Enviar pesquisa
Carregar
Mhd and heat transfer in a thin film over an unsteady stretching surface with
ā¢
0 gostou
ā¢
393 visualizaƧƵes
IAEME Publication
Seguir
Tecnologia
Denunciar
Compartilhar
Denunciar
Compartilhar
1 de 14
Baixar agora
Baixar para ler offline
Recomendados
Numerical simulation on laminar convection flow and heat transfer over an iso...
Numerical simulation on laminar convection flow and heat transfer over an iso...
eSAT Journals
Ā
A numerical solution of mhd heat transfer in a laminar liquid film on an unstead
A numerical solution of mhd heat transfer in a laminar liquid film on an unstead
IAEME Publication
Ā
Analysis of three dimensional couette flow and heat
Analysis of three dimensional couette flow and heat
eSAT Publishing House
Ā
Couette type mhd flow with suction and injection under constant pressure grad...
Couette type mhd flow with suction and injection under constant pressure grad...
eSAT Journals
Ā
Numerical study of mhd boundary layer stagnation point flow and heat transfer...
Numerical study of mhd boundary layer stagnation point flow and heat transfer...
eSAT Publishing House
Ā
Numerical study of natural convection in an enclosed
Numerical study of natural convection in an enclosed
eSAT Publishing House
Ā
Implementation of finite volume method in creeping flow around a circular cyl...
Implementation of finite volume method in creeping flow around a circular cyl...
eSAT Journals
Ā
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...
IJERA Editor
Ā
Recomendados
Numerical simulation on laminar convection flow and heat transfer over an iso...
Numerical simulation on laminar convection flow and heat transfer over an iso...
eSAT Journals
Ā
A numerical solution of mhd heat transfer in a laminar liquid film on an unstead
A numerical solution of mhd heat transfer in a laminar liquid film on an unstead
IAEME Publication
Ā
Analysis of three dimensional couette flow and heat
Analysis of three dimensional couette flow and heat
eSAT Publishing House
Ā
Couette type mhd flow with suction and injection under constant pressure grad...
Couette type mhd flow with suction and injection under constant pressure grad...
eSAT Journals
Ā
Numerical study of mhd boundary layer stagnation point flow and heat transfer...
Numerical study of mhd boundary layer stagnation point flow and heat transfer...
eSAT Publishing House
Ā
Numerical study of natural convection in an enclosed
Numerical study of natural convection in an enclosed
eSAT Publishing House
Ā
Implementation of finite volume method in creeping flow around a circular cyl...
Implementation of finite volume method in creeping flow around a circular cyl...
eSAT Journals
Ā
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...
IJERA Editor
Ā
O0131492100
O0131492100
IOSR Journals
Ā
K012237887
K012237887
IOSR Journals
Ā
J012546068
J012546068
IOSR Journals
Ā
The effect of magnetic field on the boundary layer flow over a stretching she...
The effect of magnetic field on the boundary layer flow over a stretching she...
IAEME Publication
Ā
MHD convection flow of viscous incompressible fluid over a stretched vertical...
MHD convection flow of viscous incompressible fluid over a stretched vertical...
IJERA Editor
Ā
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...
IJERA Editor
Ā
Determination of Contact Stress Distribution in Pin Loaded Orthotropic Plates
Determination of Contact Stress Distribution in Pin Loaded Orthotropic Plates
tomlinson_n
Ā
Effects of some thermo physical properties on force
Effects of some thermo physical properties on force
Alexander Decker
Ā
Application of CAD and SLA Method in Dental Prosthesis
Application of CAD and SLA Method in Dental Prosthesis
IDES Editor
Ā
A closed form solution for stress concentration around a circular hole in a l
A closed form solution for stress concentration around a circular hole in a l
IAEME Publication
Ā
Utech Presentation
Utech Presentation
tomlinson_n
Ā
30120140505004
30120140505004
IAEME Publication
Ā
Effect on heat transfer and thermal development of a radiatively participatin...
Effect on heat transfer and thermal development of a radiatively participatin...
IAEME Publication
Ā
Static and dynamic analysis of center cracked finite plate subjected to unifo...
Static and dynamic analysis of center cracked finite plate subjected to unifo...
IAEME Publication
Ā
Hertz Contact Stress Analysis and Validation Using Finite Element Analysis
Hertz Contact Stress Analysis and Validation Using Finite Element Analysis
Prabhakar Purushothaman
Ā
G04414658
G04414658
IOSR-JEN
Ā
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
IJERA Editor
Ā
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
IJERA Editor
Ā
Cfd analysis of turbulence in a gas turbine combustor with reference to the c...
Cfd analysis of turbulence in a gas turbine combustor with reference to the c...
IAEME Publication
Ā
Design and implementation of advanced security system based on one time passw
Design and implementation of advanced security system based on one time passw
IAEME Publication
Ā
Low power cmos binary counter using conventional flip flops
Low power cmos binary counter using conventional flip flops
IAEME Publication
Ā
One dimensional cutting stock problem 1-d-csp_ a study on data dependent tri
One dimensional cutting stock problem 1-d-csp_ a study on data dependent tri
IAEME Publication
Ā
Mais conteĆŗdo relacionado
Mais procurados
O0131492100
O0131492100
IOSR Journals
Ā
K012237887
K012237887
IOSR Journals
Ā
J012546068
J012546068
IOSR Journals
Ā
The effect of magnetic field on the boundary layer flow over a stretching she...
The effect of magnetic field on the boundary layer flow over a stretching she...
IAEME Publication
Ā
MHD convection flow of viscous incompressible fluid over a stretched vertical...
MHD convection flow of viscous incompressible fluid over a stretched vertical...
IJERA Editor
Ā
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...
IJERA Editor
Ā
Determination of Contact Stress Distribution in Pin Loaded Orthotropic Plates
Determination of Contact Stress Distribution in Pin Loaded Orthotropic Plates
tomlinson_n
Ā
Effects of some thermo physical properties on force
Effects of some thermo physical properties on force
Alexander Decker
Ā
Application of CAD and SLA Method in Dental Prosthesis
Application of CAD and SLA Method in Dental Prosthesis
IDES Editor
Ā
A closed form solution for stress concentration around a circular hole in a l
A closed form solution for stress concentration around a circular hole in a l
IAEME Publication
Ā
Utech Presentation
Utech Presentation
tomlinson_n
Ā
30120140505004
30120140505004
IAEME Publication
Ā
Effect on heat transfer and thermal development of a radiatively participatin...
Effect on heat transfer and thermal development of a radiatively participatin...
IAEME Publication
Ā
Static and dynamic analysis of center cracked finite plate subjected to unifo...
Static and dynamic analysis of center cracked finite plate subjected to unifo...
IAEME Publication
Ā
Hertz Contact Stress Analysis and Validation Using Finite Element Analysis
Hertz Contact Stress Analysis and Validation Using Finite Element Analysis
Prabhakar Purushothaman
Ā
G04414658
G04414658
IOSR-JEN
Ā
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
IJERA Editor
Ā
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
IJERA Editor
Ā
Mais procurados
(18)
O0131492100
O0131492100
Ā
K012237887
K012237887
Ā
J012546068
J012546068
Ā
The effect of magnetic field on the boundary layer flow over a stretching she...
The effect of magnetic field on the boundary layer flow over a stretching she...
Ā
MHD convection flow of viscous incompressible fluid over a stretched vertical...
MHD convection flow of viscous incompressible fluid over a stretched vertical...
Ā
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...
Ā
Determination of Contact Stress Distribution in Pin Loaded Orthotropic Plates
Determination of Contact Stress Distribution in Pin Loaded Orthotropic Plates
Ā
Effects of some thermo physical properties on force
Effects of some thermo physical properties on force
Ā
Application of CAD and SLA Method in Dental Prosthesis
Application of CAD and SLA Method in Dental Prosthesis
Ā
A closed form solution for stress concentration around a circular hole in a l
A closed form solution for stress concentration around a circular hole in a l
Ā
Utech Presentation
Utech Presentation
Ā
30120140505004
30120140505004
Ā
Effect on heat transfer and thermal development of a radiatively participatin...
