Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and conditions for minimization of energy losses in the process
This paper introduces a novel technique and algorithm for theoretical study of entropy changes for exothermic reactions by mechanistic modelling and dynamic simulation; considering factors such as kinetics, reaction environment and flow patterns with an ultimate objective of minimization of energy loss and entropy generation in the system. It mainly focuses on exothermic reactors cooled by means of a constant inlet temperature utility fluid which flows along the external surface of the reactor vessel. Using basic concepts of heat and mass balances and definitions in thermodynamics, variation of related system variables with time is modelled and by simulation in MS-Excel, a polynomial fit is generated for sample problems in order to make the illustrations handier. Usages of the developed expressions for energy optimization are also commented upon.
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed
Calculation method based on experimental data to estimate sunlight intensity falling on the solar
collector has been established. The technique is to evaluate the heat power using the specific heat formula.
Light intensity from 3 different light sources has been studied; the results gained by the method were compared
against other results directly measured using intensity meter, and both results showed good agreement. The
method shows powerful tools, which can estimate the light intensity in the lack of intensity meter. Although, the
specific heat formula has been used previously for a estimating different heat transfer purpose, however, this
method has advantage by providing approximation results in simple way, and it use to determine the
performance of flat panel solar thermal systems under variable solar flux.
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.
Measuring the Thermal Conductivities of Low Heat Conducting Disk Samples by M...IJERA Editor
This article aims to establish an experimental procedure to measure heat transmission coefficients in low heat conductive materials. The newly developed model takes as starting point the application of Fourier’s law to a disk sample when a temperature gradient is established between its faces. The power of a heating element is determined as the heat transfer coefficient of the problem disk. Initially, a glass vessel containing water is placed in direct contact with the heating element; then, a problem plastic disk is placed between this element and the glass vessel, treating the set as a composite wall. Prior to the above the water equivalent of a calorimetric set (vessel + water + accessories) and the thermal conductivity of the vessel must be determined. The thermal conductivity of the problem plastic disk sample is obtained for temperatures ranging from 30 to 70° C. The results reveal the existence of some type of structural transition for the problem material.
Review of magnetic refrigeration system as alternative to conventional refrig...Naji Abdullah
The refrigeration system is one of the most important systems in industry.
Developers are constantly seeking for how to avoid the damage to the environment. Magnetic
refrigeration is an emerging, environment-friendly technology based on a magnetic solid that
acts as a refrigerant by magneto-caloric effect (MCE). In the case of ferromagnetic materials,
MCE warms as the magnetic moments of the atom are aligned by the application of a magnetic
field. There are two types of magnetic phase changes that may occur at the Curie point: first
order magnetic transition (FOMT) and second order magnetic transition (SOMT). The
reference cycle for magnetic refrigeration is AMR (Active Magnetic Regenerative cycle),
where the magnetic material matrix works both as a refrigerating medium and as a heat
regenerating medium, while the fluid flowing in the porous matrix works as a heat transfer
medium. Regeneration can be accomplished by blowing a heat transfer fluid in a reciprocating
fashion through the regenerator made of magnetocaloric material that is alternately magnetized
and demagnetized. Many magnetic refrigeration prototypes with different designs and software
models have been built in different parts of the world. In this paper, the authors try to shed
light on the magnetic refrigeration and show its effectiveness compared with conventional
refrigeration methods.
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed
Calculation method based on experimental data to estimate sunlight intensity falling on the solar
collector has been established. The technique is to evaluate the heat power using the specific heat formula.
Light intensity from 3 different light sources has been studied; the results gained by the method were compared
against other results directly measured using intensity meter, and both results showed good agreement. The
method shows powerful tools, which can estimate the light intensity in the lack of intensity meter. Although, the
specific heat formula has been used previously for a estimating different heat transfer purpose, however, this
method has advantage by providing approximation results in simple way, and it use to determine the
performance of flat panel solar thermal systems under variable solar flux.
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.
Measuring the Thermal Conductivities of Low Heat Conducting Disk Samples by M...IJERA Editor
This article aims to establish an experimental procedure to measure heat transmission coefficients in low heat conductive materials. The newly developed model takes as starting point the application of Fourier’s law to a disk sample when a temperature gradient is established between its faces. The power of a heating element is determined as the heat transfer coefficient of the problem disk. Initially, a glass vessel containing water is placed in direct contact with the heating element; then, a problem plastic disk is placed between this element and the glass vessel, treating the set as a composite wall. Prior to the above the water equivalent of a calorimetric set (vessel + water + accessories) and the thermal conductivity of the vessel must be determined. The thermal conductivity of the problem plastic disk sample is obtained for temperatures ranging from 30 to 70° C. The results reveal the existence of some type of structural transition for the problem material.
Review of magnetic refrigeration system as alternative to conventional refrig...Naji Abdullah
The refrigeration system is one of the most important systems in industry.
Developers are constantly seeking for how to avoid the damage to the environment. Magnetic
refrigeration is an emerging, environment-friendly technology based on a magnetic solid that
acts as a refrigerant by magneto-caloric effect (MCE). In the case of ferromagnetic materials,
MCE warms as the magnetic moments of the atom are aligned by the application of a magnetic
field. There are two types of magnetic phase changes that may occur at the Curie point: first
order magnetic transition (FOMT) and second order magnetic transition (SOMT). The
reference cycle for magnetic refrigeration is AMR (Active Magnetic Regenerative cycle),
where the magnetic material matrix works both as a refrigerating medium and as a heat
regenerating medium, while the fluid flowing in the porous matrix works as a heat transfer
medium. Regeneration can be accomplished by blowing a heat transfer fluid in a reciprocating
fashion through the regenerator made of magnetocaloric material that is alternately magnetized
and demagnetized. Many magnetic refrigeration prototypes with different designs and software
models have been built in different parts of the world. In this paper, the authors try to shed
light on the magnetic refrigeration and show its effectiveness compared with conventional
refrigeration methods.
