This file contains slides on THERMAL RADIATION-III: Radiation energy exchange between gray surfaces.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Radiation heat exchange between gray surfaces - electrical network method – two zone enclosures – Problems - three zone enclosures – Problems - radiation shielding – Problems - radiation error in temperature measurement – Problems
It is basic information about what is critical thickness and why we should we know this. Then there is critical thickness formula for cylindrical pipe and spherical shell.
Heat transfer from extended surfaces (or fins)tmuliya
This file contains slides on Heat Transfer from Extended Surfaces (FINS). The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
Contents: Governing differential eqn – different boundary conditions – temp. distribution and heat transfer rate for: infinitely long fin, fin with insulated end, fin losing heat from its end, and fin with specified temperatures at its ends – performance of fins - ‘fin efficiency’ and ‘fin effectiveness’ – fins of non-uniform cross-section- thermal resistance and total surface efficiency of fins – estimation of error in temperature measurement - Problems
It is basic information about what is critical thickness and why we should we know this. Then there is critical thickness formula for cylindrical pipe and spherical shell.
Heat transfer from extended surfaces (or fins)tmuliya
This file contains slides on Heat Transfer from Extended Surfaces (FINS). The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
Contents: Governing differential eqn – different boundary conditions – temp. distribution and heat transfer rate for: infinitely long fin, fin with insulated end, fin losing heat from its end, and fin with specified temperatures at its ends – performance of fins - ‘fin efficiency’ and ‘fin effectiveness’ – fins of non-uniform cross-section- thermal resistance and total surface efficiency of fins – estimation of error in temperature measurement - Problems
Heat transfer due to emission of electromagnetic waves is known as thermal radiation. Heat transfer through radiation takes place in form of electromagnetic waves mainly in the infrared region. Radiation emitted by a body is a consequence of thermal agitation of its composing molecules. The underlying mechanisms and the concepts involved are discussed in the ppt
This file contains slides on Transient Heat conduction: Part-I
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010. Contents: Lumped system analysis – criteria for lumped system analysis – Biot and Fourier Numbers – Response time of a thermocouple - One-dimensional transient conduction in large plane walls, long cylinders and spheres when Bi > 0.1 – one-term approximation - Heisler and Grober charts- Problems
This chapter contains:-.
Analytical Methods of two dimensional steady state heat conduction
Finite difference Method application on two dimensional steady state heat conduction.
Finite difference method on irregular shape of a system
Thermal Radiation-II- View factors and Radiation energy exchange between blac...tmuliya
This file contains slides on THERMAL RADIATION-II: View factors and Radiation energy exchange between black bodies.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: View factor – general relations – radiation energy exchange between black bodies – properties of view factor and view factor algebra – view factor formulas and graphs – Problems
The aim of this experiment is to measurement linear thermal along z direction conductivity and to investigate and verify Fourier’s Law for linear heat conduction along z direction and we proved that K is inversely proportional with ΔT, and we have many errors in our experiment that made the result not clear.
Thermal Radiation-I - Basic properties and Lawstmuliya
This file contains slides on RADIATION-I: Basic Properties and Laws.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Introduction – Applications – Electromagnetic spectrum – Properties and definitions – Laws of black body radiation – Planck’s Law – Wein’s displacement law – Stefan Boltzmann Law – Radiation from a wave band – Emissivity – Kirchoff’s Law- Problems
Heat transfer due to emission of electromagnetic waves is known as thermal radiation. Heat transfer through radiation takes place in form of electromagnetic waves mainly in the infrared region. Radiation emitted by a body is a consequence of thermal agitation of its composing molecules. The underlying mechanisms and the concepts involved are discussed in the ppt
This file contains slides on Transient Heat conduction: Part-I
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010. Contents: Lumped system analysis – criteria for lumped system analysis – Biot and Fourier Numbers – Response time of a thermocouple - One-dimensional transient conduction in large plane walls, long cylinders and spheres when Bi > 0.1 – one-term approximation - Heisler and Grober charts- Problems
This chapter contains:-.
Analytical Methods of two dimensional steady state heat conduction
Finite difference Method application on two dimensional steady state heat conduction.
Finite difference method on irregular shape of a system
Thermal Radiation-II- View factors and Radiation energy exchange between blac...tmuliya
This file contains slides on THERMAL RADIATION-II: View factors and Radiation energy exchange between black bodies.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: View factor – general relations – radiation energy exchange between black bodies – properties of view factor and view factor algebra – view factor formulas and graphs – Problems
The aim of this experiment is to measurement linear thermal along z direction conductivity and to investigate and verify Fourier’s Law for linear heat conduction along z direction and we proved that K is inversely proportional with ΔT, and we have many errors in our experiment that made the result not clear.
Thermal Radiation-I - Basic properties and Lawstmuliya
This file contains slides on RADIATION-I: Basic Properties and Laws.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Introduction – Applications – Electromagnetic spectrum – Properties and definitions – Laws of black body radiation – Planck’s Law – Wein’s displacement law – Stefan Boltzmann Law – Radiation from a wave band – Emissivity – Kirchoff’s Law- Problems
This file contains slides on Steady State Heat Conduction in Multiple Dimensions.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: 2-D conduction - Various methods of solution – Analytical - Graphical - Analogical – Numerical – Shape factors for 2-D conduction - Problems
One dim, steady-state, heat conduction_with_heat_generationtmuliya
This file contains slides on One-dimensional, steady-state heat conduction with heat generation.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
It is hoped that these Slides will be useful to teachers, students, researchers and professionals working in this field.
Mathcad Functions for Forced convection heat transfer calculationstmuliya
This file contains notes on Mathcad Functions for Forced convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India. It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents: Forced convection formulas – boundary layer, flow over flat plates, across cylinders, spheres and tube banks
Boiling and Condensation heat transfer -- EES Functions and Procedurestmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Boiling and Condensation heat transfer. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
Contents: Summary of formulas used -
EES Functions/Procedures for boiling: Nucleate boiling heat flux for any geometry - critical heat flux for large horizontal surface, horizontal cylinder and sphere - Film boiling for horizontal cylinder, sphere and horizontal surface – Problems.
EES Functions/Procedures for condensation of: steam on vertical surface – any fluid on a vertical surface – steam on vertical cylinder – any fluid on vertical cylinder – steam on horizontal cylinder – any fluid on horizontal cylinder – steam on a horizontal tube bank – any fluid on horizontal tube bank – any fluid on a sphere – any fluid inside a horizontal cylinder - Problems.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
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
This file contains slides on One-dimensional, steady state heat conduction without heat generation. The slides were prepared while teaching Heat Transfer course to the M.Tech. students.
