The document numerically investigates natural convection heat transfer from a square cylinder placed horizontally in a square enclosure filled with nanofluids. It presents the following key points:
1) Governing equations for the laminar, steady state, two-dimensional flow of an incompressible nanofluid are developed using the vorticity-stream function formulation.
2) Variables such as thermal conductivity and viscosity are modified to account for the inclusion of nanoparticles based on existing models.
3) The equations are non-dimensionalized and discretized before being solved using the ADI method.
4) Preliminary results show an increase in average Nusselt number with increasing nanoparticle volume fraction over the range
NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER FROM CIRCULAR CYL...IAEME Publication
In the present work, the enhancement of natural convection heat transfer utilizing nano fluids as working fluid from horizontal circular cylinder situated in a square enclosure is investigated numerically. Different types of nano particles were tested. The types of the nano fluids are Cu, Al2O3 and TiO3 with water as base fluid. A model is developed to analyze heat transfer performance of nano fluids inside an enclosure taking into account the solid particle dispersionrs on the flow and heat
transfer characteristics.
Computational Analysis of Natural Convection in Spherical Annulus Using FEVIJMER
HEAT transfer by natural convection from a body to its finite enclosure is of importance
in nuclear reactor technology, electronic instrumentation packaging, aircraft cabin design, the
analysis of fluid suspension gyrocompasses, and numerous other practical situations. The steady
natural convection heat transfer of fluids between two concentric isothermal spheres is investigated
computationally with the help of FEV in ANSYS 14.5. The inner wall is subjected to a higher
temperature and outer is at room temperature. The steady behavior of the flow field and its
subsequent effect on the temperature distribution for different Rayleigh numbers and radius ratios
are analyzed.
Bossious boundary condition is taken for natural convection and which is solved in fluent
module. Steady solutions of the entire flow field is obtained for Rayleigh number (5x101<ra><105),><rr><3). The result shows that the Rayleigh number and
radius ratio have a profound influence on the temperature and flow fields and Prandlt number has
very negligible effect. The results of average Nusselt numbers are also compared with those of
previous numerical investigations. Excellent agreement is obtained.
Numerical Study of Mixed Convection of Nanofluid in a Concentric Annulus with...A Behzadmehr
In this work, the steady and laminar mixed convection of nanofluid in horizontal concentric annulus with
rotating inner cylinder is investigated numerically. The inner and outer cylinders are kept at constant
temperature Ti and To respectively, where Ti>To. The annular space is filled with Alumina-water nanofluid.
The governing equations with the corresponded boundary conditions in the polar coordinate are discretized
using the finite volume method where pressure-velocity coupling is done by the SIMPLER algorithm.
Numerical results have been obtained for Rayleigh number ranging from 102 to 105, Reynolds number from 1 to 300 and nanoparticles volume fraction from 0.01 to 0.06. The effects of the Reynolds and Rayleigh numbers, average diameter of nanoparticles and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the annuli are investigated. According to the results, the average Nusselt number decreases with increasing the Reynolds number. However, the average Nusselt number increases by increasing the Rayleigh number. Moreover, the maximum average Nusselt number occurs for an optimal nanoparticle volume fraction except situations that heat conduction predominates over the heat convection. In these conditions the average Nusselt number is close to unity.
Fuzzy numbers, Nth - order Fuzzy Initial Value Problems, Runge-Kutta method, ...IOSR Journals
A numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics
(MHD) free convection for heat flow patterns within trapezoidal enclosures. A finite element analysis is
performed to investigate the effects of unifor heating and is also used for solving the Navier-Stokes and
Energybalance equations.In this study, cold bottom walls, uniformly heated left and right (side) walls and
insulated top walls with inclination angles (ф) are considered in a trapezoidal enclosure. The present numerical
procedure adopted in this investigation yields consistent performance over a wide range of parameters, Prandtl
numbers, (Pr = 0.026 - 0.7), and Rayleigh numbers (Ra = 103 – 105), Hartmann number (Ha = 50) with various
tilt angles Ф = 450, 300 and 00(square).Numerical results are presented in terms of streamlines, isotherms, heat
function (total heat flux) and nusselt numbers.for different Ra and Pr. As Ra increases conduction dominant
region changes for different Pr. Complete heat transfer analysis is performed in terms of local and average
nusselt numbers.
NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER FROM CIRCULAR CYL...IAEME Publication
In the present work, the enhancement of natural convection heat transfer utilizing nano fluids as working fluid from horizontal circular cylinder situated in a square enclosure is investigated numerically. Different types of nano particles were tested. The types of the nano fluids are Cu, Al2O3 and TiO3 with water as base fluid. A model is developed to analyze heat transfer performance of nano fluids inside an enclosure taking into account the solid particle dispersionrs on the flow and heat
transfer characteristics.
Computational Analysis of Natural Convection in Spherical Annulus Using FEVIJMER
HEAT transfer by natural convection from a body to its finite enclosure is of importance
in nuclear reactor technology, electronic instrumentation packaging, aircraft cabin design, the
analysis of fluid suspension gyrocompasses, and numerous other practical situations. The steady
natural convection heat transfer of fluids between two concentric isothermal spheres is investigated
computationally with the help of FEV in ANSYS 14.5. The inner wall is subjected to a higher
temperature and outer is at room temperature. The steady behavior of the flow field and its
subsequent effect on the temperature distribution for different Rayleigh numbers and radius ratios
are analyzed.
Bossious boundary condition is taken for natural convection and which is solved in fluent
module. Steady solutions of the entire flow field is obtained for Rayleigh number (5x101<ra><105),><rr><3). The result shows that the Rayleigh number and
radius ratio have a profound influence on the temperature and flow fields and Prandlt number has
very negligible effect. The results of average Nusselt numbers are also compared with those of
previous numerical investigations. Excellent agreement is obtained.
Numerical Study of Mixed Convection of Nanofluid in a Concentric Annulus with...A Behzadmehr
In this work, the steady and laminar mixed convection of nanofluid in horizontal concentric annulus with
rotating inner cylinder is investigated numerically. The inner and outer cylinders are kept at constant
temperature Ti and To respectively, where Ti>To. The annular space is filled with Alumina-water nanofluid.
The governing equations with the corresponded boundary conditions in the polar coordinate are discretized
using the finite volume method where pressure-velocity coupling is done by the SIMPLER algorithm.
