The new method of enhancing heat transfer through tri- hybrid nanofluid is discussed in the current study and represented in differential equation system.
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...tmuliya
This file contains Introduction to Heat Transfer and Fundamental laws governing heat transfer.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
ppt on characterization and synthesis of nanofluid with base fluid waterabhishek singh
This document summarizes the synthesis and characterization of a nanofluid with water as the base fluid. It discusses the types of nanoparticles and nanofluids, describes the synthesis of cerium oxide nanoparticles and the nanofluid, and presents the experimental methodology used to measure properties like density, viscosity, and thermal conductivity of the nanofluid at varying temperatures and nanoparticle concentrations. The results show that the density, viscosity, and thermal conductivity of the nanofluid increase with increasing nanoparticle concentration. The maximum thermal conductivity achieved is 0.747 W/m-K at a concentration of 1.5% and temperature of 75°C.
This document discusses laminar and turbulent fluid flow in pipes. It defines laminar flow as smooth, ordered motion of fluid layers and turbulent flow as irregular motion with velocity fluctuations. The Reynolds number determines the flow regime, with laminar flow below 2000 and turbulent flow above 4000. For fully developed laminar pipe flow, the velocity profile is parabolic and the pressure drop is proportional to flow rate, pipe length, and fluid viscosity, inversely proportional to pipe diameter raised to the fourth power.
Bernoulli's equation states that the total mechanical energy of an incompressible and inviscid fluid is constant. It has applications in sizing pumps, flow sensors, ejectors, carburetors, siphons, and pitot tubes. In pumps, the volute converts kinetic energy to pressure energy. Ejectors use pressure energy to create velocity energy to entrain suction fluid and then convert it back to pressure. Pitot tubes use pressure differences to measure flow velocity. Carburetors use Bernoulli's principle to draw in fuel, where faster air has lower pressure. Siphons use the principle to move liquid over an obstruction without pumping.
This document defines and explains various types of thermodynamic processes including: isochoric, isobaric, isothermal, adiabatic, and polytropic processes. It provides the key equations for work, internal energy change, heat transfer, enthalpy change, and PVT relationships for each process type. The document also defines gas constant in terms of universal gas constant and molecular weight.
NATURAL CONVECTIVE HEAT TRANSFER BY Al2O3 &PbO NANOFLUIDSAlagappapandian M
In this presentation related about natural convective heat transfer incresed by using different nano particles. in this fluid is called nanofluids. Nanofluids improve the heat transfer rate of base fluid.
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...tmuliya
This file contains Introduction to Heat Transfer and Fundamental laws governing heat transfer.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
ppt on characterization and synthesis of nanofluid with base fluid waterabhishek singh
This document summarizes the synthesis and characterization of a nanofluid with water as the base fluid. It discusses the types of nanoparticles and nanofluids, describes the synthesis of cerium oxide nanoparticles and the nanofluid, and presents the experimental methodology used to measure properties like density, viscosity, and thermal conductivity of the nanofluid at varying temperatures and nanoparticle concentrations. The results show that the density, viscosity, and thermal conductivity of the nanofluid increase with increasing nanoparticle concentration. The maximum thermal conductivity achieved is 0.747 W/m-K at a concentration of 1.5% and temperature of 75°C.
This document discusses laminar and turbulent fluid flow in pipes. It defines laminar flow as smooth, ordered motion of fluid layers and turbulent flow as irregular motion with velocity fluctuations. The Reynolds number determines the flow regime, with laminar flow below 2000 and turbulent flow above 4000. For fully developed laminar pipe flow, the velocity profile is parabolic and the pressure drop is proportional to flow rate, pipe length, and fluid viscosity, inversely proportional to pipe diameter raised to the fourth power.
Bernoulli's equation states that the total mechanical energy of an incompressible and inviscid fluid is constant. It has applications in sizing pumps, flow sensors, ejectors, carburetors, siphons, and pitot tubes. In pumps, the volute converts kinetic energy to pressure energy. Ejectors use pressure energy to create velocity energy to entrain suction fluid and then convert it back to pressure. Pitot tubes use pressure differences to measure flow velocity. Carburetors use Bernoulli's principle to draw in fuel, where faster air has lower pressure. Siphons use the principle to move liquid over an obstruction without pumping.
This document defines and explains various types of thermodynamic processes including: isochoric, isobaric, isothermal, adiabatic, and polytropic processes. It provides the key equations for work, internal energy change, heat transfer, enthalpy change, and PVT relationships for each process type. The document also defines gas constant in terms of universal gas constant and molecular weight.
NATURAL CONVECTIVE HEAT TRANSFER BY Al2O3 &PbO NANOFLUIDSAlagappapandian M
In this presentation related about natural convective heat transfer incresed by using different nano particles. in this fluid is called nanofluids. Nanofluids improve the heat transfer rate of base fluid.
This document provides a table of contents for topics in fluid dynamics. It begins with mathematical notations for vectors, tensors, divergence, gradient, and other vector calculus topics. It then outlines the basic laws of fluid dynamics, such as conservation of mass and momentum. Later sections cover specific fluid dynamics concepts like boundary layers, compressible flow, shock waves, and potential flow. The document provides the framework for equations and analyses of fluid flows.
Understand the physical mechanism of convection and its classification.
Visualize the development of velocity and thermal boundary layers during flow over surfaces.
Gain a working knowledge of the dimensionless Reynolds, Prandtl, and Nusselt numbers.
Distinguish between laminar and turbulent flows, and gain an understanding of the mechanisms of momentum and heat transfer in turbulent flow.
