wavy Laminar
Kutateladze (1963) recommended the following relation for wavy laminar
condensation over vertical plates
1
g
Re k l 3
hvert ,wavy
1.08 Re 1.22 2
5.2 l
30 Re 1800 , v l
0.82
1
3.70 Lk l Tsat Tw g 3
Re vert ,wavy 4.81
l hfg 2
l
28. Turbulent flow over vertical plates (Re > 1800)
Labuntsov proposed the following relation
1
Re k l g 3
hvert ,turbulent
8750 58 Pr 0.5 Re 0.75 253 l2
Film condensation on an inclined Plates
hinclined hvert cos Condensate
1 1
1 2
hL l2 3
kl g
Re L0.44
3
5.82 10 6 Re L.88 PrL
0
29. Non-dimensionalised heat transfer coefficients for the wave-free laminar and
turbulent flow of condensate on vertical plates
1
Pr = 10
5
3
2
h( vl2 g )1 3
kl
1
Wave-free Wavy Turbulent
laminar laminar
0.1
10 30 100 1000 1800 10,000
Re
30. Problem: Saturated steam at atmospheric pressure condenses on a 2 m high and 3 m
wide vertical plate that is maintained at 80C by circulating cooling water through
the other side. Determine (a) the rate of heat transfer by condensation to the plate
(b) the rate at which the condensate drips off the plate at the bottom
Solution: saturated steam at 1 atm condenses on a vertical plate. The rats of heat
transfer and condensation are to be determined
Assumptions: 1. steady operating conditions exist 2. The plate is isothermal. 3. The
condensate flow is wavy laminar over the entire plate (will be verified). 4. The
density of vapour is much smaller than the density of the liquid v<<l
Properties: The properties of water at the saturation temperature of 100C are hfg =
2257 103 J/g and v = 0.6 kg/m3. The properties of liquid water at the film
temperature 90C are
T Tw 100 80
T f sat 90
2 2 hfg h fg 0.68C p ,L Tsat Tw
l 965 .3 kg / m 3
3
l 0.315 10 Pa .s hfg 2257 103 0.68 4206 100 80
l l 0.326 10 6 m 2 / s
l hfg 2314103 J / kg
C pl 4206 J / kg .K
k l 0.675 W / m .K
Pr 1.9628
31. 1 1
g 9.81 965 .3 965 .32314 1000
v h fg k l3 4 0.675 3 4
L L
hL 0.943 0.943
4 T T L 4 0.315 10 3 100 80 4
L sat w
W
hL 2656 .2
m2K
Q hL As Tsat Tw 2562 .2 2 3 100 80 307464 W
Q mh 307464 m 2314 10 3 m 0.1329 kg / s
sf
4 4 m 4 0.1329
Re 562.5
L L b 0.315 10 3 3
32. 1 1
1 2
hL l2 3
kl g
Re L0.44
3
5.82 10 6 Re L.88 PrL
0
1 1
hL 0.326 10
6 2 3
562 .5 0.44
1 2
5.82 10 6 562 .50.88 1.9628 3
0.675
9.81
W
hL 7691 .4
m2K
Q hL As Tsat Tw 7691.4 2 3 100 80 2307420 W
Q mhsf 2307420 m 2314 103 m 0.9972 kg / s
4 4 m 4 0.9972
Re b 0.315 103 3 4221
L L
This confirms that condensation is in turbulent region
Comments: This Reynolds number confirms that condensation is in Wavy laminar
domain