Numerical results have been obtained for Rayleigh number ranging from 102 to 105, Reynolds number from 1 to 300 and nanoparticles volume fraction from 0.01 to 0.06. The effects of the Reynolds and Rayleigh numbers, average diameter of nanoparticles and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the annuli are investigated. According to the results, the average Nusselt number decreases with increasing the Reynolds number. However, the average Nusselt number increases by increasing the Rayleigh number. Moreover, the maximum average Nusselt number occurs for an optimal nanoparticle volume fraction except situations that heat conduction predominates over the heat convection. In these conditions the average Nusselt number is close to unity.
Fuzzy numbers, Nth - order Fuzzy Initial Value Problems, Runge-Kutta method, ...IOSR Journals
A numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics
(MHD) free convection for heat flow patterns within trapezoidal enclosures. A finite element analysis is
performed to investigate the effects of unifor heating and is also used for solving the Navier-Stokes and
Energybalance equations.In this study, cold bottom walls, uniformly heated left and right (side) walls and
insulated top walls with inclination angles (ф) are considered in a trapezoidal enclosure. The present numerical
procedure adopted in this investigation yields consistent performance over a wide range of parameters, Prandtl
numbers, (Pr = 0.026 - 0.7), and Rayleigh numbers (Ra = 103 – 105), Hartmann number (Ha = 50) with various
tilt angles Ф = 450, 300 and 00(square).Numerical results are presented in terms of streamlines, isotherms, heat
function (total heat flux) and nusselt numbers.for different Ra and Pr. As Ra increases conduction dominant
region changes for different Pr. Complete heat transfer analysis is performed in terms of local and average
nusselt numbers.
Experiment on single-mode feedback control of oscillatory thermocapillary con...IJERA Editor
Feedback control was carried out on nonlinear thermocapillary convections in a half-zone liquid bridge of a high
Prandtl number fluid under normal gravity. In the liquid bridge, the convection changed from a two-dimensional
steady flow to a three-dimensional oscillatory flow at a critical temperature difference. Feedback control was
realized by locally modifying the free surface temperature using local temperature measured at different
positions. The present study aims to confirm whether the control method can effectively suppress oscillatory
flows with every modal structure. Consequently, the control was theoretically verified to be effective for
oscillatory flows with every modal structure in a high Marangoni number range.
THE EFFECT OF TRANSVERSE VIBRATION ON THE NATURAL CONVECTION HEAT TRANSFER IN...IAEME Publication
The effect of transverse vibration on the natural convection heat transfer in a
rectangular enclosure with an aspect ratio of 0.5 filled with air as a working fluid
aligned horizontally on a mechanical shaker generating a sinusoidal transverse
vibrational displacement was studied experimentally. The study was carried for a
Raghiely number between (3.77 - 10.8)*107 with applied heat flux between (20 - 45)
Watt. The vibrational experimental measurements were carried out for different
frequency ratio (0.87-1.6) and vibrational Rayleigh number ranged between (0.12 -
2.7)*107. The results of the heat transfer inside the enclosure without vibration show
a very close agreement with the published one. The vibrational heat transfer results
show that the behavior of different heat transfer convection parameters can be
affected by applying a forced vibration condition. It is shown that the high heat
transfer can be achieved at frequencies near to the system natural frequency at
constant heat flux. Also, it is concluded that a careful attention should be given to the
proper selection of heat flux and frequency ratio results in obtaining maximum values
of heat transfer parameters with low cost of power consumption.
The Force Convection Heat Transfer of A Nanofluid Over A Flat Plate: Using Th...AEIJjournal2
A drift-flux model is utilized to theoretically analyze the boundary layer flow and heat transfer of a
nanofluid over a flat plate. The concentration of nanoparticles at the plate is obtained using the solution of
the governing equations. Assuming a fixed magnitude of free stream velocity, the results show that the heat
transfer may enhance up to 22% or decrease about -7% by using nanofluids compared to the pure base
fluid.
Learn about Conduction, Convection, Radiation and Heat exchangers in a most comprehensive and interactive way. Derivations of formulas, concepts, Numerical, examples are inculcated in the course with advance applications. The course aims at covering all the topics and concepts of HMT as per academics of students. Following are the topics (in detail) that will be covered in the course.
Conduction
Thermal conductivity, Heat conduction in gases, Interpretation Of Fourier's law, Electrical analogy of heat transfer, Critical radius of insulation, Heat generation in a slab and cylinder, Fins, Unsteady/Transient conduction.
Convection
Forced convection heat transfer, Reynold’s Number, Prandtl Number, Nusselt Number, Incompressible flow over flat surface, HBL, TBL, Forced convection in flow through pipes and ducts, Free/Natural convection.
Heat Exchangers
Types of heat exchangers, First law of thermodynamics, Classification of heat exchangers, LMTD for parallel and counter flow, NTU, Fouling factor.
Radiation
Absorbtivity, Reflectivity, Transmitivity, Laws of thermal radiation, Shape factor, Radiation heat exchange
COPY-PASTE below URL to ENROLL in the COMPLETE course & see the hidden contents with proper explanations.
https://www.udemy.com/course/heat-and-mass-transfer
This presentation is made to provide the overall conceptual knowledge on Chilton Colburn Analogy. It includes basis, importance, assumption, advantages, limitations and applications in addition to the derivation. Make It Useful!
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mechanical and civil engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mechanical and civil engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER FROM CIRCULAR CYL...IAEME Publication
In the present work, the enhancement of natural convection heat transfer utilizing nanofluids as working fluid from horizontal circular cylinder situated in a square enclosure is investigated numerically. The type of the nanofluid is the water-based copper Cu. A model is developed to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersionrs on the flow and heat transfer characteristics. The study uses different Raylieh
numbers (104 , 105 , and 106 ), different enclosure width to cylinder diameter ratios W/D (1.667, 2.5 and 5) and volume fraction of nanoparticles between 0 to 0.2. The work included the solution of the governing equations in the vorticity-stream function formulation which were transformed into body fitted coordinate system
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
Experiment on single-mode feedback control of oscillatory thermocapillary con...IJERA Editor
Feedback control was carried out on nonlinear thermocapillary convections in a half-zone liquid bridge of a high
Prandtl number fluid under normal gravity. In the liquid bridge, the convection changed from a two-dimensional
steady flow to a three-dimensional oscillatory flow at a critical temperature difference. Feedback control was
realized by locally modifying the free surface temperature using local temperature measured at different
positions. The present study aims to confirm whether the control method can effectively suppress oscillatory
flows with every modal structure. Consequently, the control was theoretically verified to be effective for
oscillatory flows with every modal structure in a high Marangoni number range.