Derive the differential equations that govern convection on the basis of mass, momentum, and energy balances, and solve these equations for some simple cases such as laminar flow over a flat plate.
Non dimensionalize the convection equations and obtain the functional forms of friction and heat transfer coefficients.
Use analogies between momentum and heat transfer, and determine heat transfer coefficient from knowledge of friction coefficient.
The document provides an introduction to fluid dynamics and fluid mechanics. It defines key fluid properties like density, viscosity, pressure and discusses the continuum hypothesis. It also introduces important concepts like the Navier-Stokes equations, Bernoulli's equation, Reynolds number, and divergence. Applications of fluid mechanics in various engineering fields are also highlighted.
The derivation of the equation of motion for various fluids is similar to the d derivation of Eular’s equation. However ,the tangential stresses arise during the motion of a real viscous fluid, must be considered
1) The document discusses the governing equations for fluid dynamics, which are derived from conservation laws of physics, including conservation of mass, momentum, and energy.
2) These equations can be derived using either a Lagrangian description that follows fluid particles, or an Eulerian description that considers properties at fixed points in space and time.
3) Key equations derived include the continuity equation, momentum equations, and energy equation, which relate the rate of change of properties like density, momentum, and energy to surface and body forces.
This document discusses the continuity equation in fluid mechanics. It defines the continuity equation as the product of cross-sectional area and fluid speed being constant at any point along a pipe. This constant product equals the volume flow rate. The document then derives the continuity equation mathematically by considering the mass flow rate at the inlet and outlet of a pipe with varying cross-sectional areas but steady, incompressible flow. It provides an example calculation and solution for water flow rates and velocities through pipes of different diameters.
PLEASE NOTE THIS IS PART-1
By Referring or said Learning This Presentation You Can Clear Your Basics Fundamental Doubts about Fluid Mechanics. In this Presentation You Will Learn about Fluid Pressure, Pressure at Point, Pascal's Law, Types Of Pressure and Pressure Measurements.
1) The document discusses methods for calculating the friction factor f in turbulent pipe flow.
2) It provides equations from Swamee-Jain, Haaland, and Churchill that can be used to explicitly calculate f based on parameters like Reynolds number, relative roughness, and pipe diameter.
3) The example problem calculates f for water flowing in a ductile iron pipe, finding f=0.038 using Moody's diagram and the relative roughness of the pipe material.
Nanofluids are now developing technology in main purpose heat transfer stream. In paper has brief information on the introduction and preparation methods of nanofluids. This paper prepared from the study of online resources
The document discusses the derivation of the Navier-Stokes equations, which describe compressible viscous fluid flow. It derives the continuity, momentum, and energy equations using conservation principles. The equations contain terms for advection, pressure, and viscous forces. Viscous stresses are related to velocity gradients via Newton's law of viscosity. The Navier-Stokes equations, along with appropriate equations of state, form the governing equations for fluid dynamics problems.
This document discusses computational fluid dynamics (CFD). CFD uses numerical analysis and algorithms to solve and analyze fluid flow problems. It can be used at various stages of engineering to study designs, develop products, optimize designs, troubleshoot issues, and aid redesign. CFD complements experimental testing by reducing costs and effort required for data acquisition. It involves discretizing the fluid domain, applying boundary conditions, solving equations for conservation of properties, and interpolating results. Turbulence models and discretization methods like finite volume are discussed. The CFD process involves pre-processing the problem, solving it, and post-processing the results.
Physical significance of non dimensional numbersvaibhav tailor
This document discusses four non-dimensional numbers that are used in heat transfer analysis:
The Nusselt number relates convective heat transfer to conductive heat transfer through a characteristic length and thermal conductivity. The Grashof number compares buoyancy and inertia forces to viscous forces in natural convection. The Prandtl number is the ratio of momentum diffusivity to thermal diffusivity, relating how a fluid conducts momentum and heat. The Reynolds number compares inertial to viscous forces, indicating flow regime from laminar to turbulent. These non-dimensional numbers provide insight into dominant transfer mechanisms in heat transfer problems.
The lecture was delivered by me for IIChE students chapter on the theme of Student-Industry Interaction at Bharati Vidyapeeth on 8th Feb'14. Foe my blogs kindly refer: https://www.learncax.com/knowledge-base/blog/by-author/ganesh-visavale
Excess property introduction
▪ Excess volume
▪ Excess gibbs free energy
▪ Entropy of mixing
▪ what is use of Residual property and Excess property
in thermodynamics
▪ Case study
▪ Thermo-calc demo
▪ conclusion
This chapter discusses steady heat conduction through various geometries. It introduces thermal resistance networks to model conduction through multilayer walls. It also covers cylindrical and spherical conduction, the effect of insulation thickness, heat transfer from fins, and using conduction shape factors to solve two-dimensional problems. Thermal contact resistance at interfaces and improving contact conductance are also discussed.
This document discusses boundary layer development. It begins by defining boundary layers and describing the velocity profile near a surface. As distance from the leading edge increases, the boundary layer thickness grows due to viscous forces slowing fluid particles. The boundary layer then transitions from laminar to turbulent. Turbulent boundary layers have a logarithmic velocity profile and thicker boundary layer compared to laminar. Pressure gradients and surface roughness also impact boundary layer development and transition.
Obtain average velocity from a knowledge of velocity profile, and average temperature from a knowledge of temperature profile in internal flow.
Have a visual understanding of different flow regions in internal flow, and calculate hydrodynamic and thermal entry lengths.