Effect on heat transfer and thermal development of a radiatively participatin...
Ā
Static and dynamic analysis of center cracked finite plate subjected to unifo...
Static and dynamic analysis of center cracked finite plate subjected to unifo...
Ā
Hertz Contact Stress Analysis and Validation Using Finite Element Analysis
Hertz Contact Stress Analysis and Validation Using Finite Element Analysis
Ā
G04414658
G04414658
Ā
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
Ā
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...
Ā
Destaque
Cfd analysis of turbulence in a gas turbine combustor with reference to the c...
Cfd analysis of turbulence in a gas turbine combustor with reference to the c...
IAEME Publication
Ā
Design and implementation of advanced security system based on one time passw
Design and implementation of advanced security system based on one time passw
IAEME Publication
Ā
Low power cmos binary counter using conventional flip flops
Low power cmos binary counter using conventional flip flops
IAEME Publication
Ā
One dimensional cutting stock problem 1-d-csp_ a study on data dependent tri
One dimensional cutting stock problem 1-d-csp_ a study on data dependent tri
IAEME Publication
Ā
Non symbolic base64 an effective representation of ipv6 address
Non symbolic base64 an effective representation of ipv6 address
IAEME Publication
Ā
The scheme of three level inverters based on svpwm overmodulation technique
The scheme of three level inverters based on svpwm overmodulation technique
IAEME Publication
Ā
Comparative analysis of multi stage cordic using micro rotation techniq
Comparative analysis of multi stage cordic using micro rotation techniq
IAEME Publication
Ā
Employee retention in an organization through knowledge networking
Employee retention in an organization through knowledge networking
IAEME Publication
Ā
Art of fatigue analysis of helical compression spring used in two
Art of fatigue analysis of helical compression spring used in two
IAEME Publication
Ā
Destaque
(9)
Cfd analysis of turbulence in a gas turbine combustor with reference to the c...
Cfd analysis of turbulence in a gas turbine combustor with reference to the c...
Ā
Design and implementation of advanced security system based on one time passw
Design and implementation of advanced security system based on one time passw
Ā
Low power cmos binary counter using conventional flip flops
Low power cmos binary counter using conventional flip flops
Ā
One dimensional cutting stock problem 1-d-csp_ a study on data dependent tri
One dimensional cutting stock problem 1-d-csp_ a study on data dependent tri
Ā
Non symbolic base64 an effective representation of ipv6 address
Non symbolic base64 an effective representation of ipv6 address
Ā
The scheme of three level inverters based on svpwm overmodulation technique
The scheme of three level inverters based on svpwm overmodulation technique
Ā
Comparative analysis of multi stage cordic using micro rotation techniq
Comparative analysis of multi stage cordic using micro rotation techniq
Ā
Employee retention in an organization through knowledge networking
Employee retention in an organization through knowledge networking
Ā
Art of fatigue analysis of helical compression spring used in two
Art of fatigue analysis of helical compression spring used in two
Ā
Semelhante a Mhd and heat transfer in a thin film over an unsteady stretching surface with
Effect of viscous dissipation on mhd flow and heat transfer of a non newtonia...
Effect of viscous dissipation on mhd flow and heat transfer of a non newtonia...
IAEME Publication
Ā
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...
IJERA Editor
Ā
K0457278
K0457278
IOSR Journals
Ā
Numerical simulation on laminar convection flow and heat transfer over a non ...
Numerical simulation on laminar convection flow and heat transfer over a non ...
eSAT Journals
Ā
Numerical simulation of marangoni driven boundary layer flow over a flat plat...
Numerical simulation of marangoni driven boundary layer flow over a flat plat...
eSAT Journals
Ā
30120140502004 2
30120140502004 2
IAEME Publication
Ā
EFFECT OF PARTICLE SIZE AND CHEMICAL REACTION ON CONVECTIVE HEAT AND MASS TRA...
EFFECT OF PARTICLE SIZE AND CHEMICAL REACTION ON CONVECTIVE HEAT AND MASS TRA...
IAEME Publication
Ā
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...
theijes
Ā
Analysis of mhd non darcian boundary layer flow and heat transfer over an exp...
Analysis of mhd non darcian boundary layer flow and heat transfer over an exp...
eSAT Publishing House
Ā
Ijetcas14 358
Ijetcas14 358
Iasir Journals
Ā
30120130405018
30120130405018
IAEME Publication
Ā
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...
IAEME Publication
Ā
A numerical study of three dimensional darcy- forchheimer d-f- model in an
A numerical study of three dimensional darcy- forchheimer d-f- model in an
IAEME Publication
Ā
Transient Laminar MHD Free Convective Heat Transfer past a Vertical Plate wit...
Transient Laminar MHD Free Convective Heat Transfer past a Vertical Plate wit...
theijes
Ā
Numerical modeling-of-gas-turbine-engines
Numerical modeling-of-gas-turbine-engines
Cemal Ardil
Ā
Heat transfer in viscous free convective fluctuating mhd flow through porous ...
Heat transfer in viscous free convective fluctuating mhd flow through porous ...
Alexander Decker
Ā
Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Pat...
Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Pat...
IJECEIAES
Ā
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...
mathsjournal
Ā
Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant...
Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant...
mathsjournal
Ā
New technologies-for-modeling-of-gas-turbine-cooled-blades
New technologies-for-modeling-of-gas-turbine-cooled-blades
Cemal Ardil
Ā
Semelhante a Mhd and heat transfer in a thin film over an unsteady stretching surface with
(20)
Effect of viscous dissipation on mhd flow and heat transfer of a non newtonia...
Effect of viscous dissipation on mhd flow and heat transfer of a non newtonia...
Ā
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...
Ā
K0457278
K0457278
Ā
Numerical simulation on laminar convection flow and heat transfer over a non ...
Numerical simulation on laminar convection flow and heat transfer over a non ...
Ā
Numerical simulation of marangoni driven boundary layer flow over a flat plat...
Numerical simulation of marangoni driven boundary layer flow over a flat plat...
Ā
30120140502004 2
30120140502004 2
Ā
EFFECT OF PARTICLE SIZE AND CHEMICAL REACTION ON CONVECTIVE HEAT AND MASS TRA...
EFFECT OF PARTICLE SIZE AND CHEMICAL REACTION ON CONVECTIVE HEAT AND MASS TRA...
Ā
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...
Ā
Analysis of mhd non darcian boundary layer flow and heat transfer over an exp...
Analysis of mhd non darcian boundary layer flow and heat transfer over an exp...
Ā
Ijetcas14 358
Ijetcas14 358
Ā
30120130405018
30120130405018
Ā
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...
Ā
A numerical study of three dimensional darcy- forchheimer d-f- model in an
A numerical study of three dimensional darcy- forchheimer d-f- model in an
Ā
Transient Laminar MHD Free Convective Heat Transfer past a Vertical Plate wit...
Transient Laminar MHD Free Convective Heat Transfer past a Vertical Plate wit...
Ā
Numerical modeling-of-gas-turbine-engines
Numerical modeling-of-gas-turbine-engines
Ā
Heat transfer in viscous free convective fluctuating mhd flow through porous ...
Heat transfer in viscous free convective fluctuating mhd flow through porous ...
Ā
Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Pat...
Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Pat...
Ā
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...
Ā
Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant...
Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant...