Topics covered: Plane slab - composite slabs – contact resistance – cylindrical Systems – composite cylinders - spherical systems – composite spheres - critical thickness of insulation – optimum thickness – systems with variable thermal conductivity
This file contains slides on NUMERICAL METHODS IN STEADY STATE 1D and 2D HEAT CONDUCTION – Part-I.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students.
Contents: Why Numerical methods? – Advantages – Finite difference formulation from differential eqns – 1D steady state conduction in cartesian coordinates – formulation by energy balance method – different BC’s – Problems
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...tmuliya
This file contains Introduction to Heat Transfer and Fundamental laws governing heat transfer.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
Numerical Simulations on Flux Tube Tectonic Model for Solar Coronal HeatingRSIS International
The sun is a G-type main sequence star. Corona is an
aura of Plasma that Surrounds the Sun and other Stars. The
heating of solar Corona is one of most important problem in
Astrophysics. There are several mechanism of Coronal heating.
In this paper we discuss Numerical Simulation on Flux tube
Tectonic Model For Solar Coronal Heating .
Thermoelastic Damping of Vibrations in a Transversely Isotropic Hollow Cylinder IDES Editor
The purpose of the paper is to analyze the damping of three-dimensional free vibrations in a transversely isotropic, thermoelastic hollow cylinder, which is initially undeformed
and kept at uniform temperature. The surfaces of the cylinder are subjected to stress free and thermally insulated boundary conditions. The displacement potential functions have been introduced for decoupling the purely shear and longitudinal motions in the equations of motion and heat equation. The purely transverse wave gets decoupled from rest of the motion and is not affected by thermal field. By using the method of separation of variables, the system of governing partial differential equations is reduced to four second order coupled ordinary differential equation in radial coordinate. The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. In order to illustrate the analytic results, the numerical solution of various relations and equations are carried out to compute lowest frequency and thermoelastic damping factor with M ATLAB software programming for zinc material. The computer simulated results have been presented graphically.
46 optimization paper id 0017 edit septianIAESIJEECS
This paper is a comparisation study between an experimental data and Matlab simulation of output PV characteristic affected by the orientation and the tilt angle of a photovoltaic solar module with inclined plane and by the dimension of the panel. The PV panel was rotated towards the east, south and west and positioned for the angles 0°, 30°, 45°, 60° and 90°. In this position, the values of current, voltage and power are measured. In the other side, using the mathematical model to calculate the solar radiation incident on an inclined surface as a function of the tilt angle was developed in MATLAB/SIMULINK model. The optimum angles were determined as positions in which maximum values of solar irradiation and maximum power were registered to characterize the P-V and V-I photovoltaic panel.
I am Baddie K. I am a Magnetic Materials Assignment Expert at eduassignmenthelp.com. I hold a Masters's Degree in Electro-Magnetics, from The University of Malaya, Malaysia. I have been helping students with their assignments for the past 12 years. I solve assignments related to Magnetic Materials.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com. You can also call on +1 678 648 4277 for any assistance with Magnetic Materials Assignments.
Modeling and Simulation of Thermal Stress in Electrical Discharge Machining ...Mohan Kumar Pradhan
In this research the effect of input variables namely: discharge current, pulse
duration on thermal stresses has been investigated. A finite element modelling for
the EDM process and the effect of a single-pulse discharge has been presented and
results concerning the temperature distribution, the thermal stresses of AISI D2 steel
machined by EDM have been illustrated. It was found that the compressive thermal
stresses were developed beneath the crater and the tensile stresses were occur away
from the axis of symmetry however, the thermal stresses affects to a larger depth with
increasing pulse energy.
Similar to Thermal Radiation - III- Radn. energy exchange between gray surfaces (20)
EES Procedures and Functions for Heat exchanger calculationstmuliya
This file contains notes on the important topic of EES Functions for Heat Exchanger calculations. Some solved problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Overall heat transfer coefficient
• Importance of ‘Fouling factor’
• Analysis of heat exchangers by ‘Logarithmic Mean Temp Difference (LMTD)’ method
• Correction factors for Cross-flow and Shell & Tube heat exchangers
• Analysis of heat exchangers by ‘No. of Transfer Units (NTU)– Effectiveness (ε)’ method
• Compact heat exchangers
EES Functions and Procedures for Natural convection heat transfertmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Natural (or, free) convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Natural convection formulas - Tables
• Natural convection from Vertical plates & cylinders, horizontal plates, cylinders and spheres, from enclosed spaces, rotating disks and spheres, and from finned surfaces
• Combined Natural and forced convection
EES Functions and Procedures for Forced convection heat transfertmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Forced convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Forced convection – Tables of formulas
• Boundary layer, flow over flat plates, across cylinders, spheres and tube banks –
• Flow inside tubes and ducts
Mathcad Functions for Conduction heat transfer calculationstmuliya
This file contains notes on Mathcad Functions for Conduction heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Mathcad Functions for Natural (or free) convection heat transfer calculationstmuliya
This file contains notes on Mathcad Functions for Natural (or, free) convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents: Free convection from vertical plates and cylinders, horizontal plates, cylinders and spheres, enclosed spaces, rotating cylinders, disks and spheres. Finned surfaces.
Combined Natural and Forced convection.
Mathcad functions for fluid properties - for convection heat transfer calcu...tmuliya
This file contains slides on Mathcad Functions for Fluid properties--- Useful in Convection heat transfer calculations.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
It is hoped that these Slides will be useful to teachers, students, researchers and professionals working in this field.