Experimental and Exergy Analysis of A Double Pipe Heat Exchanger for Parallel...IJERA Editor
This paper presents For Experimental and Exergy Analysis of a Double Pipe Heat Exchanger for Parallel- flow Arrangement. The Double pipe heat exchanger is one of the Different types of heat exchangers. double-pipe exchanger because one fluid flows inside a pipe and the other fluid flows between that pipe and another pipe that surrounds the first.In a parallel flow, both the hot and cold fluids enter the Heatexchanger at same end andmove in same direction. The present work is taken up to carry experimental work and the exergy analysis based on second law analysis of a Double-Pipe Heat Exchanger. In experimental set up hot water and cold water will be used working fluids. The inlet Hot water will be varied from 40 0C and 50 0C and cold water temperature will be varied from between 15 and 20. It has been planned to find effects of the inlet condition of both working fluid flowing through the heat exchanger on the heat transfer characteristics, entropy generation, and Exergy loss. The Mathematical modelling of heat exchanger will based on the conservation equation of mass, energy and based on second law of thermodynamics to find entropy generation and exergy losses.
Introduction to transient Heat conduction, Lamped System Analysis, Approxiamate Analytical and graphical method and Numerical method for one and two dimensional heat conduction by using Explicit and Implicit method
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
Experimental and Analytical Performance of Gas Gap Cryogenic Thermal Switch ...ijsrd.com
Heat switches are important devices in many cryogenic setups, especially in space applications and many systems have been used to allow a good ability to make or break a thermal contact. Among them, the so-called gas gap heat switches are known to be very reliable and simple due to the nonexistence of moving parts. The ON (conducting) state of the switch are obtained by varying the gas pressure and OFF (insulating) are obtained by creating vacuum in gap. In this paper, the gas gap cryogenic thermal switch is fabricated and tested using LN2 storage vessel. The thermal characteristics (Conductance in the ON and OFF state) of a "Gas Gap Heat Switch" are obtained experimentally and analytically using nitrogen as exchange gas. It is concluded that for both ON and OFF state, thermal conductance increases as heat load increases.
Simulation of the effects of turbine exhaust recirculationZin Eddine Dadach
For an effective carbon capture by an amine mixture, the molar percentage of CO2 in the flue gas should be at least equal to 10%. Moreover, in order to reduce technical problems due to amine oxidative degradation, the molar percentage of O2 in the flue gas should be limited to 5%. One possible option for increasing the concentration of CO2 and decreasing the amount of O2 in the flue gas from power plants using natural gas is recirculation of a part of the flue gas.
Thermal Simulation of Biogas Plants Using Mat LabIJERA Editor
The major prerequisite for the optimum production of methane from a biogas plant is the sustenance of digester temperature within the narrow limits (300C-350C). It is experimentally investigated that, the MIT biogas plant is not maintaining optimum temperature, this decreases the efficiency and increases the detention time for charge. To maintain the plant in optimum temperature, it is necessary to find out the heat losses from the biogas plant and the external energy inputs need to operate the plant. Rate of gas yield, and the detention time (time necessary to anaerobically digest organic wastes) in a biogas reactor, are favorable functions of the temperature in the digester. A thermal simulation for MIT biogas plant has developed using matlab in order to understand the heat transfer from the slurry and the gas holder to the surrounding earth and air respectively. The computation has been performed when the slurry is maintained at 200C and 300C, optimum temperature of anaerobic fermentation. If the slurry is considered to be at 350C, the optimum temperature of anaerobic fermentation, the total heat loss from the plant is higher than the heat loss when the slurry is maintained at 200C. The heat calculations provide an appraisal for the heat which has to be supplied by external means to compensate for the net heat losses which occur if the slurry is to be maintained at 350C. A solar system with auxiliary electric heater is designed for maintaining the slurry at 350C.In conclusion; the results of thermal analysis are used to define a strategy for operating biogas plant at optimum temperatures.
Fuzzy Logic Modeling of Heat Transfer in a double Pipe Heat Exchanger with Wa...ijiert bestjournal
Fuzzy logic is a method which can be used to model the experiments,and it has been introduced for the first time in 1965 by Zadeh . T he present work represents the use of fuzzy logic to model and predict the experimental results of heat transfer in a double Pipe Heat Exchanger with Wavy (Corrugated) Twiste d Tape Inserts . The tape consists of the corrugations and the twisting with various twist ratios (TR=10.7,8.5,7.1) . The length,width and thickness of twisted tape were 1 m,14 mm and 2 mm respectively. The Reynolds number is varied from 5000 to 17 000. T he friction factor is varied from .0384 to .07241 . The Nusselt number is varied from 69.13 to 266.18. Here the results with various twist ratios tapes were compared with results with plain tube. The experimental results showed that the maximum heat tran sfer was obtained with twisted tape with TR � 7.1 . The Nusselt number increased by 172 % and friction factor value increased by 32.11% as compared to the smooth tube values. For Fuzzy Logic system the twist ratio,temperature and Reynolds Numbers were used as input functions and friction factor and Nusselt number were used as output functions. It is found that a fuzzy inference system named Mamdani is a powerful instrument for predicting the experiments due to its low error.
Experimental and Exergy Analysis of A Double Pipe Heat Exchanger for Parallel...IJERA Editor
This paper presents For Experimental and Exergy Analysis of a Double Pipe Heat Exchanger for Parallel- flow Arrangement. The Double pipe heat exchanger is one of the Different types of heat exchangers. double-pipe exchanger because one fluid flows inside a pipe and the other fluid flows between that pipe and another pipe that surrounds the first.In a parallel flow, both the hot and cold fluids enter the Heatexchanger at same end andmove in same direction. The present work is taken up to carry experimental work and the exergy analysis based on second law analysis of a Double-Pipe Heat Exchanger. In experimental set up hot water and cold water will be used working fluids. The inlet Hot water will be varied from 40 0C and 50 0C and cold water temperature will be varied from between 15 and 20. It has been planned to find effects of the inlet condition of both working fluid flowing through the heat exchanger on the heat transfer characteristics, entropy generation, and Exergy loss. The Mathematical modelling of heat exchanger will based on the conservation equation of mass, energy and based on second law of thermodynamics to find entropy generation and exergy losses.