Analyze heating and cooling of a fluid flowing in a tube under constant surface temperature and constant surface heat flux conditions, and work with the logarithmic mean temperature difference.
Obtain analytic relations for the velocity profile, pressure drop, friction factor, and Nusselt number in fully developed laminar flow.
Determine the friction factor and Nusselt number in fully developed turbulent flow using empirical relations, and calculate the heat transfer rate.
This document provides an outline for a course on thermal unit operations. It begins with definitions of unit operations and thermal unit operations. The three main mechanisms of heat transfer are then described: conduction, convection, and radiation. Conduction involves heat transfer through direct molecular contact in solids or stationary fluids. Convection uses fluid motion to transfer heat. Radiation transfers heat via electromagnetic waves without a medium. Equations for calculating heat transfer via these different mechanisms are also provided.
Non-Newtonian Visco-elastic Heat Transfer Flow Past a Stretching Sheet with C...IJERA Editor
In this paper two dimensional flow of a viscoelastic fluid due to stretching surface is considered. Flow analysis is carried out by using closed form solution of fourth order differential equation of motion of viscoelastic fluid. Further (Walters’ liquid B’ model) heat transfer analysis is carried out using convective surface condition. The governing equations of flow and heat transfer are non-linear partial differential equations which are unable to solve analytically hence are solved using Runge-Kutta Numerical Method with efficient shooting technique. The flow and heat transfer characteristics are studied through plots drawn. Numerical values of Wall temperature are calculated and presented in the table and compared with earlier published results which are in good agreement
Moving Lids Direction Effects on MHD Mixed Convection in a Two-Sided Lid-Driv...A Behzadmehr
Magnetohydrodynamic (MHD) mixed convection flow of Cu–water nanofluid inside a two-sided lid-driven square enclosure with adiabatic horizontal walls and differentially heated sidewalls has been investigated numerically. The effects of moving lids direction, variations of Richardson number, Hartmann number, and volume fraction of nanoparticles on flow and temperature fields have been studied. The obtained results show that for a constant Grashof number (), the rate of heat transfer increases with a decrease in the Richardson and Hartmann numbers. Furthermore, an increase of the volume fraction of nanoparticles may result in enhancement or deterioration of the heat transfer performance depending on the value of the Hartmann and Richardson numbers and the configuration of the moving lids. Also, it is found that in the presence of magnetic field, the nanoparticles have their maximum positive effect when the top lid moves rightward and the bottom one moves leftward.
This document provides a table of contents for topics in fluid dynamics. It begins with mathematical notations for vectors, tensors, divergence, gradient, and other vector calculus topics. It then outlines the basic laws of fluid dynamics, such as conservation of mass and momentum. Later sections cover specific fluid dynamics concepts like boundary layers, compressible flow, shock waves, and potential flow. The document provides the framework for equations and analyses of fluid flows.
Understand the physical mechanism of convection and its classification.
Visualize the development of velocity and thermal boundary layers during flow over surfaces.
Gain a working knowledge of the dimensionless Reynolds, Prandtl, and Nusselt numbers.
Distinguish between laminar and turbulent flows, and gain an understanding of the mechanisms of momentum and heat transfer in turbulent flow.
Derive the differential equations that govern convection on the basis of mass, momentum, and energy balances, and solve these equations for some simple cases such as laminar flow over a flat plate.
Non dimensionalize the convection equations and obtain the functional forms of friction and heat transfer coefficients.
Use analogies between momentum and heat transfer, and determine heat transfer coefficient from knowledge of friction coefficient.
The document provides an introduction to fluid dynamics and fluid mechanics. It defines key fluid properties like density, viscosity, pressure and discusses the continuum hypothesis. It also introduces important concepts like the Navier-Stokes equations, Bernoulli's equation, Reynolds number, and divergence. Applications of fluid mechanics in various engineering fields are also highlighted.
The derivation of the equation of motion for various fluids is similar to the d derivation of Eular’s equation. However ,the tangential stresses arise during the motion of a real viscous fluid, must be considered
1) The document discusses the governing equations for fluid dynamics, which are derived from conservation laws of physics, including conservation of mass, momentum, and energy.
2) These equations can be derived using either a Lagrangian description that follows fluid particles, or an Eulerian description that considers properties at fixed points in space and time.
3) Key equations derived include the continuity equation, momentum equations, and energy equation, which relate the rate of change of properties like density, momentum, and energy to surface and body forces.
This document discusses the continuity equation in fluid mechanics. It defines the continuity equation as the product of cross-sectional area and fluid speed being constant at any point along a pipe. This constant product equals the volume flow rate. The document then derives the continuity equation mathematically by considering the mass flow rate at the inlet and outlet of a pipe with varying cross-sectional areas but steady, incompressible flow. It provides an example calculation and solution for water flow rates and velocities through pipes of different diameters.
PLEASE NOTE THIS IS PART-1
By Referring or said Learning This Presentation You Can Clear Your Basics Fundamental Doubts about Fluid Mechanics. In this Presentation You Will Learn about Fluid Pressure, Pressure at Point, Pascal's Law, Types Of Pressure and Pressure Measurements.
1) The document discusses methods for calculating the friction factor f in turbulent pipe flow.
2) It provides equations from Swamee-Jain, Haaland, and Churchill that can be used to explicitly calculate f based on parameters like Reynolds number, relative roughness, and pipe diameter.
3) The example problem calculates f for water flowing in a ductile iron pipe, finding f=0.038 using Moody's diagram and the relative roughness of the pipe material.