THE EFFECT OF TRANSVERSE VIBRATION ON THE NATURAL CONVECTION HEAT TRANSFER IN...IAEME Publication
The effect of transverse vibration on the natural convection heat transfer in a
rectangular enclosure with an aspect ratio of 0.5 filled with air as a working fluid
aligned horizontally on a mechanical shaker generating a sinusoidal transverse
vibrational displacement was studied experimentally. The study was carried for a
Raghiely number between (3.77 - 10.8)*107 with applied heat flux between (20 - 45)
Watt. The vibrational experimental measurements were carried out for different
frequency ratio (0.87-1.6) and vibrational Rayleigh number ranged between (0.12 -
2.7)*107. The results of the heat transfer inside the enclosure without vibration show
a very close agreement with the published one. The vibrational heat transfer results
show that the behavior of different heat transfer convection parameters can be
affected by applying a forced vibration condition. It is shown that the high heat
transfer can be achieved at frequencies near to the system natural frequency at
constant heat flux. Also, it is concluded that a careful attention should be given to the
proper selection of heat flux and frequency ratio results in obtaining maximum values
of heat transfer parameters with low cost of power consumption.
The Force Convection Heat Transfer of A Nanofluid Over A Flat Plate: Using Th...AEIJjournal2
A drift-flux model is utilized to theoretically analyze the boundary layer flow and heat transfer of a
nanofluid over a flat plate. The concentration of nanoparticles at the plate is obtained using the solution of
the governing equations. Assuming a fixed magnitude of free stream velocity, the results show that the heat
transfer may enhance up to 22% or decrease about -7% by using nanofluids compared to the pure base
fluid.
Learn about Conduction, Convection, Radiation and Heat exchangers in a most comprehensive and interactive way. Derivations of formulas, concepts, Numerical, examples are inculcated in the course with advance applications. The course aims at covering all the topics and concepts of HMT as per academics of students. Following are the topics (in detail) that will be covered in the course.
Conduction
Thermal conductivity, Heat conduction in gases, Interpretation Of Fourier's law, Electrical analogy of heat transfer, Critical radius of insulation, Heat generation in a slab and cylinder, Fins, Unsteady/Transient conduction.
Convection
Forced convection heat transfer, Reynold’s Number, Prandtl Number, Nusselt Number, Incompressible flow over flat surface, HBL, TBL, Forced convection in flow through pipes and ducts, Free/Natural convection.
Heat Exchangers
Types of heat exchangers, First law of thermodynamics, Classification of heat exchangers, LMTD for parallel and counter flow, NTU, Fouling factor.
Radiation
Absorbtivity, Reflectivity, Transmitivity, Laws of thermal radiation, Shape factor, Radiation heat exchange
COPY-PASTE below URL to ENROLL in the COMPLETE course & see the hidden contents with proper explanations.
https://www.udemy.com/course/heat-and-mass-transfer
This presentation is made to provide the overall conceptual knowledge on Chilton Colburn Analogy. It includes basis, importance, assumption, advantages, limitations and applications in addition to the derivation. Make It Useful!
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mechanical and civil engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mechanical and civil engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER FROM CIRCULAR CYL...IAEME Publication
In the present work, the enhancement of natural convection heat transfer utilizing nanofluids as working fluid from horizontal circular cylinder situated in a square enclosure is investigated numerically. The type of the nanofluid is the water-based copper Cu. A model is developed to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersionrs on the flow and heat transfer characteristics. The study uses different Raylieh
numbers (104 , 105 , and 106 ), different enclosure width to cylinder diameter ratios W/D (1.667, 2.5 and 5) and volume fraction of nanoparticles between 0 to 0.2. The work included the solution of the governing equations in the vorticity-stream function formulation which were transformed into body fitted coordinate system
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
Effect of Radiation on Mixed Convection Flow of a Non-Newtonian Nan fluid ove...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
The Effects of Nanofluids on Forced Convection Heat Transfer Inside Parallel ...AI Publications
A numerical solution on forced convection of Al2O3-water nanofluid for different volume fractions is investigated for laminar flow through a parallel plate with flush mounted discrete heat sources. The model used for nanofluid mixture is a single-phase approach and fluid properties are considered constant with temperature. The finite difference method is used for solutions and four different volume fractions are considered varying from 0% to 4%. A fully developed laminar velocity profile is considered and the parallel plate is assumed as heated with three discrete heat sources flush mounted to the top and bottom plate with the same lengths. Uniform wall temperature boundary condition is taken for discrete heaters. Peclet numbers are in the range of 20-100. For comparison and validity of the solution the results for a classical problem, laminar flow through a parallel plate which is heated at the downstream region with constant temperature, are obtained. Results are presented in terms of bulk temperature, heat flux, and local Nusselt number. Heat transfer is enhanced with the particle volume concentration. For comparison, pure water results are also shown in the figures. At the locations where heat is applied the heat flux values decrease as the volume fraction increase and the bulk temperature values are higher for the higher volume fractions at the heated locations. As the volume fraction increases the local Nusselt number can increase up to 30% than to pure water.
MHD Chemically Reacting and Radiating Nanofluid Flow over a Vertical Cone Emb...IJLT EMAS
In this study, we examine the combined effects of
thermal radiation, chemical reaction on MHD hydromagnetic
boundary layer flow over a vertical cone filled with nanofluid
saturated porous medium under variable properties. The
governing flow, heat and mass transfer equations are
transformed into ordinary differential equations using similarity
variables and are solved numerically by a Galerkin Finite
element method. Numerical results are obtained for
dimensionless velocity, temperature, nanoparticle volume
fraction, as well as the skin friction, local Nusselt and Sherwood
number for the different values of the pertinent parameters
entered into the problem. The effects of various controlling
parameters on these quantities are investigated. Pertinent
results are presented graphically and discussed quantitatively.
The present results are compared with existing results and found
to be good agreement. It is found that the temperature of the
fluid remarkably enhances with the rising values of Brownian
motion parameter (Nb).
FREE CONVECTION HEAT TRANSFER OF NANOFLUIDS FROM A HORIZONTAL PLATE EMBEDDED ...AEIJjournal2
In this paper the natural convection heat transfer from a horizontal plate embedded in a porous medium
saturated with a nanofluid is numerically analyzed. By a similarity approach the partial differential
equations are reduced to a set of two ordinary differential equations. In order to evaluate the influence of
nanoparticles on the heat transfer, Ag and Cuo as the nanoparticles were selected. Results show that heat
transfer rate (Nur) is a decreasing function of volume fraction of nanoparticles.