Ā
New technologies-for-modeling-of-gas-turbine-cooled-blades
New technologies-for-modeling-of-gas-turbine-cooled-blades
Ā
Mais de IAEME Publication
IAEME_Publication_Call_for_Paper_September_2022.pdf
IAEME_Publication_Call_for_Paper_September_2022.pdf
IAEME Publication
Ā
MODELING AND ANALYSIS OF SURFACE ROUGHNESS AND WHITE LATER THICKNESS IN WIRE-...
MODELING AND ANALYSIS OF SURFACE ROUGHNESS AND WHITE LATER THICKNESS IN WIRE-...
IAEME Publication
Ā
A STUDY ON THE REASONS FOR TRANSGENDER TO BECOME ENTREPRENEURS
A STUDY ON THE REASONS FOR TRANSGENDER TO BECOME ENTREPRENEURS
IAEME Publication
Ā
BROAD UNEXPOSED SKILLS OF TRANSGENDER ENTREPRENEURS
BROAD UNEXPOSED SKILLS OF TRANSGENDER ENTREPRENEURS
IAEME Publication
Ā
DETERMINANTS AFFECTING THE USER'S INTENTION TO USE MOBILE BANKING APPLICATIONS
DETERMINANTS AFFECTING THE USER'S INTENTION TO USE MOBILE BANKING APPLICATIONS
IAEME Publication
Ā
ANALYSE THE USER PREDILECTION ON GPAY AND PHONEPE FOR DIGITAL TRANSACTIONS
ANALYSE THE USER PREDILECTION ON GPAY AND PHONEPE FOR DIGITAL TRANSACTIONS
IAEME Publication
Ā
VOICE BASED ATM FOR VISUALLY IMPAIRED USING ARDUINO
VOICE BASED ATM FOR VISUALLY IMPAIRED USING ARDUINO
IAEME Publication
Ā
IMPACT OF EMOTIONAL INTELLIGENCE ON HUMAN RESOURCE MANAGEMENT PRACTICES AMONG...
IMPACT OF EMOTIONAL INTELLIGENCE ON HUMAN RESOURCE MANAGEMENT PRACTICES AMONG...
IAEME Publication
Ā
VISUALISING AGING PARENTS & THEIR CLOSE CARERS LIFE JOURNEY IN AGING ECONOMY
VISUALISING AGING PARENTS & THEIR CLOSE CARERS LIFE JOURNEY IN AGING ECONOMY
IAEME Publication
Ā
A STUDY ON THE IMPACT OF ORGANIZATIONAL CULTURE ON THE EFFECTIVENESS OF PERFO...
A STUDY ON THE IMPACT OF ORGANIZATIONAL CULTURE ON THE EFFECTIVENESS OF PERFO...
IAEME Publication
Ā
GANDHI ON NON-VIOLENT POLICE
GANDHI ON NON-VIOLENT POLICE
IAEME Publication
Ā
A STUDY ON TALENT MANAGEMENT AND ITS IMPACT ON EMPLOYEE RETENTION IN SELECTED...
A STUDY ON TALENT MANAGEMENT AND ITS IMPACT ON EMPLOYEE RETENTION IN SELECTED...
IAEME Publication
Ā
ATTRITION IN THE IT INDUSTRY DURING COVID-19 PANDEMIC: LINKING EMOTIONAL INTE...
ATTRITION IN THE IT INDUSTRY DURING COVID-19 PANDEMIC: LINKING EMOTIONAL INTE...
IAEME Publication
Ā
INFLUENCE OF TALENT MANAGEMENT PRACTICES ON ORGANIZATIONAL PERFORMANCE A STUD...
INFLUENCE OF TALENT MANAGEMENT PRACTICES ON ORGANIZATIONAL PERFORMANCE A STUD...
IAEME Publication
Ā
A STUDY OF VARIOUS TYPES OF LOANS OF SELECTED PUBLIC AND PRIVATE SECTOR BANKS...
A STUDY OF VARIOUS TYPES OF LOANS OF SELECTED PUBLIC AND PRIVATE SECTOR BANKS...
IAEME Publication
Ā
EXPERIMENTAL STUDY OF MECHANICAL AND TRIBOLOGICAL RELATION OF NYLON/BaSO4 POL...
EXPERIMENTAL STUDY OF MECHANICAL AND TRIBOLOGICAL RELATION OF NYLON/BaSO4 POL...
IAEME Publication
Ā
ROLE OF SOCIAL ENTREPRENEURSHIP IN RURAL DEVELOPMENT OF INDIA - PROBLEMS AND ...
ROLE OF SOCIAL ENTREPRENEURSHIP IN RURAL DEVELOPMENT OF INDIA - PROBLEMS AND ...
IAEME Publication
Ā
OPTIMAL RECONFIGURATION OF POWER DISTRIBUTION RADIAL NETWORK USING HYBRID MET...
OPTIMAL RECONFIGURATION OF POWER DISTRIBUTION RADIAL NETWORK USING HYBRID MET...
IAEME Publication
Ā
APPLICATION OF FRUGAL APPROACH FOR PRODUCTIVITY IMPROVEMENT - A CASE STUDY OF...
APPLICATION OF FRUGAL APPROACH FOR PRODUCTIVITY IMPROVEMENT - A CASE STUDY OF...
IAEME Publication
Ā
A MULTIPLE ā CHANNEL QUEUING MODELS ON FUZZY ENVIRONMENT
A MULTIPLE ā CHANNEL QUEUING MODELS ON FUZZY ENVIRONMENT
IAEME Publication
Ā
Mais de IAEME Publication
(20)
IAEME_Publication_Call_for_Paper_September_2022.pdf
IAEME_Publication_Call_for_Paper_September_2022.pdf
Ā
MODELING AND ANALYSIS OF SURFACE ROUGHNESS AND WHITE LATER THICKNESS IN WIRE-...
MODELING AND ANALYSIS OF SURFACE ROUGHNESS AND WHITE LATER THICKNESS IN WIRE-...
Ā
A STUDY ON THE REASONS FOR TRANSGENDER TO BECOME ENTREPRENEURS
A STUDY ON THE REASONS FOR TRANSGENDER TO BECOME ENTREPRENEURS
Ā
BROAD UNEXPOSED SKILLS OF TRANSGENDER ENTREPRENEURS
BROAD UNEXPOSED SKILLS OF TRANSGENDER ENTREPRENEURS
Ā
DETERMINANTS AFFECTING THE USER'S INTENTION TO USE MOBILE BANKING APPLICATIONS
DETERMINANTS AFFECTING THE USER'S INTENTION TO USE MOBILE BANKING APPLICATIONS
Ā
ANALYSE THE USER PREDILECTION ON GPAY AND PHONEPE FOR DIGITAL TRANSACTIONS
ANALYSE THE USER PREDILECTION ON GPAY AND PHONEPE FOR DIGITAL TRANSACTIONS
Ā
VOICE BASED ATM FOR VISUALLY IMPAIRED USING ARDUINO
VOICE BASED ATM FOR VISUALLY IMPAIRED USING ARDUINO
Ā
IMPACT OF EMOTIONAL INTELLIGENCE ON HUMAN RESOURCE MANAGEMENT PRACTICES AMONG...
IMPACT OF EMOTIONAL INTELLIGENCE ON HUMAN RESOURCE MANAGEMENT PRACTICES AMONG...
Ā
VISUALISING AGING PARENTS & THEIR CLOSE CARERS LIFE JOURNEY IN AGING ECONOMY
VISUALISING AGING PARENTS & THEIR CLOSE CARERS LIFE JOURNEY IN AGING ECONOMY
Ā
A STUDY ON THE IMPACT OF ORGANIZATIONAL CULTURE ON THE EFFECTIVENESS OF PERFO...
A STUDY ON THE IMPACT OF ORGANIZATIONAL CULTURE ON THE EFFECTIVENESS OF PERFO...