Nanofluids are now developing technology in main purpose heat transfer stream. In paper has brief information on the introduction and preparation methods of nanofluids. This paper prepared from the study of online resources
The document discusses the derivation of the Navier-Stokes equations, which describe compressible viscous fluid flow. It derives the continuity, momentum, and energy equations using conservation principles. The equations contain terms for advection, pressure, and viscous forces. Viscous stresses are related to velocity gradients via Newton's law of viscosity. The Navier-Stokes equations, along with appropriate equations of state, form the governing equations for fluid dynamics problems.
This document discusses computational fluid dynamics (CFD). CFD uses numerical analysis and algorithms to solve and analyze fluid flow problems. It can be used at various stages of engineering to study designs, develop products, optimize designs, troubleshoot issues, and aid redesign. CFD complements experimental testing by reducing costs and effort required for data acquisition. It involves discretizing the fluid domain, applying boundary conditions, solving equations for conservation of properties, and interpolating results. Turbulence models and discretization methods like finite volume are discussed. The CFD process involves pre-processing the problem, solving it, and post-processing the results.
Physical significance of non dimensional numbersvaibhav tailor
This document discusses four non-dimensional numbers that are used in heat transfer analysis:
The Nusselt number relates convective heat transfer to conductive heat transfer through a characteristic length and thermal conductivity. The Grashof number compares buoyancy and inertia forces to viscous forces in natural convection. The Prandtl number is the ratio of momentum diffusivity to thermal diffusivity, relating how a fluid conducts momentum and heat. The Reynolds number compares inertial to viscous forces, indicating flow regime from laminar to turbulent. These non-dimensional numbers provide insight into dominant transfer mechanisms in heat transfer problems.
The lecture was delivered by me for IIChE students chapter on the theme of Student-Industry Interaction at Bharati Vidyapeeth on 8th Feb'14. Foe my blogs kindly refer: https://www.learncax.com/knowledge-base/blog/by-author/ganesh-visavale
Excess property introduction
▪ Excess volume
▪ Excess gibbs free energy
▪ Entropy of mixing
▪ what is use of Residual property and Excess property
in thermodynamics
▪ Case study
▪ Thermo-calc demo
▪ conclusion
This chapter discusses steady heat conduction through various geometries. It introduces thermal resistance networks to model conduction through multilayer walls. It also covers cylindrical and spherical conduction, the effect of insulation thickness, heat transfer from fins, and using conduction shape factors to solve two-dimensional problems. Thermal contact resistance at interfaces and improving contact conductance are also discussed.
This document discusses boundary layer development. It begins by defining boundary layers and describing the velocity profile near a surface. As distance from the leading edge increases, the boundary layer thickness grows due to viscous forces slowing fluid particles. The boundary layer then transitions from laminar to turbulent. Turbulent boundary layers have a logarithmic velocity profile and thicker boundary layer compared to laminar. Pressure gradients and surface roughness also impact boundary layer development and transition.
Obtain average velocity from a knowledge of velocity profile, and average temperature from a knowledge of temperature profile in internal flow.
Have a visual understanding of different flow regions in internal flow, and calculate hydrodynamic and thermal entry lengths.
Analyze heating and cooling of a fluid flowing in a tube under constant surface temperature and constant surface heat flux conditions, and work with the logarithmic mean temperature difference.
Obtain analytic relations for the velocity profile, pressure drop, friction factor, and Nusselt number in fully developed laminar flow.
Determine the friction factor and Nusselt number in fully developed turbulent flow using empirical relations, and calculate the heat transfer rate.
This document provides an outline for a course on thermal unit operations. It begins with definitions of unit operations and thermal unit operations. The three main mechanisms of heat transfer are then described: conduction, convection, and radiation. Conduction involves heat transfer through direct molecular contact in solids or stationary fluids. Convection uses fluid motion to transfer heat. Radiation transfers heat via electromagnetic waves without a medium. Equations for calculating heat transfer via these different mechanisms are also provided.
Non-Newtonian Visco-elastic Heat Transfer Flow Past a Stretching Sheet with C...IJERA Editor
In this paper two dimensional flow of a viscoelastic fluid due to stretching surface is considered. Flow analysis is carried out by using closed form solution of fourth order differential equation of motion of viscoelastic fluid. Further (Walters’ liquid B’ model) heat transfer analysis is carried out using convective surface condition. The governing equations of flow and heat transfer are non-linear partial differential equations which are unable to solve analytically hence are solved using Runge-Kutta Numerical Method with efficient shooting technique. The flow and heat transfer characteristics are studied through plots drawn. Numerical values of Wall temperature are calculated and presented in the table and compared with earlier published results which are in good agreement
Moving Lids Direction Effects on MHD Mixed Convection in a Two-Sided Lid-Driv...A Behzadmehr
Magnetohydrodynamic (MHD) mixed convection flow of Cu–water nanofluid inside a two-sided lid-driven square enclosure with adiabatic horizontal walls and differentially heated sidewalls has been investigated numerically. The effects of moving lids direction, variations of Richardson number, Hartmann number, and volume fraction of nanoparticles on flow and temperature fields have been studied. The obtained results show that for a constant Grashof number (), the rate of heat transfer increases with a decrease in the Richardson and Hartmann numbers. Furthermore, an increase of the volume fraction of nanoparticles may result in enhancement or deterioration of the heat transfer performance depending on the value of the Hartmann and Richardson numbers and the configuration of the moving lids. Also, it is found that in the presence of magnetic field, the nanoparticles have their maximum positive effect when the top lid moves rightward and the bottom one moves leftward.
