This document summarizes a study that developed a mathematical model to simulate the heat transfer during the collision of a liquid Al-33 wt.% Cu droplet impacting a 304 stainless steel substrate. The model simultaneously considers fluid flow and heat transfer in the liquid droplet, surrounding gas, and substrate, including the contact resistance between the liquid alloy and substrate. Simulation results correctly predicted the total droplet spread and variation in interlamellar spacing along the droplet radius, matching experimental measurements. The comprehensive model incorporates many factors influencing droplet solidification, including cooling during flight, fluid flow accounting for surface tension, coupled solidification and heat transfer, and variation of physical properties with temperature.
Design &Analysis of Pure Iron Casting with Different MouldsIJMER
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
Abstract
The steady boundary layer free convective flow of a dusty fluid past a vertical permeable stretching surface is studied .The governing equations are converted into first order ordinary differential equations using similarity transformations. These equations are solved numerically by using Runge kutta forth order method. The effects of physical parameters like fluid-particle interaction parameter, local Grashof number, suction parameters, Prandtl number, radiation parameter and Eckert number on the flow and heat transfer characteristics are computed and presented graphically. Also the rate of heat transfer at the surface is discussed. The present results are compared with the previous study and there is a good agreement.
AMS classification 76T10, 76T15
Keywords: Volume fraction, Interaction parameter, Dusty fluid, Thermal radiation, suction parameter, steady flow and heat transfer, Boundary layer flow, Numerical solution.
Design &Analysis of Pure Iron Casting with Different MouldsIJMER
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
Abstract
The steady boundary layer free convective flow of a dusty fluid past a vertical permeable stretching surface is studied .The governing equations are converted into first order ordinary differential equations using similarity transformations. These equations are solved numerically by using Runge kutta forth order method. The effects of physical parameters like fluid-particle interaction parameter, local Grashof number, suction parameters, Prandtl number, radiation parameter and Eckert number on the flow and heat transfer characteristics are computed and presented graphically. Also the rate of heat transfer at the surface is discussed. The present results are compared with the previous study and there is a good agreement.
AMS classification 76T10, 76T15
Keywords: Volume fraction, Interaction parameter, Dusty fluid, Thermal radiation, suction parameter, steady flow and heat transfer, Boundary layer flow, Numerical solution.
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
The effect of solids on the behaviour of the downcomer of a jameson celleSAT Journals
Abstract The effect of solids on the behaviour of the downcomer of a Jameson cell was studied in terms of the hydrophobic/hydrophilic character of the solids. Hydrophobic (carbon), and hydrophilic (silica sand) solids were used, separately. The experiments were carried out under controlled conditions of gas flow rate, pulp flow rate, and pulp consistency. The observed operating variables were the extension of the downcomer operating regions (pulp jet, mixing, and collection) and gas hold-up. It was observed that gas bubbles are smaller and more uniform in size when the pulp is comprised of silica (hydrophilic particles), as compared with pulps consisted of carbon (hydrophobic particles). When measuring a profile of gas holdup in the separation cell, experimental results show that a more homogeneous radial holdup distribution is achieved in the case of a slurry with silica sand rather than the pulp made of carbon. Key words: Jameson cell, downcomer, separation cell, superficial phase velocity, gas hold-up, hydrophobic solids, hydrophilic solids.
The influence of pressure on fluidized bed behaviourIgor Sidorenko
Sidorenko, I., & Rhodes, M. J. (2002) The influence of pressure on fluidized bed behaviour. Paper presented at the World Congress on Particle Technology 4, Sydney.
International journal of engineering and mathematical modelling vol2 no3_2015_1IJEMM
A weak nonlinear stability analysis has been performed for an oscillatory mode of convection, heat and mass transports in terms of
Nusselt, Sherwood numbers are derived and evaluated by a non$-$autonomous complex Ginzburg-Landau equation. The porous layer boundaries are heated sinusoidally with time. The basic state temperature is defined in terms of study and oscillatory parts, where study part show nonlinear throughflow effect on the system and time dependant part show modulation effect. The generalized Darcy model is employed for the momentum equation. The disturbances of the flow are expanded in power series of amplitude of modulation, which is assumed to be small and employed using normal mode technics. The effect of vertical throughflow is found to stabilize or destabilize the system depending on its direction. The time relaxation parameter $\lambda_1$ has destabilizing effect, while time retardation parameter $\lambda_2$ has stabilizing effect on the system. Three types of modulations have been analyzed, and found that, OPM, LBMO cases are effective on heat and mass transfer than IPM case. The effects of amplitude and frequency of modulation on heat and mass transports have been analyzed and depicted graphically. The study establishes that the heat and mass transports can be controlled effectively by a mechanism that is external to the system.
Experimental Investigation on Heat Transfer By Natural Convection Over A Cyli...Ijripublishers Ijri
Experiments were carried out to investigate natural convection heat transfer over uniformly heated hollow cylinder models
made of aluminium alloy and pure copper. The effect of surface temperature, heat transfer coefficient and Nusselt’s
number with respect to different heat fluxes and different orientations of two hollow cylinders. In the current study the
heat fluxes range covers from 124w/m2 to 621 w/m2 . Whereas, the different orientations consider for the present investigation
are 00(vertical), 300, 450, 600, 900(horizontal) respectively for conducting experiments on both hollow cylinders.