Ā
GANDHI ON NON-VIOLENT POLICE
GANDHI ON NON-VIOLENT POLICE
Ā
A STUDY ON TALENT MANAGEMENT AND ITS IMPACT ON EMPLOYEE RETENTION IN SELECTED...
A STUDY ON TALENT MANAGEMENT AND ITS IMPACT ON EMPLOYEE RETENTION IN SELECTED...
Ā
ATTRITION IN THE IT INDUSTRY DURING COVID-19 PANDEMIC: LINKING EMOTIONAL INTE...
ATTRITION IN THE IT INDUSTRY DURING COVID-19 PANDEMIC: LINKING EMOTIONAL INTE...
Ā
INFLUENCE OF TALENT MANAGEMENT PRACTICES ON ORGANIZATIONAL PERFORMANCE A STUD...
INFLUENCE OF TALENT MANAGEMENT PRACTICES ON ORGANIZATIONAL PERFORMANCE A STUD...
Ā
A STUDY OF VARIOUS TYPES OF LOANS OF SELECTED PUBLIC AND PRIVATE SECTOR BANKS...
A STUDY OF VARIOUS TYPES OF LOANS OF SELECTED PUBLIC AND PRIVATE SECTOR BANKS...
Ā
EXPERIMENTAL STUDY OF MECHANICAL AND TRIBOLOGICAL RELATION OF NYLON/BaSO4 POL...
EXPERIMENTAL STUDY OF MECHANICAL AND TRIBOLOGICAL RELATION OF NYLON/BaSO4 POL...
Ā
ROLE OF SOCIAL ENTREPRENEURSHIP IN RURAL DEVELOPMENT OF INDIA - PROBLEMS AND ...
ROLE OF SOCIAL ENTREPRENEURSHIP IN RURAL DEVELOPMENT OF INDIA - PROBLEMS AND ...
Ā
OPTIMAL RECONFIGURATION OF POWER DISTRIBUTION RADIAL NETWORK USING HYBRID MET...
OPTIMAL RECONFIGURATION OF POWER DISTRIBUTION RADIAL NETWORK USING HYBRID MET...
Ā
APPLICATION OF FRUGAL APPROACH FOR PRODUCTIVITY IMPROVEMENT - A CASE STUDY OF...
APPLICATION OF FRUGAL APPROACH FOR PRODUCTIVITY IMPROVEMENT - A CASE STUDY OF...
Ā
A MULTIPLE ā CHANNEL QUEUING MODELS ON FUZZY ENVIRONMENT
A MULTIPLE ā CHANNEL QUEUING MODELS ON FUZZY ENVIRONMENT
Ā
Ćltimo
Elevate Developer Efficiency & build GenAI Application with Amazon Qā
Elevate Developer Efficiency & build GenAI Application with Amazon Qā
Bhuvaneswari Subramani
Ā
Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)
Zilliz
Ā
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
MadyBayot
Ā
Artificial Intelligence Chap.5 : Uncertainty
Artificial Intelligence Chap.5 : Uncertainty
Khushali Kathiriya
Ā
Why Teams call analytics are critical to your entire business
Why Teams call analytics are critical to your entire business
panagenda
Ā
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Victor Rentea
Ā
Boost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdf
sudhanshuwaghmare1
Ā
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
DianaGray10
Ā
How to Troubleshoot Apps for the Modern Connected Worker
How to Troubleshoot Apps for the Modern Connected Worker
ThousandEyes
Ā
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
Zilliz
Ā
ICT role in 21st century education and its challenges
ICT role in 21st century education and its challenges
rafiqahmad00786416
Ā
TrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
TrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
TrustArc
Ā
AWS Community Day CPH - Three problems of Terraform
AWS Community Day CPH - Three problems of Terraform
Andrey Devyatkin
Ā
Apidays New York 2024 - APIs in 2030: The Risk of Technological Sleepwalk by ...
Apidays New York 2024 - APIs in 2030: The Risk of Technological Sleepwalk by ...
apidays
Ā
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
apidays
Ā
Mcleodganj Call Girls š„° 8617370543 Service Offer VIP Hot Model
Mcleodganj Call Girls š„° 8617370543 Service Offer VIP Hot Model
Deepika Singh
Ā
Architecting Cloud Native Applications
Architecting Cloud Native Applications
WSO2
Ā
[BuildWithAI] Introduction to Gemini.pdf
[BuildWithAI] Introduction to Gemini.pdf
Sandro Moreira
Ā
DBX First Quarter 2024 Investor Presentation
DBX First Quarter 2024 Investor Presentation
Dropbox
Ā
presentation ICT roal in 21st century education
presentation ICT roal in 21st century education
jfdjdjcjdnsjd
Ā
Ćltimo
(20)
Elevate Developer Efficiency & build GenAI Application with Amazon Qā
Elevate Developer Efficiency & build GenAI Application with Amazon Qā
Ā
Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)
Ā
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
Ā
Artificial Intelligence Chap.5 : Uncertainty
Artificial Intelligence Chap.5 : Uncertainty
Ā
Why Teams call analytics are critical to your entire business
Why Teams call analytics are critical to your entire business
Ā
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Ā
Boost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdf
Ā
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Ā
How to Troubleshoot Apps for the Modern Connected Worker
How to Troubleshoot Apps for the Modern Connected Worker
Ā
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
Ā
ICT role in 21st century education and its challenges
ICT role in 21st century education and its challenges
Ā
TrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
TrustArc Webinar - Unlock the Power of AI-Driven Data Discovery
Ā
AWS Community Day CPH - Three problems of Terraform
AWS Community Day CPH - Three problems of Terraform
Ā
Apidays New York 2024 - APIs in 2030: The Risk of Technological Sleepwalk by ...
Apidays New York 2024 - APIs in 2030: The Risk of Technological Sleepwalk by ...
Ā
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
Apidays New York 2024 - Passkeys: Developing APIs to enable passwordless auth...