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.
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...eSAT Journals
This document discusses boundary layer flow and heat transfer of a dusty fluid over a vertical permeable stretching surface. The governing equations for steady, two-dimensional flow are presented and non-dimensionalized. The equations are then solved numerically using the Runge-Kutta method. Results are presented graphically showing the effects of various parameters like fluid-particle interaction, local Grashof number, radiation parameter, and Eckert number on flow and heat transfer characteristics. Comparisons are made to previous studies to validate the numerical method.
This document summarizes a study that investigates the effect of thermophoresis on unsteady free convective heat and mass transfer in a viscoelastic fluid past a semi-infinite vertical plate. The study uses the Walters-B fluid model to simulate rheological fluids. The dimensionless governing equations are solved using an implicit finite difference scheme. Results show that increasing the thermophoretic parameter decreases velocity and concentration but increases temperature within the boundary layer. Thermophoresis is found to significantly increase the surface mass flux.
This document summarizes a study that investigates the effect of thermophoresis on unsteady free convective heat and mass transfer in a viscoelastic fluid past a semi-infinite vertical plate. The study uses the Walters-B fluid model to simulate rheological fluids. The dimensionless governing equations are solved using an implicit finite difference scheme. Results show that increasing the thermophoretic parameter decreases velocity and concentration but increases temperature within the boundary layer. Thermophoresis is found to significantly increase the surface mass flux.
Effects of Thermal Radiation and Chemical Reaction on MHD Free Convection Flo...IJERA Editor
This paper analyzes the radiation and chemical reaction effects on MHD steady two-dimensional laminar
viscous incompressible radiating boundary layer flow over a flat plate in the presence of internal heat generation
and convective boundary condition. It is assumed that lower surface of the plate is in contact with a hot fluid
while a stream of cold fluid flows steadily over the upper surface with a heat source that decays exponentially.
The Rosseland approximation is used to describe radiative heat transfer as we consider optically thick fluids.
The governing boundary layer equations are transformed into a system of ordinary differential equations using
similarity transformations, which are then solved numerically by employing fourth order Runge-Kutta method
along with shooting technique. The effects of various material parameters on the velocity, temperature and
concentration as well as the skin friction coefficient, the Nusselt number, the Sherwood number and the plate
surface temperature are illustrated and interpreted in physical terms. A comparison of present results with
previously published results shows an excellent agreement.
The Study of Heat Generation and Viscous Dissipation on Mhd Heat And Mass Dif...IOSR Journals
The present work is devoted to the numerical study of magneto hydrodynamic (MHD) natural convection flow of heat and mass transfer past a plate taking into account viscous dissipation and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made non dimensional forms using a set of dimensionless variables. Thus, the non dimensional governing equations are solved numerically using finite difference method Crank-Nicolson’s scheme. Numerical outcomes are found for different values of the magnetic parameter, Modified Grashof number, Prandtl number, Eckert number, heat generation parameter and Schmidt number for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat and mass transfer along the surface. Results are presented graphically with detailed discussion.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document presents an analysis of free convective flow and heat transfer of a viscous incompressible fluid over a linearly moving vertical porous plate with suction and viscous dissipation. The fluid viscosity is assumed to vary linearly with temperature. Governing boundary layer equations are non-dimensionalized using similarity transformations and reduced to a boundary value problem. The problem is solved numerically using a shooting method along with the 4th order Runge-Kutta method. Results for dimensionless velocity and temperature distributions are presented for various parameter values, and skin friction and Nusselt numbers are reported in tables.
MHD Stagnation Point Flow of a Jeffrey Fluid Over a Stretching/Shrinking Sheet Through Porous Medium by Eswara Rao M and Krishna Murthy M* in COJ Electronics & Communications: Crimson Publishers_ Journal of electronics and communication engineering impact factor
In this analysis the MHD stagnation point flow of Jeffrey fluid over a stretching/shrinking sheet through porous medium is studied. The governing partial differential equations are transformed into nonlinear ordinary differential equation using the similarity transformations and are solved shooting technique. The effects of governing parameters on the velocity, the temperature and the concentration while the skin friction coefficients, the rate of heat transfer are studied graphically
MHD Stagnation Point Flow of a Jeffrey Fluid Over a
Stretching/Shrinking Sheet Through Porous Medium by Eswara Rao M and Krishna Murthy M* in COJ Electronics & Communications
This document discusses research on heat source/sink effects on magnetohydrodynamic mixed convection boundary layer flow over a vertical permeable plate embedded in a porous medium saturated with a nanofluid. Numerical solutions are obtained for the governing similarity equations using a shooting method. Results show that imposition of suction increases velocity profiles and delays boundary layer separation, while injection decreases velocity profiles. Dual solutions exist for opposing flow with different nanoparticles, with upper branch solutions being physically stable. Suction also delays flow separation compared to impermeable or injection cases.
The International Journal of Engineering and Science (IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
This document summarizes a research article that investigates the steady, two-dimensional Falkner-Skan boundary layer flow over a stationary wedge with momentum and thermal slip boundary conditions. The flow considers a temperature-dependent thermal conductivity in the presence of a porous medium and viscous dissipation. Governing partial differential equations are non-dimensionalized and transformed into ordinary differential equations using similarity transformations. The equations are highly nonlinear and cannot be solved analytically, so a numerical solver is used. Numerical results are presented for the skin friction coefficient, local Nusselt number, velocity and temperature profiles for varying parameters like the Falkner-Skan parameter and Eckert number.