Contents: Mathcad Functions for properties of:
Air, Ammonia, Ethyl alcohol, Ethylene glycol, Un-used engine oil, Glycerin, Lead, and Mercury
Mathcad Functions for Boiling heat transfertmuliya
This file contains slides on Mathcad Functions for Boiling heat transfer.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Functions for properties of sat. water and steam- Nucleate boiling for water – heat flux – crit. heat flux for: flat surface, horizl. cylinder – min. heat flux for horizl. surface – Film boiling for horizl. surface , very large dia tube, horizl. cylinder, sphere - Nucleate boiling of water for submerged horizl. and vertical surfaces
Mathcad Functions for Condensation heat transfertmuliya
This file contains slides on Mathcad Functions for Condensation heat transfer.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Functions for properties of sat. water and steam- Film condensation of steam on vertical plate and inclined plate – on vertical cylinder and horizontal cylinder – on horizontal cylinders in vertical tier - on a sphere – inside horizontal tubes – on copper surfaces – Mathcad Functions for properties of sat. Ammonia – Film condensation of Ammonia on vertical plate, horizontal cylinder and tube banks, and inside horizontal tubes
Numerical methods in Transient-heat-conductiontmuliya
This file contains slides on Numerical methods in Transient heat conduction.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Finite difference eqns. by energy balance – Explicit and Implicit methods – 1-D transient conduction in a plane wall – stability criterion – Problems - 2-D transient heat conduction – Finite diff. eqns. for interior nodes – Explicit and Implicit methods - stability criterion – difference eqns for different boundary conditions – Accuracy considerations – discretization error and round–off error - Problems
NUMERICAL METHODS IN STEADY STATE, 1D and 2D HEAT CONDUCTION- Part-IItmuliya
This file contains slides on NUMERICAL METHODS IN STEADY STATE 1D and 2D HEAT CONDUCTION – Part-II.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
Contents: Methods of solving a system of simultaneous, algebraic equations - 1D steady state conduction in cylindrical and spherical systems - 2D steady state conduction in cartesian coordinates - Problems
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Vaccine management system project report documentation..pdf
Thermal Radiation - III- Radn. energy exchange between gray surfaces
1. Lectures on Heat Transfer –
THERMAL RADIATION-III:
Radiation energy exchange
between gray surfaces
by
Dr. M. ThirumaleshwarDr. M. Thirumaleshwar
formerly:
Professor, Dept. of Mechanical Engineering,
St. Joseph Engg. College, Vamanjoor,
Mangalore,
India
2. Preface:
• This file contains slides on THERMAL
RADIATION-III: Radiation energy exchange
between gray surfaces.
• The slides were prepared while teaching
Heat Transfer course to the M.Tech.Heat Transfer course to the M.Tech.
students in Mechanical Engineering Dept.
of St. Joseph Engineering College,
Vamanjoor, Mangalore, India, during Sept.
– Dec. 2010.
Aug. 2016 2MT/SJEC/M.Tech.
3. • It is hoped that these Slides will be useful
to teachers, students, researchers and
professionals working in this field.
• For students, it should be particularly
useful to study, quickly review the subject,useful to study, quickly review the subject,
and to prepare for the examinations.
•
Aug. 2016 3MT/SJEC/M.Tech.
4. References:
• 1. M. Thirumaleshwar: Fundamentals of Heat &
Mass Transfer, Pearson Edu., 2006
• https://books.google.co.in/books?id=b2238B-
AsqcC&printsec=frontcover&source=gbs_atb#v=onepage&q&f=false
• 2. Cengel Y. A. Heat Transfer: A Practical
Approach, 2nd Ed. McGraw Hill Co., 2003
Aug. 2016 MT/SJEC/M.Tech. 4
Approach, 2nd Ed. McGraw Hill Co., 2003
• 3. Cengel, Y. A. and Ghajar, A. J., Heat and
Mass Transfer - Fundamentals and Applications,
5th Ed., McGraw-Hill, New York, NY, 2014.
5. References… contd.
• 4. Incropera , Dewitt, Bergman, Lavine:
Fundamentals of Heat and Mass Transfer, 6th
Ed., Wiley Intl.
• 5. M. Thirumaleshwar: Software Solutions to• 5. M. Thirumaleshwar: Software Solutions to
Problems on Heat Transfer – Radiation Heat
Transfer-Part-II, Bookboon, 2013
• http://bookboon.com/en/software-solutions-heat-transfer-
radiation-ii-ebook
Aug. 2016 MT/SJEC/M.Tech. 5
6. Thermal Radiation – III:
Radiation energy exchange between gray
surfaces :
Outline…
Radiation heat exchange between gray
surfaces - electrical network method – two
Aug. 2016 MT/SJEC/M.Tech. 6
surfaces - electrical network method – two
zone enclosures – Problems - three zone
enclosures – Problems - radiation
shielding – Problems - radiation error in
temperature measurement – Problems
7. Radiation energy exchange
between gray surfaces:
• Following assumptions are made to simplify the
solution:
• All the surfaces of the enclosure are opaque (τ = 0),
diffuse and gray
• Radiative properties such as ρ, ε and α are uniform
and independent of direction and frequency
Aug. 2016 MT/SJEC/M.Tech. 7
• Radiative properties such as ρ, ε and α are uniform
and independent of direction and frequency
• Irradiation and heat flux leaving each surface are
uniform over the surface
• Each surface of the enclosure is isothermal, and
• The enclosure is filled with a non-participating medium
(such as vacuum or air)
8. The electrical network method:
• We shall discuss the ‘electrical network
method’, since it is simple to apply and
gives a physical ‘feel’ of the problem.
• This method, introduced by Oppenheim in
the 1950’s, is simple and direct; it
emphasizes on the physics of the problem,
Aug. 2016 MT/SJEC/M.Tech. 8
emphasizes on the physics of the problem,
and is easy to apply.
• Before we introduce this method, let us
define two new quantities, viz. irradiation
and radiosity: (See Fig. 13.25)
9. Aug. 2016 MT/SJEC/M.Tech. 9
• Irradiation, (G): is the total radiation incident upon a
surface per unit time, per unit area (W/m2).
• Radiosity, (J): is the total radiation leaving a surface,
with no regard for its origin (i.e., reflected plus emitted
from the surface) per unit time, per unit area (W/m2).
10. • Now, from Fig.(13.25), it is clear that total
radiation leaving the surface (i.e.
Radiosity, J) is:
• For a gray, opaque (τ = 0) surface, we
have:
J ρ G. ε E b
.
Aug. 2016 MT/SJEC/M.Tech. 10
have:
• Therefore,
ρ 1 α( ) 1 ε( ) ...from Kirchoff's law
J 1 ε( ) G. ε E b
.
or, G
J ε E b
.
1 ε( )
11. • Now, net rate of radiation energy transfer
from the surface is given by: (rate of
radiation energy leaving the surface minus
the rate of radiation energy incident on the
surface), i.e. Q
A
J G
Q J ε E b
.
Aug. 2016 MT/SJEC/M.Tech. 11
• Therefore,
i.e.
Q
A
J
J ε E b
.
1 ε
Q
ε A.
1 ε
E b J.
i.e. Q
E b J
1 ε( )
A ε.
W.....(13.48)
12. • By analogy with Ohm’s law, we can think of Q in
eqn.(13.48) as a current flowing through a
potential difference (Eb-J), and the factor (1-
ε)/A.ε as the resistance.
• Now, this resistance is the resistance to the flow
of radiant heat due to the nature of the surface
and is known as ‘surface resistance (R)’.
Aug. 2016 MT/SJEC/M.Tech. 12
and is known as ‘surface resistance (R)’.
• i.e.
• Surface resistance for a surface ‘i’ is shown
schematically in Fig. (13.26,a).