Introduction to transient Heat conduction, Lamped System Analysis, Approxiamate Analytical and graphical method and Numerical method for one and two dimensional heat conduction by using Explicit and Implicit method
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
Experimental and Analytical Performance of Gas Gap Cryogenic Thermal Switch ...ijsrd.com
Heat switches are important devices in many cryogenic setups, especially in space applications and many systems have been used to allow a good ability to make or break a thermal contact. Among them, the so-called gas gap heat switches are known to be very reliable and simple due to the nonexistence of moving parts. The ON (conducting) state of the switch are obtained by varying the gas pressure and OFF (insulating) are obtained by creating vacuum in gap. In this paper, the gas gap cryogenic thermal switch is fabricated and tested using LN2 storage vessel. The thermal characteristics (Conductance in the ON and OFF state) of a "Gas Gap Heat Switch" are obtained experimentally and analytically using nitrogen as exchange gas. It is concluded that for both ON and OFF state, thermal conductance increases as heat load increases.
Simulation of the effects of turbine exhaust recirculationZin Eddine Dadach
For an effective carbon capture by an amine mixture, the molar percentage of CO2 in the flue gas should be at least equal to 10%. Moreover, in order to reduce technical problems due to amine oxidative degradation, the molar percentage of O2 in the flue gas should be limited to 5%. One possible option for increasing the concentration of CO2 and decreasing the amount of O2 in the flue gas from power plants using natural gas is recirculation of a part of the flue gas.
Thermal Simulation of Biogas Plants Using Mat LabIJERA Editor
The major prerequisite for the optimum production of methane from a biogas plant is the sustenance of digester temperature within the narrow limits (300C-350C). It is experimentally investigated that, the MIT biogas plant is not maintaining optimum temperature, this decreases the efficiency and increases the detention time for charge. To maintain the plant in optimum temperature, it is necessary to find out the heat losses from the biogas plant and the external energy inputs need to operate the plant. Rate of gas yield, and the detention time (time necessary to anaerobically digest organic wastes) in a biogas reactor, are favorable functions of the temperature in the digester. A thermal simulation for MIT biogas plant has developed using matlab in order to understand the heat transfer from the slurry and the gas holder to the surrounding earth and air respectively. The computation has been performed when the slurry is maintained at 200C and 300C, optimum temperature of anaerobic fermentation. If the slurry is considered to be at 350C, the optimum temperature of anaerobic fermentation, the total heat loss from the plant is higher than the heat loss when the slurry is maintained at 200C. The heat calculations provide an appraisal for the heat which has to be supplied by external means to compensate for the net heat losses which occur if the slurry is to be maintained at 350C. A solar system with auxiliary electric heater is designed for maintaining the slurry at 350C.In conclusion; the results of thermal analysis are used to define a strategy for operating biogas plant at optimum temperatures.
Fuzzy Logic Modeling of Heat Transfer in a double Pipe Heat Exchanger with Wa...ijiert bestjournal
Fuzzy logic is a method which can be used to model the experiments,and it has been introduced for the first time in 1965 by Zadeh . T he present work represents the use of fuzzy logic to model and predict the experimental results of heat transfer in a double Pipe Heat Exchanger with Wavy (Corrugated) Twiste d Tape Inserts . The tape consists of the corrugations and the twisting with various twist ratios (TR=10.7,8.5,7.1) . The length,width and thickness of twisted tape were 1 m,14 mm and 2 mm respectively. The Reynolds number is varied from 5000 to 17 000. T he friction factor is varied from .0384 to .07241 . The Nusselt number is varied from 69.13 to 266.18. Here the results with various twist ratios tapes were compared with results with plain tube. The experimental results showed that the maximum heat tran sfer was obtained with twisted tape with TR � 7.1 . The Nusselt number increased by 172 % and friction factor value increased by 32.11% as compared to the smooth tube values. For Fuzzy Logic system the twist ratio,temperature and Reynolds Numbers were used as input functions and friction factor and Nusselt number were used as output functions. It is found that a fuzzy inference system named Mamdani is a powerful instrument for predicting the experiments due to its low error.
Check out the sample paper of UPES MET -II (June 2011). These sample questions are illustrative. The pattern, scope, arrangement, variety, difficulty level, etc in the actual question paper may vary.
A topic discussed during In-Service Training for Teachers 2016 in Baesa Elementary School, Tanque District , Caloocan City.
Positive Discipline is an approach to teaching that helps pupils to become responsible, respectful and resourceful members of their communities.
Action research in classroom setting copy (2)susanaparejo39
This Action Research in Classroom Setting is designed by the author in order to help the practitioner write the action research in a comprehensive way.
Similar to Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and conditions for minimization of energy losses in the process
Optimizing the-performance-of-a-standing-wave-loudspeaker-driven-thermoacoust...محمود الأمير
This paper investigates the design and optimization steps of a thermoacoustic refrigerator. Matlab code will be used for
optimizing the stack length and its position. DeltaEC version 6.3b11 will be used to do the code used for simulating the refrigerator to
identify the optimized operating conditions such as the mean pressure and the oscillating pressure. Behavior of changing the operating conditions effect on the performance is discussed.
Review on Design and Theoretical Model of Thermoelectricijsrd.com
This paper presents the theoretical development of the equations that allow to evaluate the performance of an air conditioning system based on the thermoelectric effect. The cooling system is based on a phenomena discovered by Jean Charles Athanase Peltier, in 1834. According to this when electricity runs through a junction between two semiconductors with different properties, heat is dissipated or absorbed. Thus, thermoelectric modules are made by semiconductors materials sealed between two plates through which a continuous current flows and keeps one plate hot and the other cold. The most important parameters to evaluate the performance of the device thermoelectric refrigeration are the coefficient of performance, the heat pumping rate and the maximum temperature difference between the hot side and the cold side of the thermoelectric module.
Peltier Thermoelectric Modules Modeling and EvaluationCSCJournals
The purpose of this work is to develop and experimentally test a model for the Peltier effect heat pump for the transient simulation in Spice software. The proposed model uses controlled sources and lumped components and its parameters can be directly calculated from the manufacturer’s data-sheets. In order to validate this model, a refrigeration chamber was designed and fabricated by using the Peltier modules. The overall system was experimentally tested and simulated with Spice. The simulation results were found to be compatible with the experimental results. This model will help designers to better design thermal systems using the Peltier modules.