This document presents a numerical solution for unsteady heat and mass transfer flow past an infinite vertical plate with variable thermal conductivity, taking into account Dufour number and heat source effects. The governing equations are non-linear and coupled, and were solved numerically using an implicit finite difference scheme. Various parameters, including Dufour number and heat source, were found to influence the velocity, temperature, and concentration profiles. Skin friction, Nusselt number, and Sherwood number were also calculated.
Similarity Solution of an Unsteady Heat and Mass Transfer Boundary Layer Flow...iosrjce
The unsteady hydromagnetic boundary layer flow of an incompressible and electrically conducting
fluid through a porous medium bounded by a moving surface has been considered. It is assumed that the moving
surface has a velocity profile with respect to time and fluid flow is taken under the influence of a transverse
magnetic field. The similarity solution is used to transform the system of partial differential equations,
describing the problem under consideration, into a boundary value problem of coupled ordinary differential
equations and an efficient numerical technique is implemented to solve the reduced system. The effects of the
parameters such as Magnetic parameter, Prandtl number and Eckert number are discussed graphically on
velocity and temperature distributions
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).
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.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Similar to Numerical Study of Heat Transfer in Ternary Nanofluid Over a Stretching Sheet.pptx (20)
The Building Blocks of QuestDB, a Time Series Databasejavier ramirez
Talk Delivered at Valencia Codes Meetup 2024-06.
Traditionally, databases have treated timestamps just as another data type. However, when performing real-time analytics, timestamps should be first class citizens and we need rich time semantics to get the most out of our data. We also need to deal with ever growing datasets while keeping performant, which is as fun as it sounds.
It is no wonder time-series databases are now more popular than ever before. Join me in this session to learn about the internal architecture and building blocks of QuestDB, an open source time-series database designed for speed. We will also review a history of some of the changes we have gone over the past two years to deal with late and unordered data, non-blocking writes, read-replicas, or faster batch ingestion.
Open Source Contributions to Postgres: The Basics POSETTE 2024ElizabethGarrettChri
Postgres is the most advanced open-source database in the world and it's supported by a community, not a single company. So how does this work? How does code actually get into Postgres? I recently had a patch submitted and committed and I want to share what I learned in that process. I’ll give you an overview of Postgres versions and how the underlying project codebase functions. I’ll also show you the process for submitting a patch and getting that tested and committed.
Analysis insight about a Flyball dog competition team's performanceroli9797
Insight of my analysis about a Flyball dog competition team's last year performance. Find more: https://github.com/rolandnagy-ds/flyball_race_analysis/tree/main
Global Situational Awareness of A.I. and where its headedvikram sood
You can see the future first in San Francisco.
Over the past year, the talk of the town has shifted from $10 billion compute clusters to $100 billion clusters to trillion-dollar clusters. Every six months another zero is added to the boardroom plans. Behind the scenes, there’s a fierce scramble to secure every power contract still available for the rest of the decade, every voltage transformer that can possibly be procured. American big business is gearing up to pour trillions of dollars into a long-unseen mobilization of American industrial might. By the end of the decade, American electricity production will have grown tens of percent; from the shale fields of Pennsylvania to the solar farms of Nevada, hundreds of millions of GPUs will hum.
The AGI race has begun. We are building machines that can think and reason. By 2025/26, these machines will outpace college graduates. By the end of the decade, they will be smarter than you or I; we will have superintelligence, in the true sense of the word. Along the way, national security forces not seen in half a century will be un-leashed, and before long, The Project will be on. If we’re lucky, we’ll be in an all-out race with the CCP; if we’re unlucky, an all-out war.
Everyone is now talking about AI, but few have the faintest glimmer of what is about to hit them. Nvidia analysts still think 2024 might be close to the peak. Mainstream pundits are stuck on the wilful blindness of “it’s just predicting the next word”. They see only hype and business-as-usual; at most they entertain another internet-scale technological change.
Before long, the world will wake up. But right now, there are perhaps a few hundred people, most of them in San Francisco and the AI labs, that have situational awareness. Through whatever peculiar forces of fate, I have found myself amongst them. A few years ago, these people were derided as crazy—but they trusted the trendlines, which allowed them to correctly predict the AI advances of the past few years. Whether these people are also right about the next few years remains to be seen. But these are very smart people—the smartest people I have ever met—and they are the ones building this technology. Perhaps they will be an odd footnote in history, or perhaps they will go down in history like Szilard and Oppenheimer and Teller. If they are seeing the future even close to correctly, we are in for a wild ride.
Let me tell you what we see.
Codeless Generative AI Pipelines
(GenAI with Milvus)
https://ml.dssconf.pl/user.html#!/lecture/DSSML24-041a/rate
Discover the potential of real-time streaming in the context of GenAI as we delve into the intricacies of Apache NiFi and its capabilities. Learn how this tool can significantly simplify the data engineering workflow for GenAI applications, allowing you to focus on the creative aspects rather than the technical complexities. I will guide you through practical examples and use cases, showing the impact of automation on prompt building. From data ingestion to transformation and delivery, witness how Apache NiFi streamlines the entire pipeline, ensuring a smooth and hassle-free experience.