Study on Thermal and Hydrodynamic Indexes of a Nanofluid Flow in a Micro Heat...A Behzadmehr
The paper numerically presents laminar forced convection of a nanofluid flowing in a duct at microscale.
Results were compared with both analytical and experimental data and observed good concordance with
previous studies available in the literature. Influences of Brinkman and Reynolds number on thermal and
hydrodynamic indexes have been investigated. For a given nanofluid, no change in efficiency (heat dissipation
to pumping power) was observed with an increasing in Reynolds number. It was shown that the pressure was
decrease with an increase in Brinkman number. Dependency of Nu increment changes with substrate material.
Convective Heat And Mass Transfer Flow Of A Micropolar Fluid In A Rectangular...IJERA Editor
In this chapter we make an investigation of the convective heat transfer through a porous medium in a Rectangular enclosure with Darcy model. The transport equations of liner momentum, angular momentum and energy are solved by employing Galerkine finite element analysis with linear triangular elements. The computation is carried out for different values of Rayleigh number – Ra micropolar parameter – R, spin gradient parameter, Eckert number Ec and heat source parameter. The rate of heat transfer and couple stress on the side wall is evaluated for different variation of the governing parameters.
A three-dimensional numerical analysis of laminar natural convection with entropy generation in an open trapezoidal cavity filled with water has been carried out. In this investigation, the inclined wall is maintained at isothermal hot temperature while cold water enters into the cavity from its right open boundary and all other walls are assumed to be perfect thermal insulators. Attention is paid on the effects of buoyancy forces on the flow structure and temperature distribution inside the open enclosure. Rayleigh number is the main parameter which changes from 103 to 105 and Prandtl number is fixed at Pr =6.2. Obtained results have been presented in the form of particles trajectories, iso-surfaces of temperature and those of entropy generated as well as the average Nusselt number. It has been found that the flow structure is sensitive to the value of Rayleigh number and that heat transfer increases with increasing this parameter.
Investigation of the Effect of Nanoparticles Mean Diameter on Turbulent Mixed...A Behzadmehr
Abstract
Turbulent mixed convection of a nanofluid (water/Al2O3, Φ=.02) has been studied numerically. Two-phase
mixture model has been used to investigate the effects of nanoparticles mean diameter on the flow parameters. Nanoparticles distribution at the tube cross section shows that the particles are uniformly dispersed. The non-uniformity of the particles distribution occurs in the case of large nanoparticles and/or high value of the Grashof numbers. The study of particle size effect showed that the effective Nusselt number and turbulent intensity increases with the decreased of particle size.
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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.
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/
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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.
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.
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.
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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Runway Orientation Based on the Wind Rose Diagram.pptx
NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFERFROM SQUARE CYLINDER IN AN ENCLOSED ENCLOSURE FILLED WITH NANOFLUIDS
1. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
DOI : 10.14810/ijmech.2015.4401 1
NUMERICAL INVESTIGATION OF NATURAL
CONVECTION HEAT TRANSFERFROM SQUARE
CYLINDER IN AN ENCLOSED ENCLOSURE
FILLED WITH NANOFLUIDS
Omar M. Ali1
and Ghalib Y. Kahwaji2
1
Department of Mech. Eng., University of Zakho, Iraq
omarsulivany@gmail.com.
2
Department of Mech. Eng., Rochester Institute of Technology-Dubai, UAE
gykcad@rit.edu
ABSTRACT
The enhancement of natural convection heat transfer using nanofluids from horizontal square cylinder
placed in a square enclosure is investigated numerically. Water-based Cu is used as the working nanofluid.
The investigation covered a range of Rayleigh numbers of 104
- 106
, nanoparticles volume fraction of
(0<ϕ≤0.2), enclosure width to cylinder height ratio, W/H of 2.5. The investigation includes the solution of
the governing equations in the Vorticity-Stream function space with the aid of a body fitted coordinate
system. Algebraic grid generation is used in the initial transformations, followed by an elliptic
transformation to complete the grid generation to computational domain. The resulting discretized system
of equations is solved using an ADI method. The built code is validated and the results showed an increase
in average Nusselt number with increasing the volume fraction of the nanoparticles for the whole range of
Rayleigh number. The isotherms are nearly similar when the volume fraction of nanoparticles is increased
from 0 to 0.2 for each Rayleigh number but a change in the streamlines is observed.
KEYWORDS:
Heat Transfer, Square Cylinder, Square Enclosure, Numerical.
NOMENCLATURE
Symbol Definition Unit
Symb
ol
Definition Unit
di,j
Source term in equation,
eqn. (18).
Greek Symbols
f
Volume fraction of
nanofluid.
∆T Temperature difference. °C
h
Convective heat transfer
coefficient.
W/m2
.
°C
µ Viscosity of the air. kg/ms
H Height of the cylinder.
m
β
Coefficient of thermal
expansion.
1/°C
J Jacobian. η
Vertical axis in computational
domain.
k
Thermal conductivity-
air.
W/m.°
C
ξ
Horizontal axis in
computational domain.
Nu Average Nusselt number Ψ Dimensionless stream function.
2. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
2
p Pressure. N/m2
ω Vorticity. 1/s
P
Coordinate control
function.
ϖ Dimensionless vorticity.
Pr Prandtl number, (ν/α). υ Kinematic viscosity. m2
/s
Q
Coordinate control
function.
θ Dimensionless temperature.
R
Maximum absolute
residual
ϕ Volume fraction of nanofluid.
Ra
Raylieh number,
(gβ∆TH3
/να).
φ Dependent variable.
t Time.
second
s
ψ Stream Function.
1/sec.
T Temperature. °C Subscript
u Velocity in x-direction. m/s s Cylinder surface.
v Velocity in y-direction. m/s ∞ Environment.
W Enclosure Width. cm X Derivative in x-direction.
W Relaxation factor. Y Derivative in y-direction.
x
Horizontal direction in
physical domain.
m
ξ Derivative in ξ-direction.
X
Dimensionless
horizontal direction in
physical domain.
D Circular cylinder diameter.
y
Vertical axis in physical
domain.
m
ψ Stream function.
Y
Dimensionless vertical
axis in physical domain.
T Temperature.