Review on Thermoelectric materials and applicationsijsrd.com
In this paper thermoelectric materials are theoretically analyzed. The thermoelectric cooler device proposed here uses semiconductor material and uses current to transport energy (i.e., heat) from a cold source to a hot source via n- and p-type carriers. This device is fabricated by combining the standard n- and p-channel solid-state thermoelectric cooler with a two-element device inserted into each of the two channels to eliminate the solid-state thermal conductivity. The heat removed from the cold source is the energy difference, because of field emitted electrons from the n-type and p-type semiconductors. The cooling efficiency is operationally defined as where V is the anode bias voltage The cooling device here is shown to have an energy transport (i.e., heat) per electron of about500 me V depending on concentration and field while, in good thermoelectric coolers, it is about 50-60 me V at room temperature.
Applications of thermoelectric modules on heat flow detectionISA Interchange
This paper presents quantitative analysis and practical scenarios of implementation of the thermoelectric module for heat flow detection. Mathematical models of the thermoelectric effects are derived to describe the heat flow from/to the detected media. It is observed that the amount of the heat flow through the thermoelectric module proportionally induces the conduction heat owing to the temperature difference between the hot side and the cold side of the thermoelectric module. In turn, the Seebeck effect takes place in the thermoelectric module where the temperature difference is converted to the electric voltage. Hence, the heat flow from/to the detected media can be observed from both the amount and the polarity of the voltage across the thermoelectric module. Two experiments are demonstrated for viability of the proposed technique by the measurements of the heat flux through the building wall and thermal radiation from the outdoor environment during daytime.
Entransy Loss and its Application to Atkinson Cycle Performance EvaluationIOSR Journals
Abstract: Based on the concept of the entransy which characterizes heat transfer ability, a new Atkinson cycle
performance evaluation criterion termed the entransy loss is established. Our analysis shows that the maximum
entransy loss leads to the maximum output work, which is the maximum principle of entransy loss in
thermodynamic processes. At the same time, it is found that minimum entropy generation alone could not
describe change of the output work for the Atkinson cycle. The operation parameters are optimized for
evaluating the maximum output work of Atkinson cycle by incorporating maximum entransy loss and minimum
entropy generation when both, entransy loss and entropy generation, are induced by dumping the used streams
into the environment is considered.
A basic information About The radial Heat Conduction and calculations on -The WL 372 experimental unit done by student (Diyar Zeki) in energy engineering department in Duhok Polytechnic university (Technical College Engineering).
Optimization of “T”-Shaped Fins Geometry Using Constructal Theory and “FEA” C...IJERA Editor
This paper reports the geometric (constructal) optimization of T-shaped fin assemblies, where the objective is to maximize the global thermal conductance of the assembly, subject to total volume and fin-material constraints. Assemblies of plate fins are considered. It is shown that every geometric feature of the assembly is delivered by the optimization principle and the constraints. These optimal features are reported in dimensionless terms for this entire class of fin assemblies. Based on the constructal theory by Dr. A Bejan, T-shaped fins are developed for better heat conductance as compared to conventional fins. Now the geometry of this T type of fin contains many geometry parameters which affect the overall conductance of the fin. With the same material constraint and volume constraints optimal geometry ratios has been calculated so as to design the fin for its best performance. With focus to the practical situations and heat flow patterns, it is quite complex to calculate the temperatures on a T-shaped fin. It requires the help of FEA concepts and CAE software to optimize the geometry.
Numerical Modeling and Simulation of a Double Tube Heat Exchanger Adopting a ...IJERA Editor
The double tube heat exchangers are commonly used in industry due to their simplicity in design and also their
operation at high temperatures and pressures. As the inlet parameters like temperatures and mass flow rates
change during operation, the outlet temperatures will also change. In the present paper, a simple approximate
linear model has been proposed to predict the outlet temperatures of a double tube heat exchanger, considering it
as a black box. The simulation of the heat exchanger has been carried out first using the commercial CFD
software FLUENT. Next the linear model of the double tube heat exchanger based on lumped parameters has
been developed using the basic governing equations, considering it as a black box. Results have been generated
for outlet temperatures for different inlet temperatures and mass flow rates of the cold and hot fluids. The results
obtained using the above two methods have then been discussed and compared with the numerical results
available in the literature to justify the basis for the assumption of a linear approximation. Comparisons of the
predicted results from the present model show a good agreement with the experimental results published in the
literature. The assumptions of linear variation of outlet temperatures with the inlet temperature of one fluid
(keeping other inlet parameters fixed) is very well justified and hence the model can be employed for the
analysis of double tube heat exchangers.
Similar to Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and conditions for minimization of energy losses in the process (20)
Due to availability of internet and evolution of embedded devices, Internet of things can be useful to contribute in energy domain. The Internet of Things (IoT) will deliver a smarter grid to enable more information and connectivity throughout the infrastructure and to homes. Through the IoT, consumers, manufacturers and utility providers will come across new ways to manage devices and ultimately conserve resources and save money by using smart meters, home gateways, smart plugs and connected appliances. The future smart home, various devices will be able to measure and share their energy consumption, and actively participate in house-wide or building wide energy management systems. This paper discusses the different approaches being taken worldwide to connect the smart grid. Full system solutions can be developed by combining hardware and software to address some of the challenges in building a smarter and more connected smart grid.
A Survey Report on : Security & Challenges in Internet of Thingsijsrd.com
In the era of computing technology, Internet of Things (IoT) devices are now popular in each and every domains like e-governance, e-Health, e-Home, e-Commerce, and e-Trafficking etc. Iot is spreading from small to large applications in all fields like Smart Cities, Smart Grids, Smart Transportation. As on one side IoT provide facilities and services for the society. On the other hand, IoT security is also a crucial issues.IoT security is an area which totally concerned for giving security to connected devices and networks in the IoT .As, IoT is vast area with usability, performance, security, and reliability as a major challenges in it. The growth of the IoT is exponentially increases as driven by market pressures, which proportionally increases the security threats involved in IoT The relationship between the security and billions of devices connecting to the Internet cannot be described with existing mathematical methods. In this paper, we explore the opportunities possible in the IoT with security threats and challenges associated with it.
In today’s emerging world of Internet, each and every thing is supposed to be in connected mode with the help of billions of smart devices. By connecting all the devises used in our day to day life, make our life trouble less and easy. We are incorporated in a world where we are used to have smart phones, smart cars, smart gadgets, smart homes and smart cities. Different institutes and researchers are working for creating a smart world for us but real question which we need to emphasis on is how to make dumb devises talk with uncommon hardware and communication technology. For the same what kind of mechanism to use with various protocols and less human interaction. The purpose is to provide the key area for application of IoT and a platform on which various devices having different mechanism and protocols can communicate with an integrated architecture.