Timothy Spann
https://www.youtube.com/@FLaNK-Stack
https://medium.com/@tspann
https://www.datainmotion.dev/
milvus, unstructured data, vector database, zilliz, cloud, vectors, python, deep learning, generative ai, genai, nifi, kafka, flink, streaming, iot, edge
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ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data LakeWalaa Eldin Moustafa
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#SQL #Views #Privacy #Compliance #DataLake
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Numerical Study of Heat Transfer in Ternary Nanofluid Over a Stretching Sheet.pptx
1.
2. Presenter: Muhammad Waqar
MS Mathematics
Session 2021-23
Supervisor: Dr. Muhammad Amjad
Department of Mathematics
COMSATS University Islamabad (Vehari Campus)
3. Abstract
Basic Definitions
Literature Review
Statement of Problems
References
5. The new method of enhancing heat transfer through tri- hybrid
nanofluid is discussed in the current study and represented in
differential equation system. Tri hybrid nanofluid is formed by
combining three different nanoparticles CuO , TiO2 and Al2O3
with water and CuO-TiO2-H2O tri hybrid nanofluid is formed by
that combination.
The properties of fluid like density ,thermal conductivity ,diffusion
and heat capacitance , etc. will be discussed mathematically .
The governing partial differential equations(PDEs) will transform
into ordinary differential equations(ODEs) and then solved by
using the Runge-Kutta-Fehlberg(RKF) method. The results will be
discussed graphically.
7. “The movement of heat across the border of the
system due to a difference in temperature between
the system and its surroundings.”
Conduction
Radiation
Convection
8. Fluid
A substance that has no fixed shape i.e. gas, plasma, or
liquid is called fluid. It adopts the shape of the
container in which it is contained. The shape of the
fluid can be changed by using outer stress.
9. Nano fluid
Nanofluid contains very small-sized particles in
Nanometer-sized. In a base fluid, these types of fluids
are made of colloidal suspensions of the nanoparticles.
10. Hybrid Nanofluid
It can be defined as the mixing of nanoparticles with
different physical and chemical bonds forms a nanofluid
called a hybrid nanofluid
11. Tri-hybrid Nanofluid
The tri-hybrid nanofluid is devolved by three different
nanomaterials with different physical properties and
chemical bonds.
12. Consider a flow on stretching sheet through
incompressible tri hybrid nanofluid TiO2-SiO2-
Al2O3-H2O which is formed by combining TiO2,
Al2O3 and SiO2 with water by velocity q with
having components (u, v) along the directions
(x, y).
The physical configuration is defined by using
Cartesian coordinates system and the sheet is
supposed to be stretching with speed Ux =ax and
temperature is of sheet is organized by T∞ and
the temperature of tri hybrid nanofluid is
defined by T described in fig.
13.
14.
15. As boundary layer flow and heat transfer of fluid find many applications in industrial usage, the
researcher was motivated to find more sources to enhance the heat transfer over the stretching sheet,
etc. Different researchers discussed the heat transfer of fluid theoretically and numerically over the
drawing of a polymer sheet, cooling a metallic plate of a bath, and the stretching sheet, etc. Industries
caused global warming, and air pollution and became a global issue. They worked to find the sources
of heat transfer that can transfer more heat as well as less environmental pollution. Therefore, the
enhancement in heat transfer properties and heat conducting abilities of tri-hybrid nano fluid motivated
the researchers to consider tri-hybrid nano fluid in industrial applications. In this view, Sakiadis [1]
studied the boundary layer flow on a continuous solid surface which is different from boundary layer
flow on a surface having a finite length. He discussed the behavior of boundary layer flow on the
continuous surface and also derived the differential and integral equations of boundary layer flow for
the such surface.
16. Equations solved on moving continuous surface and cylindrical moving surface for both laminar and
turbulent flow on boundary layer and it was experimentally supported by Tsou et al. [2]. They also
discussed flow on moving surfaces analytically. They suggested its ability to drive equations in
solution. Rollins et al. [3] discussed the heat transfer properties of a second-order fluid flowing past a
stretching sheet in two cases e.g (i) the sheet with prescribed surface temperature (PST-case) and (ii)
the sheet with prescribed surface heat flux (PHF-case). The solution and heat transfer properties were
computed by using Kummir‘s function. They further concluded that no solution exists for smaller
values of the Prandtl number ()while the opposite trend for larger values of for both PST and PHF
cases. Sheridan et al. [4] discussed the MHD flow on an unsteady stretching sheet numerically by
transforming the PDEs into ODEs and solved the obtained equation by using Keller Box Method. They
further discussed the effects of magnetic parameters on the velocity of flow and concluded that
enhancement in the values of parameters decreases the velocity of flow.
17. Puneethet al. [5] investigated the induced magnetic field that results from the three-dimensional bio
convective flow of a Casson nanofluid containing gyrotactic microorganisms along a vertical stretching
sheet. These microorganisms’ motion leads to bio convection and they serve as bioactive mixers that
aid in stabilizing nanoparticle suspension. Abel et al. [6] discussed the heat flow and temperature on
the non-isothermal stretching sheet with variable viscosity. They transformed the proposed model into
ODEs and solved using the 4th order RKF-method. They analyzed the effects of fluid viscosity and
other various parameters like Visco- fluid, etc for two cases of PST and PHF. Keblinskia et al. [7]
discussed the heat flow over the stretching sheet for various heat fluxes subjected to injection and
suction. The formed equations were transformed into ODEs and solved by RKF-Method with various
parameters and . They also discussed the effects of these parameters. They resulted that heat flow on
the surface is increased because of injection and decreased because of suction.