R
1 ε( )
A ε.
....surface resistance
13. • For a black body emissivity ε = 1;
so, the surface resistance is zero,
and
• Also, many surfaces in numerous
applications are adiabatic, i.e. well
insulated, and net heat transfer
J i E bi ...for a black body....(13.49)
Aug. 2016 MT/SJEC/M.Tech. 13
insulated, and net heat transfer
through such a surface is zero,
since in steady state, all the heat
incident on such a surface is re-
radiated. These are known as
re-radiating surfaces.
14. • Walls of a furnace is the familiar example
of a re-radiating surface. Obviously, for a
re-radiating surface, Qi = 0, and from eqn.
(13.48) we get:
• Note that the temperature of a re-radiating
J i E bi σ T i
4. ....for a re-radiating surface....(13.50)
Aug. 2016 MT/SJEC/M.Tech. 14
• Note that the temperature of a re-radiating
surface can be calculated from the above
eqn; further, note that this temperature is
independent of the emissivity of the
surface.
15. • Again, consider two diffuse, gray and
opaque surfaces i and j, maintained at
uniform temperatures Ti and Tj,
exchanging heat with each other.
• Then, remembering the definitions of
radiosity and view factor, we can write for
the radiation leaving surface ‘i’ that strikes
Aug. 2016 MT/SJEC/M.Tech. 15
the radiation leaving surface ‘i’ that strikes
surface ‘j’:
• Similarly, for surface j, we have:
Q i A i F ij
. J i
.
Q j A j F ji
. J j
.
16. • Therefore, net heat interchange between surfaces i and j
is:
Q ij A i F ij
. J i
. A j F ji
. J j
.
i.e. Q ij A i F ij
. J i J j
. W..(13.51)..since A i F ij
. A j F ji
. ...by reciprocity.
i.e. Q ij
J i J j
1
W....(13.52)
Aug. 2016 MT/SJEC/M.Tech. 16
• Again, by analogy with Ohm’s law, we can write eqn.
(13.52) as:
1
A i F ij
.
Q ij
J i J j
R ij
W
where, R ij
1
A i F ij
.
...(13.53)
17. • Rij is known as ‘space
resistance’ and it represents
the resistance to radiative heat
flow between the radiosity
potentials of the two surfaces,
due to their relative orientation
and spacing.
• Space resistance is illustrated
Aug. 2016 MT/SJEC/M.Tech. 17
• Space resistance is illustrated
in Fig. (13.26,b).
• Note from eqn. (13.52) that if
Ji > Jj, net heat transfer is from
surface i to surface j;
otherwise, the net heat transfer
is from surface j to surface i.
18. • Thus, for each diffuse, gray, opaque
surface, in radiant heat exchange with
other surfaces of an enclosure, there are
two resistances, viz. the surface
resistance, Ri = (1- εi)/(Ai.εi), and a space
resistance, Rij = 1/(Ai.Fij).
Aug. 2016 MT/SJEC/M.Tech. 18
• For a N surface enclosure, net heat
transfer from surface ‘i’ should be equal to
the sum of net heat transfers from that
surface to the remaining surfaces. i.e.
19. • This situation is shown in Fig. (13.27).
Q i
1
N
j
Q ij
= 1
N
j
A i F ij
. J i J j
.
= 1
N
j
J i J j
R ij=
...W....(13.54)
i.e.
E bi J i
R i 1
N
j
J i J j
R ij=
W...(13.55)
J
Aug. 2016 MT/SJEC/M.Tech. 19
Fig. 13.27 Radiation heat transfer from surface i
to other surfaces in a N-surface enclosure
Surface i
JiEbi
Qi
Ri
J1
J2
JN-1
JN
Ri1
Ri2
Ri(N-1)
RiN
20. • As can be seen from the above fig., rate of
radiation ‘current’ flow to surface ‘i’ through its
surface resistance must be equal to the sum of
all the radiation current flows from surface ‘i’ to
all other surfaces through the respective space
resistances.
• In general, there two types of radiation
problems:
Aug. 2016 MT/SJEC/M.Tech. 20
problems:
• first (and most common), when the surface
temperature Ti, and therefore, the emissive
power Ebi is known;
• and, the second type is when the net radiation
heat transfer at the surface i is known.
21. • Eqn. (13.55) is useful in solving the first
type of problems, i.e. when the surface
temperature is known; instead, if the net
heat transfer rate at the surface is the
known quantity, eqn. (13.52) is the
applicable equation.
Aug. 2016 MT/SJEC/M.Tech. 21
• Essentially, the problem is to solve for the
radiosities J1, J2,….Jn.
• Electrical network method is convenient to
use if the number of surfaces in an
enclosure is limited to about five.
22. • If the number of surfaces is more than five, the
direct approach is to apply eqn. (13.55) for each
surface whose temperature is known, and eqn.
(13.52) for each surface at which the net heat
transfer rate is known, and solve the resulting
set of N linear, algebraic equations for the N
unknowns, viz. J1, J2,…Jn by standard
Aug. 2016 MT/SJEC/M.Tech. 22
mathematical methods.
• Once the radiosities are known, eqn. (13.48)
may be applied to determine either the heat
transfer rate or the temperature, as the case
may be.
23. Radiation heat exchange in two-
zone enclosures:
• Two-zone enclosure- simply means that the two
surfaces, together, make up the enclosure and
‘see’ only themselves and nothing else.
• Many, practically important geometries may be
classified as two-zone enclosures, eg. a small
body enclosed by a large body, a pipe passing
Aug. 2016 MT/SJEC/M.Tech. 23
classified as two-zone enclosures, eg. a small
body enclosed by a large body, a pipe passing
through a large room, concentric spheres,
concentric, long cylinders , long, parallel plane
surfaces, etc.
• Fig. (13.28) shows a schematic of a typical two-
zone enclosure and the associated radiation (or,
thermal) network.
24. • Surfaces 1 and 2 forming the
enclosure are diffuse, gray and
opaque.
• Let their emissivities,
temperatures and areas be (ε1,
T1, A1) and (ε2, T2, A2)
respectively.
• The radiation network is shown
in Fig. 13.28.
Aug. 2016 MT/SJEC/M.Tech. 24
in Fig. 13.28.
• Each surface has one surface
resistance associated with it and
there is one space resistance
between the two radiosity
potentials, and all the
resistances are in series, as
shown.