1. INTRODUCTION
There are a number of practical applications of natural convection heat transfer from very long
horizontal cylinders of noncircular sections. This subject has received only limited attention in the
literature, Ali, [1]. Nanofluids are defined as fluids which consist of a base fluid such as water
with nano-size particles (e.g. metal, metal oxide, and carbon materials), suspended in it. The size
of the nanoparticles is between 1-100 nm. The dispersion of highly-conductive nanoparticles into
the base liquids is seen as a promising approach to improve the performance of the engineered
heat transfer fluids, Choi [2]. Zi-Tao Yu, et al. [3], reviewed the reported literature bout laminar
natural convection of nanofluids in confined regions (square and rectangular cavities, horizontal
annuli and triangular enclosures), for a variety of combinations of base liquids and nanoparticles.
Nanofluids were considered as single phase fluids and the presence of nanoparticles plays a role
in modifying the macroscopic thermo-physical properties of their base liquids. A large number of
studies have dealt with the mechanism s of thermo-physical properties of the nanofluids, Zi-Tao
Yu, et al, [4]. The results indicated a gradual decrease in Nusselt number with the decrease of the
volume at constant Rayleigh number.
Natural convection heat transfer in horizontal annuli using variable properties of Al2O3–water
nanofluid is studied numerically by Eiyad Abu-Nada [5], where the heat transfer enhancement in
the annulus is evaluated using different models of viscosity and thermal conductivity. It was
observed that the Nguyen et al. data and Brinkman model gives completely different predictions
at Ra≥104
where the difference in prediction of Nusselt number reached 30%.
Hakan, et al, [6], studied the heat transfer and fluid flow due to buoyancy forces in a partially
heated enclosure using different types of nanoparticles. A heater is located to the left vertical wall
with a finite length. The governing equations were solved using finite volume technique.
3. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
3
Different types of nanofluids are used with variable range of Rayleigh number, height of heater,
location of heater, aspect ratio and volume fraction of nanoparticles. Nusselt number increased
with the volume fraction of nanoparticles for the whole range of Rayleigh number. Heat transfer
also enhances with increasing of height of heater. It was found that the heater location affects the
flow and temperature fields and the heat transfer enhancement, using nanofluids, is more
pronounced at low aspect ratio than at high aspect ratio.
The present work deals with numerical investigation of natural convection heat transfer fora
water-based Cu nanofluid and a square horizontal cylinder situated in closed square cavity. The
work investigates the effect of nanofluids on the flow and heat transfer characteristics. The study
uses different Rayleigh numbers, and different volume fraction of nanoparticles.
2. MATHEMATICAL FORMULATION
Figure (1) displays a schematic diagram of the flow between the heated horizontal square cylinder
and the enclosure. The fluid is water containing nano-sized particles of copper. It is assumed that
the fluid is incompressible, the base fluid (water) and nanoparticles are in thermal equilibrium and
no slip condition occurs between them. The governing equations were solved under the
assumptions that the flow is laminar, no internal heat sources, flow is two-dimensional and
Boussinesq approximation applies. The thermo-physical properties, given in table (1), are
assumed to be constant, [6].
Table 1. Thermo-physical properties of the pure fluid and the nanoparticles, Hakan, et al, [6]
Physical Properties Fluid phase (water) Nanoparticles (Cu)
Cp (J/kg.°K) 4197 385
ρ (kg/m3
) 997.1 8933
k (W/m.°K) 0.613 400
α×107
(m2
/sec) 1.47 1163.1
β×10-5
(m2
/sec) 21 1.67
Figure 1. Configuration of cylinder-enclosure combination
The steady, incompressible continuity equation is given by, [6]:
0=
∂
∂
+
∂
∂
y
v
x
u
(1)
The x –momentum equation is:
W
W
TT∞
T∞
4. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
4
( ) Tgg
y
u
x
u
x
p
y
u
v
x
u
u
t
u
nf
nf
nf
nf
∆+
∂
∂
+
∂
∂
+
∂
∂
−=
∂
∂
+
∂
∂
+
∂
∂
ρ
βρ
ν
ρ
&
2
2
2
2
1
(2)
The y–momentum equation is:
( )
Tgg
y
v
x
v
x
p
y
v
v
x
v
u
t
v
nf
nf
nf
nf
∆+
∂
∂
+
∂
∂
+
∂
∂
−=
∂
∂
+
∂
∂
+
∂
∂
ρ
βρ
ν
ρ
&
2
2
2
2
1
(3)
And the energy equation is given by:
∂
∂
+
∂
∂
=
∂
∂
+
∂
∂
+
∂
∂
2
2
2
2
y
T
x
T
y
T
v
x
T
u
t
T
nfα (4)
With Boussinesq approximations, the density is constant for all terms in the governing equations
except for the buoyancy force term where the density is a assumed a linear function of the
temperature.
( )To ∆−= βρρ &1 (5)
where β is the coefficient of thermal expansion. The stream function (ψ) and vorticity (ω) are
defined as follows, Anderson [7], and Petrovic [8]:
x
v
y
u
∂
∂
−=
∂
∂
=
ψψ
, (6)
y
u
x
v
∂
∂
−
∂
∂
=ω (7)
Or V
r
×∇=ω
Substitution in the governing equations yields:
Energy Equation:
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
∂
Ψ∂
−
∂
∂
∂
Ψ∂
+
∂
∂
yyxxyxxyt
θ
λ
θ
λ
θθθ
(8)
Momentum Equation:
5. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
5
( ) ( )
( )
( )
x
Ra
yx
yxxyt
s
f
f
s
s
f
f
s
∂
∂
+
−
+
+
−
+
∂
∂
+
∂
∂
+−−
=
∂
∂
∂
Ψ∂
−
∂
∂
∂
Ψ∂
+
∂
∂
θ
ρ
ρ
ϕ
ϕ
β
β
ρ
ρ
ϕ
ϕ
ϖϖ
ρ
ρ
ϕϕϕ
ϖϖϖ
1
1
1
1
1
1
Pr
11
Pr
2
2
2
2
25.0
(9)
Continuity Equation:
ϖ−=
∂
Ψ∂
+
∂
Ψ∂
2
2
2
2
yx
(10)
Where
λ =
ೖ
ೖ
ሺଵିఝሻାఝ
൫ഐು൯ೞ
൫ഐು൯
(11)
ߙ =
ሺఘುሻ
(12)
The effective density and heat capacitance of the nanofluid are calculated from:
ߩ = ሺ1 − ߮ሻߩ + ߮ߩ௦ (13)
ሺߩܥሻ = ሺ1 − ߮ሻሺߩܥሻ + ߮ሺߩܥሻ௦ (14)
Assuming that the nanoparticles are spherical, the effective thermal conductivity of the nanofluid
is approximated by the Maxwell–Garnetts model:
=
ೞାଶିଶఝ൫ିೞ൯
ೞାଶାఝ൫ିೞ൯
(15)
The viscosity of the nanofluid can be considered as that of a base fluid containing dilute
suspension of fine spherical particles, Brinkman [9]:
ߤ =
ఓ
ሺଵିఝሻమ.ఱ (16)
Introducing the following dimensionless variables:
6. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
6
H
x
X = ,
H
y
Y = ,
f
uH
U
α
= ,
f
vH
V
α
= ,
2
H
t fα
τ = ,
fα
ψ
=Ψ ,
f
H
α
ω
ϖ
2
= ,
∞
∞
Τ−Τ
Τ−Τ
=
c
θ (17)
Transforms the governing equations to:
(18)
Whereφ is any dependent variable. The governing equations are obtained by replacing the
dependent variable φin the three governing equations as follow:
φ aφ bφ dφ
ψ 0 1 ω
ω 1 ( ) ( )
+−−
f
s
ρ
ρ
ϕϕϕ 11
Pr
25.0
( )
( )
( ) ( )[ ]ηξξη θθ
ρ
ρ
ϕ
ϕβ
β
ρ
ρ
ϕ
ϕ
yyRa
s
ff
s
s
f
−
+
−
+
+
−
1
1
1
1
1
1
Pr
T 1 λ 0
Note that
t∂
∂φ
represents the unsteady term,
∂
∂
−
∂
∂
ηξ
φ
ξ
ψ
φ
η
ψ
J
1
is the convective term,
( )φφ∇∇b ;is the diffusion term, and φd is the source term.