Study on Issues in Managing and Protecting Data of IOTijsrd.com
This paper discusses variety of issues for preserving and managing data produced by IoT. Every second large amount of data are added or updated in the IoT databases across the heterogeneous environment. While managing the data each phase of data processing for IoT data is exigent like storing data, querying, indexing, transaction management and failure handling. We also refer to the problem of data integration and protection as data requires to be fit in single layout and travel securely as they arrive in the pool from diversified sources in different structure. Finally, we confer a standardized pathway to manage and to defend data in consistent manner.
Interactive Technologies for Improving Quality of Education to Build Collabor...ijsrd.com
Today with advancement in Information Communication Technology (ICT) the way the education is being delivered is seeing a paradigm shift from boring classroom lectures to interactive applications such as 2-D and 3-D learning content, animations, live videos, response systems, interactive panels, education games, virtual laboratories and collaborative research (data gathering and analysis) etc. Engineering is emerging with more innovative solutions in the field of education and bringing out their innovative products to improve education delivery. The academic institutes which were once hesitant to use such technology are now looking forward to such innovations. They are adopting the new ways as they are realizing the vast benefits of using such methods and technology. The benefits are better comprehensibility, improved learning efficiency of students, and access to vast knowledge resources, geographical reach, quick feedback, accountability and quality research. This paper focuses on how engineering can leverage the latest technology and build a collaborative learning environment which can then be integrated with the national e-learning grid.
Internet of Things - Paradigm Shift of Future Internet Application for Specia...ijsrd.com
In the world more than 15% people are living with disability that also include children below age of 10 years. Due to lack of independent support services specially abled (handicap) people overly rely on other people for their basic needs, that excludes them from being financially and socially active. The Internet of Things (IoT) can give support system and a better quality of life as well as participation in routine and day to day life. For this purpose, the future solutions for current problems has been introduced in this paper. Daunting challenges have been considered as future research and glimpse of the IoT for specially abled person is given in the paper.
A Study of the Adverse Effects of IoT on Student's Lifeijsrd.com
Internet of things (IoT) is the most powerful invention and if used in the positive direction, internet can prove to be very productive. But, now a days, due to the social networking sites such as Face book, WhatsApp, twitter, hike etc. internet is producing adverse effects on the student life, especially those students studying at college Level. As it is rightly said, something which has some positive effects also has some of the negative effects on the other hand. In this article, we are discussing some adverse effects of IoT on student’s life.
Pedagogy for Effective use of ICT in English Language Learningijsrd.com
The use of information and communications technology (ICT) in education is a relatively new phenomenon and it has been the educational researchers' focus of attention for more than two decades. Educators and researchers examine the challenges of using ICT and think of new ways to integrate ICT into the curriculum. However, there are some barriers for the teachers that prevent them to use ICT in the classroom and develop supporting materials through ICT. The purpose of this study is to examine the high school English teachers’ perceptions of the factors discouraging teachers to use ICT in the classroom.
In recent years usage of private vehicles create urban traffic more and more crowded. As result traffic becomes one of the important problems in big cities in all over the world. Some of the traffic concerns are traffic jam and accidents which have caused a huge waste of time, more fuel consumption and more pollution. Time is very important parameter in routine life. The main problem faced by the people is real time routing. Our solution Virtual Eye will provide the current updates as in the real time scenario of the specific route. This research paper presents smart traffic navigation system, based on Internet of Things, which is featured by low cost, high compatibility, easy to upgrade, to replace traditional traffic management system and the proposed system can improve road traffic tremendously.
Ontological Model of Educational Programs in Computer Science (Bachelor and M...ijsrd.com
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Understanding IoT Management for Smart Refrigeratorijsrd.com
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Double wishbone designs allow the engineer to carefully control the motion of the wheel throughout suspension travel. 3-D model of the Lower Wishbone Arm is prepared by using CAD software for modal and stress analysis. The forces and moments are used as the boundary conditions for finite element model of the wishbone arm. By using these boundary conditions static analysis is carried out. Then making the load as a function of time; quasi-static analysis of the wishbone arm is carried out. A finite element based optimization is used to optimize the design of lower wishbone arm. Topology optimization and material optimization techniques are used to optimize lower wishbone arm design.
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Application of FACTS controller called Static Synchronous Compensator STATCOM to improve the performance of power grid with Wind Farms is investigated .The essential feature of the STATCOM is that it has the ability to absorb or inject fastly the reactive power with power grid . Therefore the voltage regulation of the power grid with STATCOM FACTS device is achieved. Moreover restoring the stability of the power system having wind farm after occurring severe disturbance such as faults or wind farm mechanical power variation is obtained with STATCOM controller . The dynamic model of the power system having wind farm controlled by proposed STATCOM is developed . To validate the powerful of the STATCOM FACTS controller, the studied power system is simulated and subjected to different severe disturbances. The results prove the effectiveness of the proposed STATCOM controller in terms of fast damping the power system oscillations and restoring the power system stability.
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Defending Reactive Jammers in WSN using a Trigger Identification Service.ijsrd.com
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TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
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The family offers a choice of engines
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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.
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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/
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
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Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
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
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.
Immunizing Image Classifiers Against Localized Adversary Attacks
Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and conditions for minimization of energy losses in the process
1. IJSRD - International Journal for Scientific Research & Development| Vol. 1, Issue 8, 2013 | ISSN (online): 2321-0613
All rights reserved by www.ijsrd.com 1580
Development and theoretical analysis of mathematical expressions for
change of entropy for exothermic reactions in different reacting
environments and conditions for minimization of energy losses in the
process
P. V. Kherdekar1
1
B. Tech (Student)
1
Department of Chemical Engineering
1
Vishwakarma Institute of Technology, Pune
Abstract—This paper introduces a novel technique and
algorithm for theoretical study of entropy changes for
exothermic reactions by mechanistic modelling and dynamic
simulation; considering factors such as kinetics, reaction
environment and flow patterns with an ultimate objective of
minimization of energy loss and entropy generation in the
system. It mainly focuses on exothermic reactors cooled by
means of a constant inlet temperature utility fluid which
flows along the external surface of the reactor vessel. Using
basic concepts of heat and mass balances and definitions in
thermodynamics, variation of related system variables with
time is modelled and by simulation in MS-Excel, a
polynomial fit is generated for sample problems in order to
make the illustrations handier. Usages of the developed
expressions for energy optimization are also commented
upon.