25. • The ‘heat current’ (Q12) in this circuit is calculated by
dividing the ‘total potential’ (Eb1 – Eb2) by the ‘total
resistance’ (R1 + R12 +R2). So, we write:
Q 12 Q 1 Q 2
E b1 E b2
R 1 R 12 R 2
i.e. Q 12
E b1 E b2
1 ε 1 1 1 ε 2
Aug. 2016 MT/SJEC/M.Tech. 25
A 1 ε 1
. A 1 F 12
. A 2 ε 2
.
i.e. Q 12
σ T 1
4
T 2
4.
1 ε 1
A 1 ε 1
.
1
A 1 F 12
.
1 ε 2
A 2 ε 2
.
W......(13.56)
Eqn. (13.56) is an important equation, which gives net rate of heat
transfer between two gray, diffuse, opaque surfaces which form an
enclosure, i.e. which ‘see’ only each other and nothing else.
26. • Let us consider a few special cases of
two-surface enclosure:
• Case (i): Radiant heat exchange
between two black surfaces:
• For a black body, ε = 1, and J = Eb, as
explained earlier. i.e. surface resistance
[= (1 - ε)/(A.ε)] of a black body is zero.
Aug. 2016 MT/SJEC/M.Tech. 26
[= (1 - ε)/(A.ε)] of a black body is zero.
Then, the radiation network will consist of
only a space resistance between the two
radiosity potentials, as shown in Fig.
(13.29):
27. • Then, from eqn. (13.56), we get:
Fig. 13.29 Radiation network for two black
surfaces forming an enclosure
Eb1= J1
R12
= 1/(A1
.F12
)
Q12
Eb2= J2
Aug. 2016 MT/SJEC/M.Tech. 27
Q 12
σ T 1
4
T 2
4.
1
A 1 F 12
.
i.e. Q 12 A 1 F 12
. σ. T 1
4
T 2
4. W....for two black surfaces forming an
enclosure....(13.57)
28. • Next, we shall consider four cases of practical interest
where the view factor between the inner surface 1 and
the outer surface 2 (i.e. F12) is equal to 1:
• Case (ii): Radiant heat exchange for a
small object in a large cavity:
• See Fig. (13.30,a). A practical example of a small object
in a large cavity is the case of a steam pipe passing
through a large plant room.
Aug. 2016 MT/SJEC/M.Tech. 28
through a large plant room.
• For this case, we have:
A 1
A 2
0
and, F 12 1
29. • And, eqn.(13.56) becomes:
• Case (iii): Radiant heat exchange
between infinitely large parallel plates:
• See Fig. (13.30,b). In this case, A1 = A2 =
A, say, and F12 = 1.
Q 12 A 1 σ. ε 1
. T 1
4
T 2
4. ....for small object in a large cavity.....(13.58)
Aug. 2016 MT/SJEC/M.Tech. 29
A, say, and F12 = 1.
• Then, eqn. (13.56) becomes:
Q 12
A σ. T 1
4
T 2
4.
1
ε 1
1
ε 2
1
....for infinitely large parallel plates.....(13.59)
31. • Case (iv): Radiant heat exchange between infinitely
long concentric cylinders:
• See Fig. (13.30,c). In this case:
• Then, eqn. (13.56) becomes:
F 12 1
Q 12
A 1 σ. T 1
4
T 2
4.
1
ε 1
A 1
A 2
1
ε 2
1.
....for infinitely long concentric cylinders.....(13.60)
Aug. 2016 MT/SJEC/M.Tech. 31
• Remember that A1 refers to the inner (or enclosed) surface.
• Eqn. (13.60) is known as ‘Christiansen’s equation’.
where
A 1
A 2
r 1
r 2
32. • Case (v): Radiant heat exchange between
concentric spheres:
• See Fig. (13.30,d). In this case:
• Then, eqn. (13.56) becomes:
F 12 1
Q 12
A 1 σ. T 1
4
T 2
4.
1
ε 1
A 1
A 2
1
ε 2
1.
....for concentric spheres.....(13.61)
Aug. 2016 MT/SJEC/M.Tech. 32
• Remember, again, that A1 refers to the inner (or
enclosed) surface.
1 2 2
where
A 1
A 2
r 1
r 2
2
33. Problems on two-surface enclosures:
• Example 13.19 (M.U. 1991): A long pipe, 50
mm in diameter, passes through a room and is
exposed to air at 20 deg. C. Pipe surface
temperature is 93 deg.C. Emissivity of the
surface is 0.6. Calculate the net radiant heat losssurface is 0.6. Calculate the net radiant heat loss
per metre length of pipe.
• Solution:
• The pipe is enclosed by the room; so, it is two-surface enclosure
problem. Further, area of the pipe is very small, compared to the
area of the room. Therefore, this is a case of a small object
surrounded by a large area, and we have:
Aug. 2016 33MT/SJEC/M.Tech.
43. Radiation heat exchange in three
zone enclosures:
• Fig. (13.32,a) shows an enclosure made of three
opaque, diffuse, gray surfaces.
• Let the surfaces A1, A2, A3 be maintained at uniform
temperatures of T1, T2 and T3 respectively. Also, let the
emissivities be ε1, ε2 and ε3 respectively.
• The radiation network for this system of three surface
Aug. 2016 MT/SJEC/M.Tech. 43
• The radiation network for this system of three surface
enclosure is shown in Fig. (13.32,b).
• While drawing the radiation network, the principle to be
followed is quite simple: first, draw the surface resistance
associated with each gray surface; then, connect the
radiosity potentials between surfaces by the respective
space resistances.
45. • It is considered that the temperature of
each surface is known; i.e. emissive power
Eb for each surface is known.
• Then, the problem reduces to determining
the radiosities J1, J2 and J3.
• This is done by applying Kirchoff’s law of
Aug. 2016 MT/SJEC/M.Tech. 45
• This is done by applying Kirchoff’s law of
d.c. circuits to each node: i.e. sum of the
currents (or, rate of heat transfers)
entering into each node is zero.
• Doing this, we get the following three
algebraic equations:
46. Node J1:
E b1 J 1
R 1
J 2 J 1
R 12
J 3 J 1
R 13
0 .....(13.63,a)
Node J2:
E b2 J 2
R 2
J 1 J 2
R 12
J 3 J 2
R 23
0 .....(13.63,b)
Node J :
E b3 J 3 J 1 J 3 J 2 J 3
0 .....(13.63,c)
Aug. 2016 MT/SJEC/M.Tech. 46
• Solving these three eqns. simultaneously, we get J1, J2
and J3.
• Remember to write each eqn. such that current flows
into the node; then, the magnitudes of the radiosities
would adjust themselves when all the three equations
are solved simultaneously.
Node J3:
b3 3
R 3
1 3
R 13
2 3
R 23
0 .....(13.63,c)
47. • Once the magnitudes of the radiosities are
known, expressions for net heat flows between
the surfaces are:
Q 12
J 1 J 2
R 12
J 1 J 2
1
A 1 F 12
.