Based on the experimental result (surface temperature) the following parameters such as theoretical heat transfer
coefficient, experimental heat transfer coefficient and Nusselt number are evaluated and depicted graphically for both
hollow cylinders made of aluminium alloy and pure copper.
The Elevated Temperature Deformation of G115 Steel and the Associated Deforma...IJAMSE Journal
The next Generation-IV reactors need to be stand for a very high temperature. Structural materials have to resist that temperature; otherwise, damages could appear. G115 steel is a candidate structural material which has been considered in this work. The hot deformation behavior of G115 steel was carried out at elevated temperatures 500, 550 and 600°C with different strain rates ranging from 1x10-5 to 1x10-3 s-1. To derive the hot deformation constitutive equation, the universal hyperbolic-sine Arrhenius-type equation was utilized considering the ultimate stresses values for each condition. As a result, the activation energy of G115, which will assess the high-temperature deformation mechanism, was obtained to be 331 KJ/mol.
The results show that, with proper selection of physical parameters, significant heat transfer
enhancements and pressure drop reductions can be achieved simultaneously with porous pin fins and
the overall heat transfer performances in porous pin fin channels are much better than those in
traditional solid pin fin channels. The effects of pore density are significant. As PPI increases, the
pressure drops and heat fluxes in porous pin fin channels increase while the overall heat transfer
efficiencies decrease and the maximal overall heat transfer efficiencies are obtained at PPI 20.
Furthermore, the effects of pin fin form are also remarkable. With the same physical parameters, the
overall heat transfer efficiencies in the long elliptic porous pin fin channels are the highest while they
are the lowest in the short elliptic porous pin fin channels
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.
PRESSURE DROP STUDIES IN WAVY CORRUGATED PLATE HEAT EXCHANGERSIAEME Publication
Wavy type heat exchangers are one of the prominent corrugated plate heat exchangers. The experimental studies have been carried out on wavy type heat exchangers with glycerol and water as test fluids. The experimental work involves in studying the various factors affecting the fluid flow mostly Friction factor and Pressure Drop , where the energy losses are calculated across the wavy type corrugated plate heat exchanger.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Heat transfer to down flowing viscous films with Evaporation from the interfaceinventionjournals
Introduction: Within long vertical boiling tubes thermo hydrodynamic processes in liquid film take place at a regime of cycling mixing in the bulk of the film by the powerful waves. The existing Heat Transfer models of such phenomena do not take info account such intermittent mixing of fluid Materials and methods: The heat transfer and hydrodynamic processes that take place in down flowing film of water and sugar solutions at the regimes of evaporation from the interface have been studied. There were developed mathematical models, which then were compared with the result of direct experimentation of heat transfer in tubes at the regimes of solutions concentrations. Results and discussion: A mathematical model of heat transfer in laminar, heated to the saturation temperatures liquid films with the developed wavy structures on the free interface have been developed. The model takes into consideration cyclic relaxation of transient temperature field which happens right after the passage of a powerful big wave. The developed mathematical model describes the time history of the two dimensional temperature fields as a function of the Peclet number and the core characteristic of the wavy motion (the length of big waves). Based upon the proposed model a set of correlations have been obtained. These are proposed as a means for the generalization of heat transfer experimental data, obtained within the experimental studies of liquid films, heated to the saturation temperatures and evaporating from the interface. A generalized equation has been derived, which can be used for the calculations of Heat Transfer Coefficients (HTC) to the saturated sugar solutions liquid films. This equation contains wavy characteristics of down flowing films and valid within the range of parameters characteristic for the sugar industry evaporators, namely: concentrations – 0…70 % dry matter; liquid mass flow rate density–0.01×10-3…0.6×10-3 m 2 /sec, the Peclet number range – 400…25000. The mathematical model of the temperature field cyclic relaxation turned out efficient for generalization of heat transfer experimental data not only laminar, but turbulent liquid films either, despite of the fact that the transport equations do not contain turbulent characteristics. Conclusions: A correlation between the liquid film wavy structure with the heat transfer has been established. The correlation is based upon the model of temperature field cyclic relaxation after passage of big waves. The respective correlations have been presented.
Getting Git with Atlassian Stash - Choose Your Own Adventure - WEBINARServiceRocket
We conducted a webinar to discuss how software companies are using enterprise software training to grow their businesses. Training sometimes gets a bad wrap as a cost center when, in fact, it can be a strategic means for growing an early stage enterprise software company, especially those that are preparing to cross the chasm. Whether it is helping to drive qualified leads or directly adding revenue through training sales, software companies can build and run a training department that contributes to growth. This is a copy of the presentation slide used in the webinar.