I. INTRODUCTION
In almost all process plants involving exothermic reactions
and/or heat exchange, formation of energy cascades is
gaining prominence owing to the increasing costs of energy
and in order to minimize energy expenditures of the plant.
Exergy available for a process can be most effectively used
by selection of correct parameters for energy cascading. The
values of thermodynamic variables also need to be chosen
so as to optimize the performance of the cascade.
Quality of energy is often associated with amount
of entropy generation associated with utilization of that
energy. More the generation of entropy, lower is the grade
of the energy for practical purposes [1]. Frequently it is
observed in engineering systems that with time exergy
degradation takes place leading to rise in entropy making
some part of energy unavailable for practical use.
For chemical reactors incorporating exothermic
reactions, the reactor is often jacketed and another fluid is
made to flow through the jacket. The fluid gains heat from
the outer surface of reactor and flows out. The heat gained
by the utility fluid is used to heat other systems installed in
the plant that require heating. The temperatures of the
process fluid and the utility fluid are expected to have effect
on the rate of degradation of available exergy. A reactor
may be continuously operated or batch operated. The mode
of operation may also affect the trends of availability of
energy at a certain instant of time.
This paper aims at analysis of exergy degradation
(i.e.) entropy generation as a function of time for different
systems encountered in process plant design that make a
certain amount of heat available to the external surface of
the system by means of heat conduction. Further the focus is
upon ideal utilization of the available energy for the
different systems considered. Certain assumptions are made
prior to the analysis which rarely poses a problem to
practical feasibility of the generated expressions as far as
chemical reactors are considered. They are:
1) Assume heat transfer by conduction to be the most
dominant mode of heat transfer as compared to other
modes and hence the other modes can be neglected.
2) Assume that entropy generation due to factors like
turbulence, friction (internal factors) is negligible.
3) The insulation over the jacket of an exothermic reactor
is a perfect insulator and isolates the system thermally
from rest of the universe.
4) The reaction takes place in unit volume.
II. DEVELOPMENT OF MODELS FOR ENTROPY
GENERATION
Development of expressions for entropy data for pureA.
conduction heat transfer from heated surface:
Let us assume a hypothetical isolated system separated into
two compartments by a conducting surface of mean surface
area A, thickness x and thermal conductivity k. The left
hand side of the surface is at a higher temperature (T1) than
the right hand side of the surface which is at temperature
(T2). Let us also assume that temperature is uniformly
distributed at every thickness value x in the surface.
Accordingly, multidimensional temperature gradients are
eliminated.
Fourier's law for heat conduction is given as [2]:
̇
For an infinitesimal time interval, the equation can be
written as:
For heat donating part of system,
(2.1)
As dQ =TdS [3]
(2.2)
Similarly, for heat gaining part of system
(2.3)
Differentiating equation 2.2 with respect to time,
Similarly, differentiating equation 2.3 with respect to time,
2. Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and
conditions for minimization of energy losses in the process (IJSRD/Vol. 1/Issue 8/2013/0014)
All rights reserved by www.ijsrd.com 1581
Assuming
( ) (2.4)
Usually, for conduction heat transfer, temperature varies
almost linearly with thickness.
(2.5)
Substituting equation (2.5) in equation (2.4),
( ) ( )
( ) ( )
( ) ( )
( ) ( ) (2.6)
( ) (2.7)
For local minimization of entropy [4],
More positive is the value of d2
S/dt2
, less is the entropy
generated. This will be practically feasible when terms on
RHS give the most positive value. However T1 is subject to
decrease with time for no heat generation after t=0.
Accordingly,
On the other hand,
For more positive value of d2
S/dt2
, both and should
be as small as possible. This suggests constant temperature
for utility stream.
Development of expressions for entropy data forB.
constant T2, decreasing T1, and no heat generation in the
system after t=0:
For varying T1 and constant T2, the modelled equation
becomes:
( ) ( )
( ) (2.8)
( )
( ) (2.9)
For such a case, heat must be getting transferred from a high
temperature 'body' to a low temperature 'reservoir'[4]. If m
and cp represent mass and specific heat capacity of the
'body', by first law of thermodynamics [5],
Heat lost by body = heat conducted by the wall
( )
( )
(2.10)
Where T1 is initial temperature and T1new is new temperature
of the inner surface due to loss of heat to the surroundings
by conduction in one iteration.
Development of expressions for entropy data; forC.
constant T2, decreasing T1, for heat generation in the system
after t=0:
This case is observed when rate of conduction of heat is
greater than the rate of generation of heat. For exothermic
reactors, generation of heat occurs by means of a chemical
reaction. Hence few terms will get added to the original
equation; due to generation of heat. Let r = rate of
exothermic reaction taking place in the system (moles of
reactant consumed/time)
Rate of generation of heat [6] =
̇
Rate of generation of entropy:
Assume first order reaction [7]
( )
( )
( )
( )
[ ( )]
Rate of heat generation = Rate of enthalpy rise + Rate of
heat conduction
( )
For a first order reaction,
( )
( )
( )
( )
(2.11)
( )
( )
[ ( )]
(2.12)
From equation (2.11) and (2.12)
( )
( )
( )
( )
[ ( )] (2.13)
Also,
( )
( ) (2.14)
( )
( )
(2.15)
Development of expressions for entropy data; forD.
constant T1 and T2, with heat generation in the system after
t=0:
For this case, the equation,
( ) ( )
Reduces to
( ) (2.16)
3. Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and
conditions for minimization of energy losses in the process (IJSRD/Vol. 1/Issue 8/2013/0014)
All rights reserved by www.ijsrd.com 1582
For no heat generated in the system. This is possible only at
thermal equilibrium, or when the two bodies exchanging
heat are heat reservoirs [8]
Although above both possibilities exist; in chemical
reactors, it is more probable that generation of heat takes
place in the process fluid section and if rate of heat
generated = rate of heat removed by conduction, a steady
state non-changing temperature T1 is obtained at the process
fluid section. On the other hand, the heat is rejected to
constant inlet temperature utility. In this case, the equation
reduces as:
( )
( )
[
( )]
( )
[ ( )] (2.17)
On analyzing a process that could yield constant T1, and T2,
considering same surface as that considered in previous
sections, it is observed that if total amount of heat generated
in the system is flown out of the system by conduction, T1
remains constant. For T2 to remain constant, continuous
circulation of utility fluid is necessary.