....(13.64,a)
Aug. 2016 MT/SJEC/M.Tech. 47
Q 13
J 1 J 3
R 13
J 1 J 3
1
A 1 F 13
.
....(13.64,b)
Q 23
J 2 J 3
R 23
J 1 J 2
1
A 2 F 23
.
....(13.64,c)
48. • And, net heat flow from each surface is:
Q 1
E b1 J 1
R 1
E b1 J 1
1 ε 1
A 1 ε 1
.
.....(13.65,a)
Q
E b2 J 2 E b2 J 2
.....(13.65,b)
Aug. 2016 MT/SJEC/M.Tech. 48
Q 2
b2 2
R 2
b2 2
1 ε 2
A 2 ε 2
.
.....(13.65,b)
Q 3
E b3 J 3
R 3
E b3 J 3
1 ε 3
A 3 ε 3
.
.....(13.65,c)
49. • Eqn. set (13.64) is a set of general
equations for three diffuse, opaque, gray
surfaces.
• However, these equations will be modified
depending upon any constraint that may
be attached to any of the surfaces, i.e.
• say, if the surface is black or re-radiating:
Aug. 2016 MT/SJEC/M.Tech. 49
• say, if the surface is black or re-radiating:
Ji = Ebi = σ.Ti
4.
• And, Qi = 0 for a re-radiating surface.
• If Qi at any surface is specified instead of
the temperature (i,.e. Ebi), then,
(Ebi – Ji)/Ri is replaced by Qi.
50. Few special cases of three-zone
enclosures:
• Case (i): Two black surfaces connected to a
third refractory surface:
• This is a three-zone enclosure, with two of the
surfaces being black and the third surface being
a re-radiating, insulated surface.
Aug. 2016 MT/SJEC/M.Tech. 50
a re-radiating, insulated surface.
• Typical example is a furnace whose bottom is
the ‘source’ and the top is the ‘sink’ and the two
surfaces are connected by a refractory wall
which acts as a re-radiating surface.
• In effect, the source and sink exchange heat
through the re-radiating wall.
51. • However, in steady state, the re-radiating
wall radiates as much heat as it receives,
which means that net heat exchange
through the re-radiating wall (= Q) is zero,
i.e. Eb = J for the re-radiating wall.
• Therefore, once J (i.e. Eb) is calculated for
the re-radiating surface, its steady state
Aug. 2016 MT/SJEC/M.Tech. 51
b
the re-radiating surface, its steady state
temperature can easily be calculated from:
Eb = σ. T4.
52. Eb1
= J1
E = J R
Eb2
= J2
R12
R12=1/(A1.F12 )
EbR= JR
R2RR1R
R1R=1/(A1.F1R )
R2R=1/(A2.F2R )
Fig.(a)
Aug. 2016 MT/SJEC/M.Tech. 52
Fig. 13.33 Two black surfaces connected by a third re-radiating
surface and its radiation network
Eb1 = J1 Eb2 = J2
R12
R2RR1R JR
Fig.(b)
53. • The radiation network is drawn very easily by
remembering the usual principles, i.e.
• for a black surface, the surface resistance is
zero, i.e. Eb = J.
• For a re-radiating surface too, Eb = J, as already
explained;
• Further, for a re-radiating surface, Q = 0.
• Between two given surfaces, the radiosity
Aug. 2016 MT/SJEC/M.Tech. 53
• Between two given surfaces, the radiosity
potentials are connected by the respective
space resistances, as shown.
• It may be observed that the system reduces to a
series-parallel circuit of resistances as shown in
Fig. (13.33,b).
54. • So, we write, for the total resistance of the circuit, Rtot:
1
R tot
1
R 12
1
R 1R R 2R
and, Q 12
E b1 E b2
R tot
E b1 E b2
1
R 12
1
R 1R R 2R
.
Aug. 2016 MT/SJEC/M.Tech. 54
• Here, Q12 is the net radiant heat transferred between surfaces 1 and
2. Similar expressions can be written for heat transfer between
surfaces 2 and 3 (= Q23) and the heat transfer between surfaces 1
and 3 (= Q13).
i.e. Q 12 σ T 1
4
T 2
4. A 1 F 12
. 1
1
A 1 F 1R
.
1
A 2 F 2R
.
. .....(13.66)
55. Case (ii): Two gray surfaces surrounded
by a third re-radiating surface:
Aug. 2016 MT/SJEC/M.Tech. 55
56. • In this case, there are two gray surfaces, and the
third surface is an insulated, re-radiating
surface.
• As already explained, the re-radiating surface
radiates as much energy as it receives;
therefore, net radiant heat transfer for that
surface is zero, i.e. Q 3 0
Aug. 2016 MT/SJEC/M.Tech. 56
surface is zero, i.e. Q 3 0
i.e.
E b3 J 3
1 ε 3
A 3 ε 3
.
0
i.e. E b3 J 3
57. • i.e. once the radiosity of the re-radiating surface
is known, its temperature can easily be
calculated, since Eb3 = σ.T3
4.
• Further, note that T3 is independent of the
emissivity of surface 3.
• Now, the radiation network reduces to a simple
series-parallel circuit of the relevant resistances.
Aug. 2016 MT/SJEC/M.Tech. 57
series-parallel circuit of the relevant resistances.
• Expression for heat flow rate is:
Q 1 Q 2
E b1 E b2
R tot
where, Rtot is the total resistance, given by:
58. R tot R 1
1
1
R 12
1
R 13 R 23
R 2
i.e. R tot
1 ε 1
A 1 ε 1
.
1
A 1 F 12
. 1
1 1
1 ε 2
A 2 ε 2
.
....(13.67)
Aug. 2016 MT/SJEC/M.Tech. 58
1
A 1 F 13
.
1
A 2 F 23
.
64. Radiation shielding:
• One or more ‘radiation shields’ are used to
reduce radiant heat transfer between two given
surfaces.
• Radiation shield is, simply a thin, high reflectivity
Aug. 2016 MT/SJEC/M.Tech. 64
• Radiation shield is, simply a thin, high reflectivity
surface placed in between the surfaces which
exchange heat between themselves.
• Radiation shields may be made of aluminium
foils, copper foils, or aluminized mylar sheets
etc.
65. • Fig. (13.36,a) shows to large parallel plates, 1
and 2 exchanging heat between themselves;
• Let their areas, temperatures (in Kelvin) and
emissivities be (A1, T1, ε1) and (A2, T2, ε2).
• Let a radiation shield 3, be placed between
these plates. Plate 3 is thin and made of a
material of high reflectivity.