Ā
Mcleodganj Call Girls š„° 8617370543 Service Offer VIP Hot Model
Mcleodganj Call Girls š„° 8617370543 Service Offer VIP Hot Model
Ā
Architecting Cloud Native Applications
Architecting Cloud Native Applications
Ā
[BuildWithAI] Introduction to Gemini.pdf
[BuildWithAI] Introduction to Gemini.pdf
Ā
DBX First Quarter 2024 Investor Presentation
DBX First Quarter 2024 Investor Presentation
Ā
presentation ICT roal in 21st century education
presentation ICT roal in 21st century education
Ā
Mhd and heat transfer in a thin film over an unsteady stretching surface with
1.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 387 MHD AND HEAT TRANSFER IN A THIN FILM OVER AN UNSTEADY STRETCHING SURFACE WITH COMBINED EFFECT OF VISCOUS DISSIPATION AND NON-UNIFORM HEAT SOURCE Anand H. Agadi1* , M . Subhas Abel2 and Jagadish V. Tawade3 1* Department of Mathematics, Basaveshwar Engineering College, Bagalkot-587102, INDIA 2 Department of Mathematics, Gulbarga University, Gulbarga- 585 106, INDIA 3 Department of Mathematics, Bheemanna Khandre Institute of Technology, Bhalki-585328 ABSTRACT We have studied two-dimensional flow of a thin film over a horizontal stretching surface. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of non-linear ordinary differential equations. Numerical computation for the resulting nonlinear differential equations is obtained by Runge-Kutta fourth order method with efficient shooting technique, which agrees well with the analytic solution. It is shown that the heat fluxes from the liquid to the elastic sheet decreases with S forPr 0.1ā¤ and increases with S forPr 1ā„ . Some important findings reported in this work reveals that the effect of non-uniform heat source have significant impact in controlling rate heat transfer in the boundary layer region. Key words: Eckert number, MHD, Prandtl number, thin film, unsteady stretching surface. 1. INTRODUCTION The study of the flow resulting from a stretching boundary is important in process industry such as the extrusion of sheet material into the coolant environment. The tangential velocity imparted by the stretching sheet induces motion in the extruding fluid which ultimately solidified and formed a sheet. In fact, stretching imparts a unidirectional orientation to the extrudate, thereby improving its mechanical properties and the quality of the final product. Crane [1] first modeled this flow configuration as a steady two-dimensional boundary layer flow caused by the stretching of a sheet which moves in its own plane with velocity varying with distance from the slit and obtained an exact INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) ISSN 0976 ā 6340 (Print) ISSN 0976 ā 6359 (Online) Volume 4, Issue 4, July - August (2013), pp. 387-400 Ā© IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com IJMET Ā© I A E M E
2.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 388 solution analytically. This simple configuration has attracted several researchers [2 - 6] for the last four decades and is extensively studied. The hydrodynamics of the finite fluid domain ( thin liquid film), over a stretching sheet was first considered by Wang [8] who reduced the unsteady NervierāStokes equations to a nonlinear ordinary differential equations by means of similarity transformation and solved the same using a kind of multiple shooting method (see Robert and Shipman [9]). Wang [10] himself has used homotopy analysis method to reinvestigate the thin film flow over a stretching sheet. Of late the works of Wang [8] to the case of finite fluid domain are extended by several authors [11-15] for fluids of both Newtonian and non-Newtonian kinds using various velocity and thermal boundary conditions. Motivated by all these works we contemplate to study the effects of non-uniform heat source, and viscous dissipation in presence of thermal radiation on the flow and heat transfer in a thin liquid film over an unsteady stretching sheet, which is subjected to an external magnetic field. 2. MATHEMATICAL FORMULATION Let us consider a thin elastic sheet which emerges from a narrow slit at the origin of a Cartesian co-ordinate system for investigations as shown schematically in Fig 1. The continuous sheet at 0y = is parallel with the x-axis and moves in its own plane with the velocity ( ), (1 ) bx U x t tĪ± = ā (1) where b and Ī± are both positive constants with dimension per time. The surface temperature sT of the stretching sheet is assumed to vary with the distance x from the slit as ( ) 32 2 0, (1 ) 2 s ref bx T x t T T tĪ± Ļ āļ£® ļ£¹ = ā āļ£Æ ļ£ŗ ļ£° ļ£» (2) Where 0T is the temperature at the slit and refT can be taken as a constant reference temperature such that 00 refT Tā¤ ā¤ . The term 2 (1 ) bx tĻ Ī±ā can be recognized as the Local Reynolds number based on the surface velocityU . The expression (1) for the velocity of the sheet ( , )U x t reflects that the elastic sheet which is fixed at the origin is stretched by applying a force in the positive x-direction and the effective stretching rate (1 ) b tĪ±ā increase with time as 0 1Ī±ā¤ < . The applied transverse magnetic field is assumed to be of variable kind and is chosen as ( ) ( ) 1 2 0, 1- .B x t B tĪ± ā = (3) The sheet is assumed to have velocity U as defined in equation (1) and the flow field is exposed to the influence of an external transverse magnetic field of strength B as defined in equation (3). The velocity and temperature fields of the liquid film obey the following boundary layer equations
3.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 389 0, u v x y ā ā + = ā ā (4) 2 2 2 , u u u u B u v u t x y y Ļ Ļ Ļ ā ā ā ā + + = ā ā ā ā ā (5) 22 2 p p p T T T k T u q u v t x y C y C y C Āµ Ļ Ļ Ļ ā²ā²ā²ļ£« ļ£¶ā ā ā ā ā + + = + +ļ£¬ ļ£· ā ā ā ā āļ£ ļ£ø (6) The non-uniform heat source/sink (see [30]) is modeled as 0 0 ( ) [ *( ) ( ) *],w s ku x q A T T f T T B xĻ ā²ā²ā² ā²= ā + ā (7) Where A* and B* are the coefficients of space and temperature dependent heat source/sink respectively. Here we make a note that the case 0*,0* >> BA corresponds to internal heat generation and that 0*,0* << BA corresponds to internal heat absorption. The associated boundary conditions are given by , 0, at 0,su U v T T y= = = = (8) 0 at , u T y h y y ā ā = = = ā ā (9) at . dh v y h dt = = (10) At this juncture we make a note that the mathematical problem is implicitly formulated only for 0x ā„ . Further it is assumed that the surface of the planar liquid film is smooth so as to avoid the complications due to surface waves. The influence of interfacial shear due to the quiescent atmosphere, in other words the effect of surface tension is assumed to be negligible. The viscous shear stress u y Ļ Āµ ļ£« ļ£¶ā = ļ£¬ ļ£· āļ£ ļ£ø and the heat flux T q k y ļ£« ļ£¶ā = ā ļ£¬ ļ£· āļ£ ļ£ø vanish at the adiabatic free surface (at y = h). We now introduce dimensionless variables andf Īø and the similarity variable Ī· as ( ) ( ) 1 2 , , , 1 x y t f b x t Ļ Ī· Ļ Ī± = ļ£« ļ£¶ ļ£¬ ļ£· āļ£ ļ£ø (11) ( ) 1 2 . 1 b y t Ī· Ļ Ī± ļ£« ļ£¶ = ļ£¬ ļ£·ļ£¬ ļ£·āļ£ ļ£ø (12)
4.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 390 ( ) ( ) ( ) 0 2 3 2 , , , 2 1 ref T T x y t b x T t Īø Ī· Ļ Ī± ā ā = ļ£« ļ£¶ ļ£¬ ļ£· ļ£¬ ļ£·ļ£¬ ļ£·āļ£ ļ£ø (13) The physical stream function ( ), ,x y tĻ automatically assures mass conversion given in equation (4). The velocity components are readily obtained as: ( ), 1 bx u f y t Ļ Ī· Ī± ā ļ£« ļ£¶ ā²= = ļ£¬ ļ£· ā āļ£ ļ£ø (14) ( ) 1 2 . 1 b v f x t Ļ Ļ Ī· Ī± ā ļ£« ļ£¶ = ā = āļ£¬ ļ£· ā āļ£ ļ£ø (15) The mathematical problem defined in equations (4) ā (6) and (8) ā (9) transforms exactly into a set of ordinary differential equations and their associated boundary conditions: ( ) 2 Mn , 2 S f f f ff f f Ī·ļ£« ļ£¶ ā² ā²ā² ā² ā²ā² ā²ā²ā² ā²+ + ā = āļ£¬ ļ£· ļ£ ļ£ø (16) ( ) 2S Pr 3 2 EcPr ( * * ), 2 f f f A f BĪø Ī·Īø Īø Īø Īø Īø ļ£® ļ£¹ā² ā² ā² ā²ā² ā²ā² ā²+ + ā = ā ā +ļ£Æ ļ£ŗļ£° ļ£» (17) (0) 1, (0) 0, (0) 1,f f Īøā² = = = (18) ( ) 0, ( ) 0,f Ī² Īø Ī²ā²ā² ā²= = (19) S ( ) . 2 f Ī² Ī² = (20) Here S b Ī± ā” is the dimensionless measure of the unsteadiness and the prime indicates differentiation with respect toĪ· . Further, Ī² denotes the value of the similarity variable Ī· at the free surface so that equation (12) gives ( ) 1 2 . 1 b h t Ī² Ļ Ī± ļ£« ļ£¶ = ļ£¬ ļ£·ļ£¬ ļ£·āļ£ ļ£ø (21) Yet Ī² is an unknown constant, which should be determined as an integral part of the boundary value problem. The rate at which film thickness varies can be obtained differentiating equation (21) with respect to t, in the form