Hence,
̇ ̇
( )
For dT1/dt = 0
( )
Take natural logarithm on both sides,
( ) ( ) ( )
( ) ( ) ( ) (2.18)
k, A, x, Hr, ko , E, R being constants, we have to decide
either of the variables (i.e.) T1 or T2
III. OBSERVATIONS FOR SAMPLE SYSTEMS
Analysis of expressions developed for entropy data forA.
constant T2, decreasing T1, and no heat generation in the
system after t=0:
Let us consider following sample problem [9]. (system) for
effective production of the results of the theoretical
experiments presented in previous section
"The inner and outer surfaces of a closed brick well of
surface area 30m2
and thickness 30 cm are maintained at
temperatures of 20 0
C and 5 0
C respectively. For variable T1
and constant T2, we make following assumptions. Inner
surface of wall gets heat from 100 kg of a process fluid of
temperature independent specific heat capacity 1070
J/kg.0
C. Initial temperature at inner surface, as stated in the
problem is 20 0
C. Whereas the outer surface of the wall is
exposed to a thermal reservoir at constant temperature 5
0
C.There is no generation of heat in the process fluid
compartment."
For this problem,
Heat lost by process fluid = Heat conducted by the wall
For the above problem,
( )
( )
After 10000 such iterations, following type of profiles were
obtained for dS/dt and d2
S/dt2
. Here each iteration can be
considered to be equivalent to time as the iterations are done
for processes that occur immediately one after the other in
series.
Also, by substituting above obtained values for d/dt(dT/dx),
we can easily obtain the value for d2
S/dt2
The profiles obtained are as follows:
Fig. 1: Variation of dS/dt with time equivalent for (III-A)
The data plot fits the fourth order polynomial equation
dS/dt= 4E-13t4
- 6E-09t3
+ 4E-05t2
- 0.119t + 154.6
Which on integrating gives
∫
Fig. 2: A Variation in d2
S/dt2
w.r.t. time for (III-A)
The graph below shows that the data fits a polynomial
equation of order three
= 6E-12t3
- 3E-08t2
+ 8E-05t - 0.099
Analysis of expressions developed for entropy data forB.
constant T2, decreasing T1 with heat generation in the
system after t=0:
Let us assume the same problem that we have analyzed (in
section II, A) with only one difference (i.e.) unlike in
previous section, here we consider an exothermic reaction
with slow rate going on in the brick well at the time of
analysis. Let the reaction be decomposition [10] of N2O to
N2 and O2.
If the reaction is assumed to be of first order, the rate of
reaction can be written as:
( )
y = -1E-17x5 + 4E-13x4 - 6E-09x3 + 4E-05x2 -
0.1197x + 154.6
R² = 0.9999
dS/dt
No. Of iterations (Time equivalent)
4. Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and
conditions for minimization of energy losses in the process (IJSRD/Vol. 1/Issue 8/2013/0014)
All rights reserved by www.ijsrd.com 1583
The system needs to be analyzed separately for high and low
initial values of (T1-T2).
Case-1: CA ≈ Constant, Low initial temperature differences
For a very low rate of reaction, CA may be assumed to be
unit concentration; constant for a definite interval of time.
Let T1 = 300 K and T2 = 270 K,
If the transient behaviour of the system is simulated using
MS-Excel, following profiles are obtained
Fig. 3: Change in dT/dt with time equivalent for (III-B)
This data also fits a polynomial equation of order 5.
= -3E-09t5
+ 8E-07t4
- 1E-04t3
+ 0.005t2
- 0.154t + 1.736
Graph for second order differential of entropy with respect
to time can also be generated as shown below
Fig. 4: Variation in d2
S/dt2
w.r.t. time for (III-B, Case 1)
The analysis of data fits a polynomial equation of degree 6
= -3E-12t6
+ 1E-09t5
- 1E-07t4
+ 1E-05t3
- 0.000t2
+
0.006t - 0.040
The rate of entropy generation can also be plotted as:
Fig. 5: Variation of dS/dt w.r.t. time equivalent, for (III-B,
Case-1)
The polynomial equation that fits the observations is:
dS/dt = 5E-11t6
- 2E-08t5
+ 2E-06t4
- 0.000t3
+ 0.005t2
-
0.094t + 0.630
Integrating gives,
The rate of generation of entropy as function of time
equivalent (t) can be plotted from above equation.
Fig. 6: Change in entropy with time equivalent, for (III-B,
Case-1)
The data better fits a 4th order polynomial equation
perfectly:
ΔS= 24.03t4
- 302.1t3
+ 1491.t2
- 3054.t + 1954
Case 2: CA ≈ constant, Large initial (T1-T2)
Keeping all other parameters same, if the initial temperature
of the system is maintained at 2000 K, following type of
profile is obtained for the reaction:
Fig. 7: Variation of d2
S/dt2
w.r.t. time equivalent, for (III-B,
Case-2)
Fig. 8: Variation of dS/dt w.r.t. time equivalent, for (III-B,
Case-2)
5. Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and
conditions for minimization of energy losses in the process (IJSRD/Vol. 1/Issue 8/2013/0014)
All rights reserved by www.ijsrd.com 1584
The polynomial equation that fits the observations is:
dS/dt = 0.130t2
- 12.33t + 375.8
Integrating above expression gives
Fig. 9: Change in entropy with time equivalent, for (III-B,
Case-2)
This gives plot of entropy generation as function of time
equivalent (t).