2.1 Grid Generation
The initial computational grid, generated using an algebraic grid generation technique are fed into
elliptic, Poisson equations to generate the final orthogonal computational grid points:
( )ηξξξ ,Pyyxx =+ (19a)
( )ηξηη ,Qyyxx =+ (19b)
Interchanging dependent and independent variables for equations (19a, and b), gives:
( ) 0
2
2
=+
++−
ηξ
ηηξηξξ γβα
xQxPJ
xxx
(20a)
( ) φφ
ηξ
φ φφ
ξ
ψ
φ
η
ψφ
db
Jt
a +∇∇=
∂
∂
−
∂
∂
+
∂
∂ 1
7. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
7
( ) 0
2
2
=+
++−
ηξ
ηηξηξξ γβα
yQyPJ
yyy
(20b)
Where 22
ηηα yx += , ηξηξβ yyxx += , and 22
ξξγ yx +=
The coordinate control functions P and Q are chosen to influence the structure of the grid, [10].
The solution of these equations is obtained using Successive over Relaxation (SOR) method with
relaxation factor value equal to 1.4, [11and 12].The transformed computational grid is shown in
figure (2) below.
Figure 2. Physical to computational domains transformation using elliptic grid generation.
2.2 Solution Procedure
The governing equations were converted into algebraic equations using Finite Volume based
Finite Difference method, Ferziger [13].
The hybrid scheme (of the central and the upwind differencing schemes) is used to avoid the
instability of the central differencing scheme (second order for convective term) at high Peclet
number (Cell Reynolds Number) and the inaccuracy of the upwind differencing scheme (first
order for convective term).
( ) jijijijijiM
o
P
o
PSSNNWWEEPP
da
aaaaaa
,1,11,11,11,1 ++−−
+++++=
+−−+−−++ φφφφ
φφφφφφ
(21)
o
PSNWEP aaaaaa ++++= (22)
The resulting algebraic equation is solved using alternating direction implicit method ADI in two
sweeps; in the first sweep, the equations are solved implicitly in ξ-direction using Cyclic Tri-
Diagonal Matrix Algorithm (CTDMA), because of its cyclic boundary conditions, and explicitly
in η-direction. In the second sweep, the equations are solved implicitly in η-direction using Tri-
Diagonal Matrix Algorithm (TDMA) and explicit in ξ-direction.
8. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
8
The solution of the stream function equation was obtained using Successive Over-Relaxation
method (SOR).
The initial conditions of the flow between heated cylinder and vented enclosure are:
Ψ=0, θ = 0, ω= 0; for t = 0 (23)
The temperature boundary condition of the cylinder surface was assumed as constant.
0=
∂
∂
m
η
θ
; atthe enclosure wall (24a)
Using 2nd
order difference equation, the temperature at the enclosure surface becomes:
2,1,,
3
1
3
4
−− −= mimimi θθθ (24b)
Vorticity boundary conditions, Roache [14], are
( )1,,2
2
−−= mimi
J
ψψ
γ
ϖ at enclosure wall (25a)
( )2,1,2
2
ii
J
ψψ
γ
ϖ −= at cylinder surface (25b)
The stream function of the cylinder and the enclosure are assumed equal to zero.
The Nusselt number Nu is a non-dimensional heat transfer coefficient that calculated in the
following manner:
fk
hD
Nu =
(27)
The heat transfer coefficient is expressed as
h =
୯౭
ౄିై
(28)
The thermal conductivity is expressed as
k୬ = −
୯౭
பθ ப୬⁄
(29)
Substituting Equations (24), (25), and (7) into Equation (23), using the dimensionless quantities,
the Nusselt number on the left wall is written as:
ζ
θπ
∂
∂
∂
−= ∫
2
0
nk
k
Nu
f
nf
(30a)
The derivative of the non-dimensional temperature is calculated using the following formula,
Fletcher [15]:
9. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
9
( ) η
θγ
γθβθ
γ
θ
ηξ
η ∂
∂
=+−=
∂
∂
= JJn const
1
.
(30b)
And θξ = 0 at cylinder surface
A computer program in (Fortran 90) was built to execute the numerical algorithm explained
above; it is general for a natural convection from heated cylinder situated in an enclosure.
3. RESULTS AND DISCUSSION
The developed numerical solution is used to solve the natural convection heat transfer from a
square horizontal cylinder placed in a square enclosure. The enclosure is filled with nano-fluid
with Prandtl number of 6.2. The enclosure width to cylinder characteristic length ratio W/H =2.5,
Rayleigh numbers of 104
, 105
, and 106
, and volume fractions of nanofluid ϕ are 0, 0.05, 0.1, 0.15
and 0.2were studied.
The convergence criteria are chosen as RT<10-6
, Rψ<10-6
and Rω<10-6
for T, ψ and ω
respectively. When all the three criteria are satisfied, the convergent results are subsequently
obtained.
3.1 Stability and Grid Independency Study
The stability of the numerical method is investigated for the case Ra=105
, W/D=2.5, Pr = 0.7.