5.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 391 ( ) 1 2 . 2 1 dh dt b t Ī±Ī² Ļ Ī± ļ£« ļ£¶ = ā ļ£¬ ļ£·ļ£¬ ļ£·āļ£ ļ£ø (22) Thus the kinematic constraint at ( )y h t= given by equation (10) transforms into the free surface condition (22). It is noteworthy that the momentum boundary layer equation defined by equation (16) subject to the relevant boundary conditions (18) ā (20) is decoupled from the thermal field; on the other hand the temperature field ( )Īø Ī· is coupled with the velocity field ( )f Ī· . Since the sheet is stretched horizontally the convection least affects the flow and hence there is a one-way coupling of velocity and thermal fields. 3. NUMERICAL SOLUTION The non-linear differential equations (16) and (17) with appropriate boundary conditions given in (18) to (20) are solved numerically, by the most efficient numerical shooting technique with fourth order RungeāKutta algorithm (see references [16]). The non-linear differential equations (16) and (17) are first decomposed to a system of first order differential equations in the form ( ) ( ) 20 1 2 1 2 1 2 1 0 2 1 20 1 1 0 1 1 0 1 0 2 , , +Mn , 2 S , Pr 3 2 Ec Pr ( * * ) . 2 df df df f f S f f f f f f d d d d d f f f A f B d d Ī· Ī· Ī· Ī· Īø Īø Īø Īø Ī·Īø Īø Īø Īø Ī· Ī· ļ£« ļ£¶ = = = + + āļ£¬ ļ£· ļ£ ļ£ø ļ£« ļ£¶ļ£® ļ£¹ ā²= = + + ā ā + +ļ£¬ ļ£·ļ£Æ ļ£ŗļ£° ļ£»ļ£ ļ£ø (25) Corresponding boundary conditions take the form, 1 0 0(0) 1, (0) 0, (0) 1,f f Īø= = = (26) 2 1( ) 0, ( ) 0,f Ī² Īø Ī²= = (27) 0 S ( ) . 2 f Ī² Ī² = (28) Here 0 0( ) ( ) and ( ) ( ).f fĪ· Ī· Īø Ī· Īø Ī·= = The above boundary value problem is first converted into an initial value problem by appropriately guessing the missing slopes 2 1(0) and (0)f Īø . The resulting IVP is solved by shooting method for a set of parameters appearing in the governing equations and a known value of S. The value of Ī² is so adjusted that condition (28) holds. This is done on the trial and error basis. The value for which condition (28) holds is taken as the appropriate film thickness and the IVP is finally solved using this value of Ī². The step length of h = 0.01 is employed for the computation purpose. The convergence criterion largely depends on fairly good guesses of the initial conditions in the shooting technique. The iterative process is terminated until the relative difference between the current and the previous iterative values of ( )f Ī² matches with the value of 2 SĪ² up to a tolerance of 6 10ā . Once the convergence in achieved we integrate the resultant ordinary differential equations using standard fourth order RungeāKutta method with the given set of parameters to obtain the required solution.
6.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 392 4. RESULTS AND DISCUSSION The exact solution do not seem feasible for a complete set of equations (16)-(17) because of the non linear form of the momentum and thermal boundary layer equations. This fact forces one to obtain the solution of the problem numerically. Appropriate similarity transformation is adopted to transform the governing partial differential equations of flow and heat transfer into a system of non- linear ordinary differential equations. The resultant boundary value problem is solved by the efficient shooting method. It is note worthy to mention that the solution exists only for small value of unsteadiness parameter0 2Sā¤ ā¤ . Moreover, when 0S ā the solution approaches to the analytical solution obtained by Crane [1] with infinitely thick layer of fluid ( Ī² ā ā ). The other limiting solution corresponding to 2S ā represents a liquid film of infinitesimal thickness ( 0Ī² ā ). The numerical results are obtained for0 2Sā¤ ā¤ . Present results are compared with some of the earlier published results in some limiting cases which are tabulated in Table 1. The effects of magnetic parameter on various fluid dynamic quantities are shown in Fig.2 ā Fig.13 for different unsteadiness parameter. Fig.2 shows the variation of film thickness Ī² with the unsteadiness parameter. It is evident from this plot that the film thickness Ī² decreases monotonically when S is increased from 0 to 2. This result concurs with that observed by Wang [10]. The variation of film thickness Ī² with respect to the magnetic parameter Mn is projected in Fig.3 for different values of unsteadiness parameter. It is clear from this plot that the increasing values of magnetic parameter decreases the film thickness. The result holds for different values of unsteadiness parameter S. The variation of free-surface velocity ( )f Ī²ā² with respect to Mn is shown in Fig.4. The free surface velocity behaves almost as a constant function of Mn as can be seen from Fig.4. The effect of Mn on the wall shear stress parameter ( )0f ā²ā²ā is illustrated in Fig.5. Clearly, increasing values Mn results in increasing the wall shear stress. Fig.6 demonstrates the effect of Mn on the free- surface temperature ( )Īø Ī² . From this plot it is evident that the free surface temperature increases monotonically with Mn. Fig.7 highlights the effect of Mn on the dimensionless wall heat flux ( )0Īøā²ā . It is found from this plot that the dimensionless wall heat flux ( )0Īøā²ā decreases with the increasing values of Mn. The effect of Mn on ( )f Ī²ā² , ( )0f ā²ā²ā , ( )Īø Ī² and ( )0Īøā²ā is observed to be same for different values of unsteadiness parameter S. The effect of Mn on the axial velocity is depicted in Figs.8(a) and (b) for two different values of S. From these plots it is clear that the increasing values of magnetic parameter decreases the axial velocity. This is due to the fact that applied transverse magnetic field produces a drag in the form of Lorentz force thereby decreasing the magnitude of velocity. The drop in horizontal velocity as a consequence of increase in the strength of magnetic field is observed for both the values of S = 0.8 and S = 1.2. Figs.9 (a) and (b) depicts the effect of Mn on temperature profiles for two different values of S. The results show that the thermal boundary layer thickness increases with the increasing values of Mn. The increasing frictional drag due to the Lorentz force is responsible for increasing the thermal boundary layer thickness. Fig.10 (a) and 10(b) demonstrate the effect of Prandtl number Pr on the temperature profiles for two different values of unsteadiness parameter S. These plots reveals the fact that for a particular value of Pr the temperature increases monotonically from the free surface temperature sT to wall velocity the 0T .
7.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 393 Fig.11 (a) and 11(b) project the effect of Eckert number Ec on the temperature profiles for two different values of unsteadiness parameter S. The effect of viscous dissipation is to enhance the temperature in the fluid film. i.e., increasing values of Ec contributes in thickening of thermal boundary layer. Fig.12 (a) and Fig.12 (b) presents the effect of space dependent heat source/sink parameter A* and Fig.13 (a) and Fig.13 (b) presents the effect of temperature dependent heat source/sink parameter B* on the temperature profile for different values of unsteadiness parameter S .The effect of sink parameter ( * 0, * 0)A B< < reduces the temperature in the fluid as the effect of source parameter ( * 0, * 0)A B> > enhances the temperature. For effective cooling of the sheet, heat sink is preferred. Table 1 and Table 2 give the comparison of present results with that of Wang [10]. Without any doubt, from these tables, we can claim that our results are in excellent agreement with that of Wang [10] under some limiting cases. Table 3 tabulates the values of surface temperature ( )Īø Ī² for various values of Mn, Pr, Ec, A* and B*. This table also reveals that Mn, Ec, A* and B* proportionately increase the surface temperature whereas opposite effect is seen in case of Pr. 5. CONCLUSIONS A theoretical study of the boundary layer behavior in a liquid film over an unsteady stretching sheet is carried out including the effects of a variable transverse magnetic field including viscous dissipation and non-uniform heat source/sink. The effect of several parameters controlling the velocity and temperature profiles are shown graphically and discussed briefly. Some of the important findings of our analysis obtained by the graphical representation are listed below. 1. The effect of transverse magnetic field on a viscous incompressible electrically conducting fluid is to suppress the velocity field which in turn causes the enhancement of the temperature field. 2. For a wide range of Pr, the effect viscous dissipation is found to increase the dimensionless free-surface temperature ( )Īø Ī² for the fluid cooling case. The impact of viscous dissipation on ( )Īø Ī² diminishes in the two limiting cases: Pr 0 and Prā ā ā , in which situations ( )Īø Ī² approaches unity and zero respectively. 3. The viscous dissipation effect is characterized by Eckert number (Ec) in the present analysis. Comparing to the results without viscous dissipation, one can see that the dimensionless temperature will increase when the fluid is being heated (Ec>0) but decreases when the fluid is being cooled (Ec<0). This reveals that effect of viscous dissipation is to enhance the temperature in the thermal boundary layer. 4. The effect of non-uniform heat source/sink parameter is to generate temperature for increasing positive values and absorb temperature for decreasing negative values. Hence non- uniform heat sinks are better suited for cooling purpose.