18. [8] discussed the factors that affect the rate of flow of the hybrid nanofluid. They concluded that the
performance of the nanofluid system increased by different factors. Manjunatha et al. [9] explored how
we can increase the flow of heat through the hybrid nanofluid deviation of the general properties of the
general fluid in the presence of Lorentz force on the flow. They used the RKF method to solve the
equations numerically. They further analyzed the consequence of the temperature-dependent
viscosity onward with free convection and magnetic parameter on an increase in heat flow in a
boundary layer field with the assistance of a hybrid nanofluid. Manjuntha et al. [10] analyzed the
complication magnetohydrodynamic (MHD) flow and heat flow of the viscous, incompressible, and
electronically dominant dusty flow through the unsteady stretching sheet numerically. The derived
equations are transformed in ODEs that are solved by the RKF method. The results were presented
for certain parameters including the Nusselt number (), skin coefficient of friction, and different flow
parameters included for both VWT and VHF.
19. Tayebi et al. [11] studied the consequence of a magnetic field on the decay formation and natural
convection inside the cage through the hybrid nanofluid containing conducting wavy solid block. They
further investigated the effects of fluid-solid in the research. Ghalambaz et al. [12] studied the hybrid
nanofluid (/water) in conjugate natural convection. The physical model is described in terms of PDEs
and further converted into a dimensionless form solved by using the finite element method (FEM). The
results depictedthe heat flow being enhanced by adding hybrid nanoparticles in the convection regime
(low Rayleigh number).
Khanet al. [13] discussed the heat flow in nanofluid over the stretching sheet numerically. This was the
1st research paper in which working on stretching sheets in nanofluid was discussed. They purposed
similarity equation solutions that depend on the variation of and Sherwood numbers on the values of
constant numbers like , Lewis number (), Brownian number (), and thermophoresis number (). They
discussed the values function in graphical forms. They concluded that is decreasing function on the
different values of constants and the Sherwood number is increasing on the greater values of .
Various researchers work to enhance the heat flow rates.
20. Manjunatha et al. [14] purposed a thermotical model for the enhancement of heat flow using tri-hybrid
nanofluid by using a combination of nanoparticles and with water and formed a hybrid nanofluid
which decomposed the harmful particles' environmental purity and other various appliance used for
cooling. They presented the thermal conductivity and specific heat capacitance by mathematical
equations that are transformed in ODEs and further the mathematical equations are solved by using
the mathematical RKF method. They represented the results using graphs that clearly observed tri
hybrid nanofluid can transfer more heat than hybrid nanofluid.
21. 1. Sakiadis, B. C. (1961). Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and
axisymmetric flow. AIChE Journal, 7(1), 26-28.
2. Tsou, F. K., Sparrow, E. M., & Goldstein, R. J. (1967). Flow and heat transfer in the boundary layer on a continuous moving
surface. International Journal of Heat and Mass Transfer, 10(2), 219-235.
3. Rollins, D., & Vajravelu, K. (1991). Heat transfer in a second-order fluid over a continuous stretching surface. Acta
mechanica, 89(1), 167-178.
4. Sharidan, S., Mahmood, M., & Pop, I. (2006). Similarity solutions for the unsteady boundary layer flow and heat transfer due to a
stretching sheet. Applied Mechanics and Engineering, 11(3), 647.
5. Puneeth, V., Manjunatha, S., Gireesha, B. J., & Gorla, R. S. R. (2021). Magneto convective flow of Casson nanofluid due to Stefan
blowing in the presence of bio-active mixers. Proceedings of the Institution of Mechanical Engineers, Part N: Journal of
Nanomaterials, Nanoengineering and Nanosystems, 235(3-4), 83-95.
6. Abel, M. S., Khan, S. K., & Prasad, K. V. (2002). Study of visco-elastic fluid flow and heat transfer over a stretching sheet with
variable viscosity. International journal of non-linear mechanics, 37(1), 81-88.
7. Elbashbeshy, E. M. (1998). Heat transfer over a stretching surface with variable surface heat flux. Journal of Physics D: Applied
Physics, 31(16), 1951.
8. Sakiadis, B. C. (1961). Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and
axisymmetric flow. AIChE Journal, 7(1), 26-28.
9. Tsou, F. K., Sparrow, E. M., & Goldstein, R. J. (1967). Flow and heat transfer in the boundary layer on a continuous moving
surface. International Journal of Heat and Mass Transfer, 10(2), 219-235.
10. Rollins, D., & Vajravelu, K. (1991). Heat transfer in a second-order fluid over a continuous stretching surface. Acta
mechanica, 89(1), 167-178.
11. Sharidan, S., Mahmood, M., & Pop, I. (2006). Similarity solutions for the unsteady boundary layer flow and heat transfer due to a
stretching sheet. Applied Mechanics and Engineering, 11(3), 647.
12. Puneeth, V., Manjunatha, S., Gireesha, B. J., & Gorla, R. S. R. (2021). Magneto convective flow of Casson nanofluid due to Stefan
blowing in the presence of bio-active mixers. Proceedings of the Institution of Mechanical Engineers, Part N: Journal of
Nanomaterials, Nanoengineering and Nanosystems, 235(3-4), 83-95.
13. Abel, M. S., Khan, S. K., & Prasad, K. V. (2002). Study of visco-elastic fluid flow and heat transfer over a stretching sheet with
variable viscosity. International journal of non-linear mechanics, 37(1), 81-88.
14. Elbashbeshy, E. M. (1998). Heat transfer over a stretching surface with variable surface heat flux. Journal of Physics D: Applied
Physics, 31(16), 1951.