Three time steps are chosen with values 1×10-4
, 5×10-4
, 5×10-6
. The maximum difference between
the values of Nu with different time steps is 2%. The grid-independence of numerical results is
studied for the case with Ra=104
, and 105
, W/D =2.5, Pr = 6.2. Three mesh sizes of 96×25,
128×45, and 192×50 were used for the grid-independence study. It is noted that the total number
of grid points for the above three mesh sizes is 2425, 5805, and 9650 respectively. Numerical
experiments showed that when the mesh size is above 96×45, the computed Nu remain the same.
3.2 Validation Test
The developed code validation included numerical investigation of the natural convection
problem for a low temperature outer square enclosure and high temperature inner circular
cylinder. The average Nusselt numbers and maximum stream function ψmax are compared with
the benchmark values by Moukalled and Acharya [16]. Comparisons are conducted for Prandtl
number Pr=0.7, enclosure width to cylinder diameter ratios (W/H=2.5) and Ra=104
and 105
as
given in table (2). The results show a good agreement with Moukalled and Acharya [16].
10. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
10
Table (2): Comparisons of Nusselt numbers and maximum stream function
L/D Ra
ψmax ܰݑതതതത
Present
Moukalled and
Acharya [16]
Present
Moukalled and
Acharya [16]
5.0
104
2.45 2.08 1.7427 1.71
2.5 3.182 3.24 0.9584 0.97
1.67 5.22 5.4 0.4274 0.49
5.0
105
10.10 10.15 3.889 3.825
2.5 8.176 8.38 4.93 5.08
1.67 4.8644 5.10 6.23 6.212
3.3 Flow Patterns and Isotherms
The flow patterns and isotherms displayed in figures (3-5) are for volume fraction range ϕ= 0 to
0.2. Figure (3) shows a comparison of streamlines and isotherms between Cu-water nanofluid
(ϕ=0.1) and pure fluid (ϕ=0) for W/H=2.5 with Rayleigh number values Ra=104
, 105
, and 106
. At
Ra=104
and 105
, the isotherms of two cases are nearly identical. There are some differences in
isotherms between the two cases for Ra =106
. The isotherms at the upper region above the square
cylinder for ϕ=0.1 are different as compared with pure fluid. The width of the thermal plume for
pure fluid is narrower than those for ϕ=0.1. The same behavior occurs with thermal plumes at the
corners of the square cylinder. The isotherms are symmetrical around vertical center line above
the square cylinder for pure fluid, while, the isotherms appear as nearly asymmetrical around
vertical center line for ϕ=0.1. The aspects of the streamlines are different for two cases. The flow
circulation for ϕ=0.1 is greater than those for pure fluid for all Rayleigh numbers. Table (3)
display the values of maximum stream function for pure fluid and ϕ=0.1 with Ra = 104
, 105
, 106
.
Table 3. Comparisons of maximum stream functions between pure fluid and ϕ=0.1
Ra
Maximum Stream Function
Pure fluid ϕ = 0.1
104
2.071321 4.2414815
105
4.7592694 6.95287233
106
8.893556 12.736855
At Ra=104
, the dominant heat transfer is the conduction, therefore, the streamlines of the two
cases are nearly similar except that the sizes of the internal eddies are different. At Ra=105
, the
streamlines appear as nearly kidney-shaped for two cases. Two circular tiny eddies display at the
upper region near the center line above the square cylinder. For ϕ=0.1, the flow cover the most
region between the square cylinder and the enclosure, therefore; the stagnant area is very small.
The coverage of the flow reduces for pure fluid, therefore; the stagnant area increases. The
densely package of the flow for ϕ=0.1 is more than those for pure fluid. At Ra=106
, the flow
moves upward for two cases. The coverage of the flow in the region between the square cylinder
11. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
11
and the enclosure for pure fluid is more than those for ϕ=0.1. The densely packed of the kidney-
shaped eddies and tiny eddies for pure fluid are more than those for ϕ=0.1.
Figure 3. Streamlines (on the top) and Isotherms (on the bottom) for Cu-water nanofluids (- - -), pure
fluid (___
), W/D=2.5, (a) Ra = 104
, (b) Ra = 105
(c) Ra =106
Figures (4-5) display the streamlines and isotherms for W/H= 2.5, and nanofluid volume fractions
ϕ=0.05, 0.1, 0.15 and 0.2. The strength of the flow circulation varies with the variation of the
Rayleigh number values. The maximum stream function value varies between Ψmax= 0.94 at
Ra=104
and ϕ=0.05 to Ψmax = 43 at Ra=106
and ϕ=0.2. At Ra=104
, the flow circulation is weak,
therefore; the maximum stream function value is small. The flow is symmetrical about the
vertical line through center of the square cylinder. The flow patterns appear as a curved kidney-
shaped single longitudinal eddy. The eddy core is small and the vertical boundary layers are thick,
indicative of the weak driving buoyancy. As the nanofluid volume fraction increases to ϕ=0.1, the
flow circulation enhances (Ψmax = 1.19) and the eddy core becomes wider. The flow strength
further increases for ϕ=0.15 (Ψmax = 1.44) and 0.2 (Ψmax = 1.675), however, the core starts
growing smaller indicative of the hydrodynamic boundary layer growth with viscosity. At
Ra=105
, the strength of the flow circulation becomes higher and two tiny eddies appear at the
upper region of the cylinder near the vertical center line. The tiny eddies appear as rings. The
densely packed of the flow for φ=0.1 and 0.15 are more than other flows. As Rayleigh number
increases to Ra=106
, the flow becomes stronger and the maximum stream function increases for
all cases (Ψmax= 27.4, 32.6, 37.6, and 43.0 for ϕ=0.05, 0.1, 0.15 and 0.2 respectively). The flow is
asymmetrical about the vertical center line. The streamlines near the bottom enclosure wall move
to the upward that lead to an increase in the stagnant area. The kernel eddy size becomes more
and it takes a triangular shape. The flow region moves upwards and the lower stagnant area
enlarges with increasing the volume fractions of the nanofluids.
12. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
12
ϕ=0.05 ϕ=0.1 ϕ=0.15 ϕ=0.2
Figure 4. Effect of volume fraction of nanofluids on streamlines at W/H = 2.5, (a) Ra = 104
, (b) Ra = 105
,
(c) Ra = 106
.
The temperature distributions for W/H=2.5 are presented by means of isotherms in figure (5). The
isotherms do not change with changing the volume fractions of the nanofluids for all Rayleigh
numbers. The isotherms are symmetrical about vertical center line for Ra=104
and Ra=105
for all
volume fractions. As Rayleigh number increases, the thermal boundary layer adjacent to the
cylinder becomes thinner and thinner.