Analysis of expressions for entropy data; for constant T1C.
and T2, with heat generation in the system after t=0:
Let us assume the same problem that we have analyzed (in
section II-A) with only one difference (i.e.) unlike in that
section, here we consider an exothermic reaction with slow
rate going on in the brick well at the time of analysis. Let
the reaction be decomposition of N2O to N2 and O2. [11]
If the reaction is assumed to be of first order, the rate of
reaction can be written as:
( )
The variation of values of T2 with values of T1 for having
constant values of T1 and T2 considering the problem of
'decomposition of N2O' is as follows:
Fig. 10: Values of T2 corresponding to values of T1 for (III-
C)
The plot follows a linear equation:
T2 = 0.967T1 + 28.02
Corresponding entropy change rates for universe and the
surroundings are respectively plotted as function of T1 as
follow:
Fig. 11: Change in entropy of universe with T1 for (III-C)
Fig. 12: Change in entropy of universe with T1 for (III-C)
Note that we have not considered / analyzed any case where
temperature of the process fluid side undergoing exothermic
chemical reaction increases with time. Such process may
take place if not all of the heat generated by exothermic
reaction is removed by conduction. As rate of any general
exothermic reaction decreases with increase in temperature
[10], accumulation of heat in process fluid section may lead
to decrease in rate of entropy generation in some cases, but
at the cost of reduction in rate of reaction, which is not
practically acceptable. Hence, the case needs to be discarded
in material selection for conducting surface itself.
IV. RESULTS AND DISCUSSIONS
Development of an algorithm for entropy analysis ofA.
exothermic reactors:
In order to obtain the transient entropy changes in a system
and accordingly to manipulate the variables in order to
minimize the energy losses according to the technique used
in section II, III, IV, hereby an algorithm can be proposed
that suggests sequence of steps for how any system is to be
analyzed for entropy change.
Step. 1 : Using energy balances and definitions in classical
thermodynamics develop expressions for first and second
order differentials of entropy with respect to time.
6. Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and
conditions for minimization of energy losses in the process (IJSRD/Vol. 1/Issue 8/2013/0014)
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Step. 2 : Using heat balances, develop an expression for
change in temperature of the system under observation with
time.
Step. 3 : Feeding the initial conditions and process
parameters to the expression developed in STEP 2, obtain
new value for temperature attained by the system (For one
iteration)
Step. 4 : At the new temperature attained, calculate values
for entropy differentials from expressions developed in
STEP 1.
Step. 5 : If no temperature gradient is left between system
and surroundings, stop the calculation and go to next step.
Else go to STEP 4.
Step. 6 : Plot entropy differentials with respect to time and
obtain a polynomial fit for them. Integrating the first
differential of entropy would produce data for actual entropy
changes in the universe.
Step. 7 : Repeat the procedure for different values of
variable parameters and obtain the most optimum set by trial
and error method.
Proposing a suitable mechanism:B.
From the mathematical analysis of entropy for pure
conductive heat transfer, in order to minimize entropy rise,
we considered a constant temperature utility. However, this
is possible if a huge amount of utility is used. In such case, a
negligible rise in the utility temperature after heat transfer
may cause the energy absorbed by utility to be significantly
lost. Accordingly, a mechanism as follows can be suggested:
Fig. 13: Suitable mechanism for less energy losses from the
process
The utility stream is made to enter the jacket of the reactor
at say temperature T2. The utility fluid gets heated due to
heat of reaction and attains temperature T3. The heated
utility is circulated through rest of the plant for heat
exchange (as heating fluid) in such a way that it again
reaches the original temperature T2. In such a way the
temperature of contacting of the reactor surface and the
utility fluid remains can be kept constant and accordingly,
entropy losses can be minimized. The decision parameters
that need to be optimally fixed in this case are- temperature
of utility and flow rate of utility. However evaluation of
these parameters is out of the scope of this paper.
Significance of the expressions developed for variousC.
cases:
The modelled expressions in section (II-B) are developed
for constant T2, decreasing T1, assuming no heat generation
in the system after t=0. In practical life, this situation is
observed in case of instantaneous reactions and especially in
case of exothermic batch reactors wherein conversion is
rapid while removal of heat is gradual.
The modelled expressions in section (II-C) are
developed for constant T2, decreasing T1 with continuous
heat generation in the reactor system. This depicts moderate
or low rate reactions taking place in the exothermic batch
reactors with gradual heat removal arrangement.
Finally, expressions derived in section (II-D)
represent reactions taking place in continuous reactors as,
due to continuous flow of reactants and utility at definite
inlet temperature, both T1and T2 remain constant. The
choice is offered in temperatures T1and T2 case and no
transient variation of entropy is plotted in this case owing to
the constant entropy change with respect to time
Usage of the equations:D.
As mentioned before, this technique of entropy analysis is
totally trial and error based. Accordingly, one can change
the values of system variables (e.g. k, T1(initial),T2, mass flow
rates, etc.) and obtain different trends of entropy change
with respect to time. Finally, the set of values that offer
lower entropy change without altering the performance of
the reactor in successfully carrying out the process reactions
much, can be selected. Again the energy lost from reactor to
the surrounding fluid can be calculated[3] by formula
. The point at which Q starts falling to a negligible
value, the circulation of utility can be stopped and the
control of heating can be shifted to another utility section.
For non-continuous processes (variable T1and T2), it should
be suggested that two separate parallel utility systems
should be used as far as possible (one-exothermic heat based
and other operating with other source of sufficient exergy),
and a control system should be adopted, sensitive to the heat
output changes of the exothermic reaction such that only
extra amount of heat needed be drawn from the external
utility, the main source being the constant temperature
utility used to cool the exothermic reactor.
LIST OF IMPORTANT SYMBOLS USED
TABLE-I
SYMBOL UNITS DESCRIPTION
T1 K Temperature of higher
temperature section/process fluid
T2 K Temperature of lower
temperature section/utility fluid
k J/m.0
K Thermal conductivity of the
conducting surface
x m Thickness of conducting surface
A m2
Surface area of conducting
surface
t - Time equivalent (No. of
iterations)
Q J Amount of heat transferred
S J/K Amount of entropy
delS J/K Change in entropy
Hr J/mol Heat of exothermic reaction
m kg Mass of process fluid
cp J/kgK Specific heat of process fluid
CA mol Concentration of reactant in pure
terms
7. Development and theoretical analysis of mathematical expressions for change of entropy for exothermic reactions in different reacting environments and
conditions for minimization of energy losses in the process (IJSRD/Vol. 1/Issue 8/2013/0014)
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ACKNOWLEDGMENT
I humbly thank Prof. Dr. M. M. Upkare, Dept. of Chemical
Engineering, Vishwakarma Institute of Technology, Pune
for his consistent help and inspiration for working on
development of mathematical models. I also thank my
mother Shubhangi Kherdekar, the largest source of support
for me in my research work and life.
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