8.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 394 TABLE 1: Comparison of values of skin friction coefficient ( )0f ā²ā² with Mn = 0.0 S Wang [10] Present Results Ī² ( )0f ā²ā² ( )0f Ī² ā²ā² Ī² ( )0f ā²ā² 0.4 5.122490 -6.699120 -1.307785 4.981455 -1.134098 0.6 3.131250 -3.742330 -1.195155 3.131710 -1.195128 0.8 2.151990 -2.680940 -1.245795 2.151990 -1.245805 1.0 1.543620 -1.972380 -1.277762 1.543617 -1.277769 1.2 1.127780 -1.442631 -1.279177 1.127780 -1.279171 1.4 0.821032 -1.012784 -1.233549 0.821033 -1.233545 1.6 0.576173 -0.642397 -1.114937 0.576176 -1.114941 1.8 0.356389 -0.309137 -0.867414 0.356390 -0.867416 Note: Wang [10] has used different similarity transformation due to which the value of ( )0f Ī² ā²ā² in his paper is the same as ( )0f ā²ā² of our results. TABLE 2: Comparison of values of surface temperature ( )Īø Ī² and wall temperature gradient ( )0Īøā²ā with Mn = Ec = A* = B* = 0.0 Pr Wang [10] Present Results ( )Īø Ī² ( )0Īøā²ā ( )0Īø Ī² ā²ā ( )Īø Ī² ( )0Īøā²ā S = 0.8 and Ī² = 2.15199 0.01 0.960480 0.090474 0.042042 0.960438 0.042120 0.1 0.692533 0.756162 0.351378 0.692296 0.351920 1 0.097884 3.595790 1.670913 0.097825 1.671919 2 0.024941 5.244150 2.436884 0.024869 2.443914 3 0.008785 6.514440 3.027170 0.008324 3.034915 S = 1.2 and Ī² = 1.127780 0.01 0.982331 0.037734 0.033458 0.982312 0.033515 0.1 0.843622 0.343931 0.304962 0.843485 0.305409 1 0.286717 1.999590 1.773032 0.286634 1.773772 2 0.128124 2.975450 2.638324 0.128174 2.638431 3 0.067658 3.698830 3.279744 0.067737 3.280329 Note: Wang [10] has used different similarity transformation due to which the value of ( )0Īø Ī² ā²ā in his paper is the same as ( )0Īøā²ā of our results.
9.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 395 TABLE 3: Values of surface temperature ( )Īø Ī² for various values of Mn, Pr, Ec, A*, B* and S Mn Pr Ec A* B* ( )Īø Ī² S = 0.8 S = 1.2 0.0 1.0 0.02 0.05 0.05 0.257696 0.496022 1.0 1.0 0.02 0.05 0.05 0.420739 0.618190 2.0 1.0 0.02 0.05 0.05 0.526782 0.692995 5.0 1.0 0.02 0.05 0.05 0.695757 0.806962 8.0 1.0 0.02 0.05 0.05 0.776253 0.913333 1.0 0.01 0.02 0.05 0.05 1.030899 1.009712 1.0 0.1 0.02 0.05 0.05 0.931433 0.959465 1.0 1 0.02 0.05 0.05 0.420739 0.618190 1.0 10 0.02 0.05 0.05 0.011137 0.061941 1.0 100 0.02 0.05 0.05 0.000095 0.000238 1.0 1.0 0.01 0.05 0.05 0.420304 0.617857 1.0 1.0 1.0 0.05 0.05 0.463423 0.650865 1.0 1.0 2.0 0.05 0.05 0.506978 0.684207 1.0 1.0 5.0 0.05 0.05 0.637642 0.784232 1.0 1.0 0.02 0.05 0.05 0.227566 0.423871 1.0 1.0 0.02 0.05 0.05 0.420739 0.618190 1.0 1.0 0.02 0.05 0.05 0.715871 0.838324 1.0 1.0 0.02 0.05 0.05 0.826899 0.906104 1.0 1.0 0.02 -0.4 0.05 0.379098 0.586395 1.0 1.0 0.02 0.0 0.05 0.416112 0.614657 1.0 1.0 0.02 0.4 0.05 0.453127 0.642920 1.0 1.0 0.02 0.05 -0.4 0.353675 0.578066 1.0 1.0 0.02 0.05 0.0 0.412373 0.613518 1.0 1.0 0.02 0.05 0.4 0.487372 0.652540
10.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 396 Fig.1 Schematic representation of a liquid film on an elastic sheet 0.0 0.5 1.0 1.5 2.0 0 10 20 30 40 50 S Ī² Fig.2 Variation of film thickness Ī² with unsteadiness parameter S with Mn = 0.0 0 2 4 6 8 0.0 0.4 0.8 1.2 1.6 2.0 Fig.3 Variation of film thickeness Ī² with magnetic parameter Mn Ī² S = 1.2 S = 0.8 Mn 0 2 4 6 8 0.0 0.1 0.2 0.3 0.4 0.5 f'(Ī²) Mn Fig.4 Variation of free-surface velocity f ' (Ī²) with magnetic parameter Mn S = 0.8 S = 1.2 0 2 4 6 8 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 -f''(0) Mn Fig.5 Variation of wall shear stress parameter -f '' (0) with Magnetic parameter Mn S = 1.2 S = 0.8 Forc Slit u Ts h(t) y = 0 y = h y x
11.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 397 0 2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 Fig.6 Variation of free-surface temperature Īø(Ī²) with the Magnetic parameter Mn S = 1.2 S = 0.8 Īø(Ī·) Ī· 0 2 4 6 8 0.4 0.6 0.8 1.0 1.2 Fig. 7 Dimensionless emperature gradien -Īø '(Ī·) at the sheet vs Magnetic parameter Mn for S = 0.8 and S = 1.2 S = 1.2 S = 0.8 -Īø'(0) Mn 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 f '(Ī·) Ī· Fig. 8(a) Variation in the velocity profile f ' (Ī·) for different values of magnetic parameer Mn with S = 0.8 Mn = 0, 1, 2, 5, 8 Ī² = 0.806512 Ī² = 0.979193 Ī² = 1.350880 Ī² = 1.616880 Ī² = 2.151990 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 Fig. 8(b) Variation in the velocity profile f ' (Ī·) for different values of magnetic parameer Mn with S = 1.2 f ' (Ī·) Ī· Ī² = 0.483049 Ī² = 0.579900 Ī² = 0.775795 Ī² = 0.903878 Ī² = 1.127780 M = 0, 1, 2, 5, 8 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 Fig.9(a) Variation oin the temperature profile Īø (Ī·) for different values of magnetic parameter Mn with S = 0.8 Ī· Īø (Ī·) Ī² = 0.806512 Ī² = 0.979193 Ī² = 1.350880 Ī² = 1.616880 Ī² = 2.151990 M = 0, 1, 2, 5, 8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 M = 0, 1, 2, 5, 8 Ī· Īø (Ī·) Fig.9(b) Variation on the temperature profile Īø (Ī·) for different values of magnetic parameter Mn with S = 1.2 Ī² = 0.483049 Ī² = 0.579900 Ī² = 0.775795 Ī² = 0.903878 Ī² = 1.127780