• Let the emissivities of two sides of the radiation
shield be ε and ε as shown.
Aug. 2016 MT/SJEC/M.Tech. 65
shield be ε3-1 and ε3-2 as shown.
• Radiation network for this system is shown in
Fig. (13.36,b).
• This is drawn, as usual, remembering that each
gray surface has a ‘surface resistance’
associated with it, and the two radiosity
potentials are connected by a ‘space resistance’.
67. • When there is no shield, the radiation heat
transfer between plates 1 and 2 is already
shown to be:
• With one shield placed between plates 1 and 2,
Q 12
A σ. T 1
4
T 2
4.
1
ε 1
1
ε 2
1
....for infinitely large parallel plates.....(13.59)
Aug. 2016 MT/SJEC/M.Tech. 67
• With one shield placed between plates 1 and 2,
the radiation network will be as shown in Fig. (b)
above.
• Note that now all the relevant resistances are in
series.
68. • Net heat transfer between plates 1 and 2
is given as:
Q12-one shield = (Eb1-Eb2)/Rtot where Rtot is
the total resistance.
• i.e.
E b1 E b2
Aug. 2016 MT/SJEC/M.Tech. 68
Q 12_one_shield
E b1 E b2
1 ε 1
A 1 ε 1
.
1
A 1 F 13
.
1 ε 3_1
A 3 ε 3_1
.
1 ε 3_2
A 3 ε 3_2
.
1
A 3 F 32
.
1 ε 2
A 2 ε 2
.
....for two gray surfaces with one radiation shield
placed in between.....(13.70)
69. • Now, for two large parallel plates, we note:
• Then, eqn. (13.70) simplifies to:
F 13 F 32 1 and, A 1 A 2 A 3 A
Q 12_one_shield
A σ. T 1
4
T 2
4.
1 1
1
1 1
1
....(13.71)
Aug. 2016 MT/SJEC/M.Tech. 69
• Note that as compared to eqn. (13.59) for the
case of no-shield, we have, with one shield, an
additional term appearing in the denominator of
eqn. (13.71).
1
ε 1
1
ε 2
1
1
ε 3_1
1
ε 3_2
1
70. • Therefore, if there are N radiation shields, we
have, for net radiation heat transfer:
• If emissivities of all surfaces are equal, eqn.
(13.72) becomes:
Q 12N_shields
A σ. T 1
4
T 2
4.
1
ε 1
1
ε 2
1
1
ε3_1
1
ε 3_2
1 .....
1
ε N_1
1
ε N_2
1
...(13.72)
Aug. 2016 MT/SJEC/M.Tech. 70
(13.72) becomes:
Q 12N_shields
A σ. T 1
4
T 2
4.
N 1( )
1
ε
1
ε
1.
1
N 1( )
Q 12no_shield
. ....(13.73)
71. • Note this important result, which implies that, when all
emissivities are equal, presence of one radiation shield
reduces the radiation heat transfer between the two
surfaces to one-half,
• Two radiation shields reduce the heat transfer to one-
third, 9 radiation shields reduce the heat transfer to one-
tenth etc.
• For a more practical case of the two surfaces having
ε ε
Aug. 2016 MT/SJEC/M.Tech. 71
emissivities of ε1 and ε2, and all shields having the same
emissivity of εs, eqn. (13.72) becomes:
Q 12N_shields
A σ. T 1
4
T 2
4.
1
ε 1
1
ε 2
1 N
2
ε s
1.
....(13.74)
72. • To determine the equilibrium temperature of the
radiation shield:
• Once Q12 is determined from eqn. (13.71), the temperature of the
shield is easily found out by applying the condition that in steady
state:
• We can use either of the conditions: Q12 = Q13 or Q12 = Q32.
• Q13 or Q32 is determined by applying eqn. (13.59); i.e. we get:
Q 12 Q 13 Q 32 ...(13.75)
A σ. T 1
4
T 3
4.
Aug. 2016 MT/SJEC/M.Tech. 72
• In both the above eqns., T3 is the only unknown, which can easily be
determined.
Q 12 Q 13
A σ. T 1 T 3
.
1
ε 1
1
ε 3
1
...(13.76,a)
or,
Q 12 Q 32
A σ. T 3
4
T 2
4.
1
ε 3
1
ε 2
1
....(13.76,b)
73. For a cylindrical radiation shield placed in
between two, long concentric cylinders:
Aug. 2016 MT/SJEC/M.Tech. 73
• Consider the case of radiation heat transfer
between two long, concentric cylinders.
• The radiation heat transfer between two long,
concentric cylinders is already shown to be:
74. Q 12
A 1 σ. T 1
4
T 2
4.
1
ε 1
A 1
A 2
1
ε 2
1.
....for infinitely long concentric cylinders.....(13.60)
where
A 1
A 2
r 1
r 2
Aug. 2016 MT/SJEC/M.Tech. 74
• Now, let a cylindrical radiation shield, 3, be
placed in between the inner cylinder (1)
and the outer cylinder (2), as shown in Fig.
75. • The radiation network for this system is exactly the same
as shown in Fig. (13.36,b):
• And, the radiation heat transfer between cylinders 1 and
2, when the shield is present, is given by:
Aug. 2016 MT/SJEC/M.Tech. 75
2, when the shield is present, is given by:
• Now, for the cylindrical system, we have:
Q 12_one_shield
E b1 E b2
1 ε 1
A 1 ε 1
.
1
A 1 F 13
.
1 ε 3_1
A 3 ε 3_1
.
1 ε 3_2
A 3 ε 3_2
.
1
A 3 F 32
.
1 ε 2
A 2 ε 2
.
....for two gray surfaces with one radiation shield
placed in between.....(13.70)
76. F 13 F 32 1
A 1 2 π. r 1
. L.
A 2 2 π. r 2
. L.
and, A 3 2 π. r 3
. L.
Aug. 2016 MT/SJEC/M.Tech. 76
• Then, eqn. (13.70) reduces to:
• In eqn. (13.77), we have: (A1/A2) = (r1/r2), and (A1/A3) = (r1/r3).
Q 12one_shield
A 1 σ. T 1
4
T 2
4.
1
ε 1
A 1
A 2
1
ε 2
1.
A 1
A 3
1
ε 3_1
1
ε 3_2
1.
...for concentric cylinders with one radiation shield...(13.77)
77. • Note that as compared to the relation for two
concentric cylinders with no shield (i.e. eqn.
13.60), an additional term appears in the
denominator of eqn. (13.77) (i.e. the third term)
when one radiation shield is introduced;
• If there is a second radiation shield, say (4), then
one more similar term will have to be added in
Aug. 2016 MT/SJEC/M.Tech. 77
one more similar term will have to be added in
the denominator to take care of the resistance of
that shield.