At Ra=104
, the isotherms are similar for all volume fractions of the nanofluids. The mode of heat
transfer is conduction and the effect of convection heat transfer is very low. The isotherms
display as rings around the cylinder. As Rayleigh number increases to Ra=105
, the isotherms
distorts below the cylinder due to the effect of the convection heat transfer. A thermal plume
appears on the top of the cylinder. Two thermal plumes appear at the upper corners of the square
cylinder. The isotherms appear as curved below the cylinder with low distortion due to the effect
of the convection flow. At Ra=106
, the isotherms are nearly similar and independent of volume
fractions of the nanofluids. The convection becomes the dominant mode of heat transfer. The
width of the thermal plume at the middle of the cylinder becomes narrow, and it impinging on the
top of the enclosure. The widths of the two thermal plums at the upper corners become narrow.
The isotherms appear asymmetrical about the vertical center line. The thermal stratification
(nearly horizontal and flat isotherms) is formed near the bottom region of the enclosure.
13. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
13
ϕ=0.05 ϕ=0.1 ϕ=0.15 ϕ=0.2
Figure 5. Effect of volume fraction of nanofluids on isotherms at W/H = 2.5 and (a) Ra = 104
, (b) Ra = 105
,
(c) Ra = 106
.
3.4 Local and average Nusselt numbers
The distributions of local Nusselt number around the square cylinder are presented in figures (6)
for Rayleigh numbers Ra=104
, 105
and 106
and ϕ= 0, 0.05, 0.1, 0.15 and 0.2. The measured angle
starts from the middle of the right side of the enclosure and ends at the same point. The local
Nusselt numbers increase with increasing volume fractions of the nanofluid for all Rayleigh
numbers. The peak values of the local Nu occur at the corners of the square cylinder with all
Rayleigh numbers and volume fractions of the nanofluid. The maximum enhancement of the local
Nu occurs at the lower corners of the square cylinder.
14. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
14
Figure 6. Effect of volume fraction of Nanofluids on the local Nusselt number for each enclosure width to
square height W/D, (a) Ra=104
, (b) Ra=105
, (c) Ra=106
.
0
2
4
6
8
10
12
14
16
18
0 40 80 120 160 200 240 280 320 360
Nu
θθθθ
f=0
f=0.05
f=0.1
f=0.15
f=0.2
0
5
10
15
20
25
30
0 40 80 120 160 200 240 280 320 360
Nu
Ɵ
f=0
f=0.05
f=0.1
f=0.15
f=0.2
0
5
10
15
20
25
30
35
40
45
0 40 80 120 160 200 240 280 320 360
Nu
Axis Title
f=0
f=0.05
f=0.1
f=0.15
f=0.2
15. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
15
The average Nusselt number is chosen as the measure to investigate the heat transfer from the
square cylinder. The effect of volume fraction of the nanofluids on the average Nusselt numbers
with Ra=104
, 105
, and 106
for enclosure width to the cylinder height W/H= 2.5 is presented in
figure (7). The volume fractions,ϕwas varied as:0, 0.05, 0.1, 0.15, 0.2. The Nusselt number
increases with increasing the Rayleigh number for all values of ϕϕϕϕ. Nusselt number increases with
increasing the volume fraction of the nanofluids. The enhancement of the Nusselt number due to
increasing the nanofluid volume fraction is magnified with increasing Rayleigh number as
indicated by the increased slop of the Nu-ϕϕϕϕ curves. The maximum enhancement in the Nusselt
number when the volume fraction of nanoparticles is increased from 0 to 0.2, using Ra=104
, is
approximately 41%, the maximum enhancement is around 49% for Ra= 105
, whereas the
maximum enhancement is around 48% for Ra= 106
. This tells that the enhancement in heat
transfer, due to the presence of nanoparticles, is pronounced for all Rayleigh numbers. The heat
transfer enhances with increasing the volume fraction of the nanofluids because more particles
suspended and the effect of thermal conductivity and viscosity of the nanofluids on the heat
transfer.
Figure 7. Effect of volume fraction of Nanofluids on the average Nusselt number for each enclosure width
to square height W/D, (a) Ra=104
, (b) Ra=105
, (c) Ra=106
.
3.5 Fluid flow and Heat Transfer Correlations
The average Nusselt number and the maximum stream function from square cylinder in a vented
enclosure are correlated in terms of the Rayleigh number in the range (104
-106
) and the nanofluid
volume fractions between 0-0.2, using the results from the present work. The correlation of the
average Nusselt number can be expressed as:
Nuതതതത = 1.491ሺ0.194 + φଵ.଼ଵ
ሻ (31)
With R2
= 0.998
The correlation of the maximum stream function can be expressed as:
ψ୫ୟ୶
= 0.035൫0.209 + φ.ଽ଼ହ
൯Ra.ହ଼
(32)
With R2
= 0.997
0
2
4
6
8
10
12
14
16
18
20
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Nu
ϕϕϕϕ
Ra=10000
Ra=100000
Ra=1000000
16. International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.4, No.4, November 2015
16
4. CONCLUSIONS
Effect of the presence of the nanofluids on the natural convection heat transfer from square
horizontal cylinder in a square enclosure was investigated numerically over a fairly wide range of
Ra. The main conclusions of the present work can be summarized as follows:
1. The numerical results show that the Nusselt number increases with increasing the Rayleigh
number for all cases.
2. The flow patterns and isotherms display the effect of Ra, and volume fractions of the
nanofluids on the thermal and hydrodynamic characteristics.
3. The Conduction is the dominant of the heat transfer at Ra=104
for all cases. The contribution of
the convective heat transfer increases with increasing the Rayleigh number.
4. The results show that the isotherms are nearly similar when the volume fraction of
nanoparticles is increased from 0 to 0.2 for each Rayleigh number.
5. The streamlines are asymmetrical when the volume fraction of nanoparticles is increased from
0 to 0.2 for each Rayleigh number.
6. The average Nusselt number enhances gradually when the volume fraction of nanoparticles is
increased from 0 to 0.2 for each Rayleigh number.
7. The correlation equation of the average Nusselt number is:
Nuതതതത = 1.491ሺ0.194 + φଵ.଼ଵ
ሻ
8. The correlation equation of the maximum stream function is:
ψ୫ୟ୶
= 0.035ሺ0.209 + φ.ଽ଼ହ
ሻRa.ହ଼
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