12.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 398 0.0 0.4 0.8 1.2 1.6 0.0 0.2 0.4 0.6 0.8 1.0 Ī² = 1.61688 Mn = 1, Ec = 0.02, A* = B* = 0.05 Fig.10(a) Variation of the temperature profile Īø (Ī·) for different values of Prandtl number Pr with S = 0.8 Pr=100 Pr=10 Pr=5 Pr=1 Pr=0.1 Īø(Ī·) Ī· 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mn=1, Pr = 1, Ec = 0.02, A* = B* = 0.05 Fig.10(b) Variation in he temperaure profile Īø (Ī·) for different values of Prandtl number Pr with S = 1.2 Pr = 100 Pr = 10 Pr = 5 Pr = 1 Pr = 0.1 Ī² = 0.903878 Īø (Ī·) Ī· 0.0 0.4 0.8 1.2 1.6 0.0 0.2 0.4 0.6 0.8 1.0 Fig.11(a) Variation in the temperature profile Īø (Ī·) for different values of Eckert number Ec with S = 0.8 Mn=1, Pr = 1, A* = B* = 0.05 Ec = 0.01, 1, 2, 5 Ī² = 1.61688 Īø(Ī·) Ī· 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Fig.11(b) Variation in the temperature profile Īø (Ī·) for different values of Eckert number Ec with S = 1.2 Mn = 1, Pr = 1, A* = B* = 0.05 Ī² = 0.903878 Ec = 0.01, 1, 2, 5 Īø (Ī·) Ī· 0.0 0.4 0.8 1.2 1.6 0.0 0.2 0.4 0.6 0.8 1.0 Fig 12(a). Variation of temperature profile Īø (Ī·) for different values of space dependent heat source/sink A * with S = 0.8 Mn = 1, Pr = 1.0, Ec = 0.02, B* = 0.5 A* = -0.4, -0.2, 0, 0.2, 0.4 Ī² 1.61688 Īø (Ī·) Ī· 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 Fig 12(b). Variation of temperature profile Īø (Ī·) for different values of space dependent heat source/sink A * with S = 1.2 A* = -0.4, -0.2, 0, 0.2, 0.4 Mn=1, Pr = 1, Ec = 0.02, B* = 0.05 Ī² = 0.903878 Īø (Ī·) Ī·
13.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 399 0.0 0.4 0.8 1.2 1.6 0.0 0.2 0.4 0.6 0.8 1.0 Fig 13 (a). Variation of the temperature profile Īø(Ī·) for different values of temperature dependent heat source/sink B * with S = 0.8 Mn = 1, Pr = 1, Ec = 0.02, A* = 0.05 B* = -0.4, -0.2, 0, 0.2, 0.4 Ī² = 1.61688 Īø (Ī·) Ī· 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 Fig 13 (b). Variation of the temperature profile Īø(Ī·) for different values of temperature dependent heat source/sink B * with S = 1.2 B* = -0.4, -0.2, 0, 0.2, 0.4 Mn = 1, Pr = 1, Ec = 0.02, A* = 0.05 Ī² = 0.903878 Īø (Ī·) Ī· REFERENCES [1] L.J. Crane, flow past a stretching plate, Z. Angrew. Math. Phys. 21 (1970) 645-647. [2] P.S. Gupta, A.S. Gupta, Heat and Mass transfer on a stretching sheet with suction or blowing, Can. J. Chem. Eng. 55 (1977) 744-746. [3] L.G. Grubka, K.M, Bobba, Heat Transfer characteristics of a continuous stretching surface with variable temperature, J. Heat Transfer 107 (1985) 248-250. [4] B.K. Dutta, A.S. Gupta, cooling of a stretching sheet in a various flow, Ind. Eng. Chem. Res. 26 (1987) 333-336. [5] A. Chakrabarti, A.S. Gupta, Hydromagnetic flow and heat transfer over a stretching sheet, Q. Appl. Math. 37 (1979) 73-78. [6] M.S. Abel, P.G. Siddheshwar, Mahantesh M. Nandeppanavar, Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source. Int. J. Heat Mass Transfer, 50(2007), 960-966. [7] M.S. Abel, Mahantesh M. Nandeppanavar, Jagadish V. Tawade, Heat transfer in a Walterās liquid B fluid over an impermeable stretching sheet with non-uniform heat source/ sink and elastic deformation. Commun Nonlinear Sci Numer Simulat 15 (2010) 1791ā1802. [8] C.Y. Wang, Liquid film on an unsteady stretching surface, Quart Appl. Math 48 (1990) 601- 610. [9] S.M. Roberts, J.S. Shipman, Two point boundary value problems: Shooting Methods, Elsevier, New York, 1972. [10] C. Wang, Analytic solutions for a liquid film on an unsteady stretching surface, Heat Mass Transfer 42 (2006) 759ā766. [11] R. Usha, R. Sridharan, On the motion of a liquid film on an unsteady stretching surface, ASME Fluids Eng. 150 (1993) 43-48. [12] E.M. Sparrow, J.L. Gregg, A boundary-layer treatment of laminar film condensation, ASME J. Heat Transfer 81 (1959) 13-18. [13] C.-H. Chen, Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet, J. Non-Newtonian Fluid Mech. 135 (2006) 128. [14] B. S. Dandapat, S. Maity, A. Kitamura, Liquid film flow due to an unsteady stretching sheet, Int. J. non-Linear Mech. 43 (2008) 880-886.
14.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 ā 6340(Print), ISSN 0976 ā 6359(Online) Volume 4, Issue 4, July - August (2013) Ā© IAEME 400 [15] Z. Abbas, T. Hayat, M. Sajid, S. Asghar, Unsteady flow of a second grade fluid film over an unsteady stretching sheet, Math. Comp. Modelling 48 (2008) 518-526. [16] S.D. Conte, C. de Boor, Elementary Numerical Analysis, McGraw-Hill, New York, 1972 [17] T. Cebeci, P. Bradshaw, Physical and computational aspects of convective heat transfer, Springer-Verlag, New York, 1984. [18] Dr P.Ravinder Reddy, Dr K.Srihari and Dr S. Raji Reddy, āCombined Heat and Mass Transfer in MHD Three-Dimensional Porous Flow with Periodic Permeability & Heat Absorptionā, International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 2, 2012, pp. 573 - 593, ISSN Print: 0976 ā 6340, ISSN Online: 0976 ā 6359. [19] M N Raja Shekar and Shaik Magbul Hussain, āEffect of Viscous Dissipation on MHD Flow and Heat Transfer of a Non-Newtonian Power-Law Fluid Past a Stretching Sheet with Suction/Injectionā, International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 4, Issue 3, 2013, pp. 296 - 301, ISSN Print: 0976-6480, ISSN Online: 0976-6499. [20] M N Raja Shekar and Shaik Magbul Hussain, āEffect of Viscous Dissipation on MHD Flow of a Free Convection Power-Law Fluid with a Pressure Gradientā, International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 4, Issue 3, 2013, pp. 302 - 307, ISSN Print: 0976-6480, ISSN Online: 0976-6499. [21] Dr. Sundarammal Kesavan, M. Vidhya and Dr. A. Govindarajan, āUnsteady MHD Free Convective Flow in a Rotating Porous Medium with Mass Transferā, International Journal of Mechanical Engineering & Technology (IJMET), Volume 2, Issue 2, 2011, pp. 99 - 110, ISSN Print: 0976 ā 6340, ISSN Online: 0976 ā 6359.
Baixar agora