• Equilibrium temperature of the shield is
determined by applying the principle that, in
steady state: Q 12 Q 13 Q 32
78. For a Spherical radiation shield placed in
between two concentric spheres:
• The radiation network for this system is shown in Fig.
(13.36,b).
• When there is no radiation shield, radiation heat transfer
between surfaces 1 and 2 is given by eqn. (13.61), viz.
Aug. 2016 MT/SJEC/M.Tech. 78
Q 12
A 1 σ. T 1
4
T 2
4.
1
ε 1
A 1
A 2
1
ε 2
1.
....for concentric spheres.....(13.61)
where
A 1
A 2
r 1
r 2
2
79. • Again, when the radiation shield is present, the general relation for
radiation heat transfer between surfaces 1 and 2 is eqn. (13.70).
• Relation for radiant heat transfer between surfaces 1 and 2, is
exactly as eqn. (13.77), i.e.
Q 12one_shield
A 1 σ. T 1
4
T 2
4.
1
ε 1
A 1
A 2
1
ε 2
1.
A 1
A 3
1
ε 3_1
1
ε 3_2
1.
...for concentric spheres with one radiation shield...(13.78)
Aug. 2016 MT/SJEC/M.Tech. 79
• In eqn. (13.78), we have:
• Equilibrium temperature of the shield is determined by applying the
principle that, in steady state:
A 1
A 2
r 1
r 2
2
and,
A 1
A 3
r 1
r 3
2
Q 12 Q 13 Q 32
83. Radiation error in temperature
measurement:
• An important application of radiation shields is in
reducing the radiation error in temperature
measurement.
• Consider the case of a hot fluid at a temperature
Tf, flowing through a channel, whose walls are at
a temperature T .
Aug. 2016 MT/SJEC/M.Tech. 83
Tf, flowing through a channel, whose walls are at
a temperature Tw.
• Let the convective heat transfer coefficient
between the fluid and the thermometer bulb be
h.
• To measure the temperature of the fluid, a
thermometer (or a thermocouple) is introduced
into the stream, as shown in Fig. (13.39 a).
84. Tf , h
(a) Thermometer without radiation shield
Tw
qrad
qconv
Tc
Thermometer
Tc
Thermometer
Tw
Aug. 2016 MT/SJEC/M.Tech. 84
Fig. 13.39 Radiation shielding of thermometers
Tw
Tc
Ts
Tw
Tf
, h
(b) Thermometer with radiation shield
85. • Let the reading shown by the thermometer be
Tc.
• This reading, however, does not represent the
true temperature of the fluid Tf, since the
thermometer bulb will lose heat by radiation to
the walls of the channel which are at a lower
temperature Tw (which is usually the case).
• So, in steady state, the thermometer bulb will
gain heat by convection from the flowing fluid
Aug. 2016 MT/SJEC/M.Tech. 85
gain heat by convection from the flowing fluid
and will lose heat by radiation to the walls, and
as a result, the temperature Tc shown by the
thermometer will be some value in between Tf
and Tw .
• We wish to find out the true temperature of the
fluid Tf , by knowing the thermometer reading Tc.
86. • Making an energy balance on the thermometer bulb, in
steady state, we have:
• Without radiation shield:
• qconv to the bulb = qrad from the bulb
i.e. h A c
. T f T c
. ε c A c
. σ. T c
4
T w
4.
i.e. T f T c
ε c σ. T c
4
T w
4.
.....(13.79)
Aug. 2016 MT/SJEC/M.Tech. 86
where Ac = surface area of thermometer bulb,
εc = emissivity of thermometer bulb surface
• Eqn. (13.79) gives the true temperature of the fluid Tf.
• Second term on the RHS of eqn. (13.79) represents the
error in temperature measurement due to radiation effect
i.e. T f T c
h
.....(13.79)
87. • Radiation error can be minimized by:
• (i) having low value of εc i.e. high reflectivity for the
bulb surface
• (ii) high value for h, the convective heat transfer
coefficient
• In practice, even if we start with a thermometer bulb
surface of high reflectivity, soon the emissivity value
rises to about 0.8 or 0.9 due to deposit formation,
Aug. 2016 MT/SJEC/M.Tech. 87
rises to about 0.8 or 0.9 due to deposit formation,
corrosion or erosion of the bulb surface, etc.
• So, the most practical way to reduce the radiation error
in temperature measurement is to provide a cylindrical
radiation shield around the thermometer bulb, as shown
in Fig. (13.39,b) above.
88. • In steady state, the shield temperature (Ts) will stabilize
somewhere in between the fluid temperature Tf and the
wall temperature Tw.
• Then, in eqn. (13.79), Tw will be replaced by the effective
shield temperature Ts.
• Energy balance on the thermometer bulb:
• Heat transferred to the bulb from the fluid by convection =
Heat transferred from the bulb to the shield by radiation
Aug. 2016 MT/SJEC/M.Tech. 88
Heat transferred from the bulb to the shield by radiation
• In eqn. (13.80), Fcs = view factor of thermometer bulb w.r.t the shield
and is, generally equal to 1.
i.e. h A c
. T f T c
.
σ T c
4
T s
4.
1 ε c
A c ε c
.
1
A c F cs
.
1 ε s
A s ε s
.
....(13.80)
89. • Making an energy balance on the shield:
heat transferred to shield from the fluid by convection +
heat transferred to shield from bulb by radiation =
heat transferred from shield to walls by radiation
i.e. 2 A s
. h. T f T s
.
σ T c
4
T s
4.
1 ε c
A c ε c
.
1
A c F cs
.
1 ε s
A s ε s
.
ε s A s
. σ. T s
4
T w
4. ....(13.81)
Aug. 2016 MT/SJEC/M.Tech. 89
where, A s = area of shield on one side
ε s = emissivitty of shield surface
A c = area of bulb surface
ε c = emissivity of bulb surface
F cs = view factor of bulb w.r.t. shield
90. • In the first term of the above eqn. factor 2 appears since
convective heat transfer to the shield occurs on both
surfaces of the shield.
• Also, in writing the RHS, the inherent assumption is that:
F sw 1 ...view factor between the shield and the walls
and,
Aug. 2016 MT/SJEC/M.Tech. 90
• Solving eqns. (13.80) and (13.81) simultaneously, we
obtain the shield temperature Ts and the thermometer
reading Tc, (if Tf is known), or Tf (if Tc is known).
A s
A w
0 ...i.e. surface area of shield is negligible compared to the area of the channel
walls