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
The effect of solids on the behaviour of the downcomer of a jameson celleSAT Journals
Abstract The effect of solids on the behaviour of the downcomer of a Jameson cell was studied in terms of the hydrophobic/hydrophilic character of the solids. Hydrophobic (carbon), and hydrophilic (silica sand) solids were used, separately. The experiments were carried out under controlled conditions of gas flow rate, pulp flow rate, and pulp consistency. The observed operating variables were the extension of the downcomer operating regions (pulp jet, mixing, and collection) and gas hold-up. It was observed that gas bubbles are smaller and more uniform in size when the pulp is comprised of silica (hydrophilic particles), as compared with pulps consisted of carbon (hydrophobic particles). When measuring a profile of gas holdup in the separation cell, experimental results show that a more homogeneous radial holdup distribution is achieved in the case of a slurry with silica sand rather than the pulp made of carbon. Key words: Jameson cell, downcomer, separation cell, superficial phase velocity, gas hold-up, hydrophobic solids, hydrophilic solids.
The influence of pressure on fluidized bed behaviourIgor Sidorenko
Sidorenko, I., & Rhodes, M. J. (2002) The influence of pressure on fluidized bed behaviour. Paper presented at the World Congress on Particle Technology 4, Sydney.
International journal of engineering and mathematical modelling vol2 no3_2015_1IJEMM
A weak nonlinear stability analysis has been performed for an oscillatory mode of convection, heat and mass transports in terms of
Nusselt, Sherwood numbers are derived and evaluated by a non$-$autonomous complex Ginzburg-Landau equation. The porous layer boundaries are heated sinusoidally with time. The basic state temperature is defined in terms of study and oscillatory parts, where study part show nonlinear throughflow effect on the system and time dependant part show modulation effect. The generalized Darcy model is employed for the momentum equation. The disturbances of the flow are expanded in power series of amplitude of modulation, which is assumed to be small and employed using normal mode technics. The effect of vertical throughflow is found to stabilize or destabilize the system depending on its direction. The time relaxation parameter $\lambda_1$ has destabilizing effect, while time retardation parameter $\lambda_2$ has stabilizing effect on the system. Three types of modulations have been analyzed, and found that, OPM, LBMO cases are effective on heat and mass transfer than IPM case. The effects of amplitude and frequency of modulation on heat and mass transports have been analyzed and depicted graphically. The study establishes that the heat and mass transports can be controlled effectively by a mechanism that is external to the system.
Experimental Investigation on Heat Transfer By Natural Convection Over A Cyli...Ijripublishers Ijri
Experiments were carried out to investigate natural convection heat transfer over uniformly heated hollow cylinder models
made of aluminium alloy and pure copper. The effect of surface temperature, heat transfer coefficient and Nusselt’s
number with respect to different heat fluxes and different orientations of two hollow cylinders. In the current study the
heat fluxes range covers from 124w/m2 to 621 w/m2 . Whereas, the different orientations consider for the present investigation
are 00(vertical), 300, 450, 600, 900(horizontal) respectively for conducting experiments on both hollow cylinders.
Based on the experimental result (surface temperature) the following parameters such as theoretical heat transfer
coefficient, experimental heat transfer coefficient and Nusselt number are evaluated and depicted graphically for both
hollow cylinders made of aluminium alloy and pure copper.
The Elevated Temperature Deformation of G115 Steel and the Associated Deforma...IJAMSE Journal
The next Generation-IV reactors need to be stand for a very high temperature. Structural materials have to resist that temperature; otherwise, damages could appear. G115 steel is a candidate structural material which has been considered in this work. The hot deformation behavior of G115 steel was carried out at elevated temperatures 500, 550 and 600°C with different strain rates ranging from 1x10-5 to 1x10-3 s-1. To derive the hot deformation constitutive equation, the universal hyperbolic-sine Arrhenius-type equation was utilized considering the ultimate stresses values for each condition. As a result, the activation energy of G115, which will assess the high-temperature deformation mechanism, was obtained to be 331 KJ/mol.
The results show that, with proper selection of physical parameters, significant heat transfer
enhancements and pressure drop reductions can be achieved simultaneously with porous pin fins and
the overall heat transfer performances in porous pin fin channels are much better than those in
traditional solid pin fin channels. The effects of pore density are significant. As PPI increases, the
pressure drops and heat fluxes in porous pin fin channels increase while the overall heat transfer
efficiencies decrease and the maximal overall heat transfer efficiencies are obtained at PPI 20.
Furthermore, the effects of pin fin form are also remarkable. With the same physical parameters, the
overall heat transfer efficiencies in the long elliptic porous pin fin channels are the highest while they
are the lowest in the short elliptic porous pin fin channels
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.
PRESSURE DROP STUDIES IN WAVY CORRUGATED PLATE HEAT EXCHANGERSIAEME Publication
Wavy type heat exchangers are one of the prominent corrugated plate heat exchangers. The experimental studies have been carried out on wavy type heat exchangers with glycerol and water as test fluids. The experimental work involves in studying the various factors affecting the fluid flow mostly Friction factor and Pressure Drop , where the energy losses are calculated across the wavy type corrugated plate heat exchanger.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Heat transfer to down flowing viscous films with Evaporation from the interfaceinventionjournals
Introduction: Within long vertical boiling tubes thermo hydrodynamic processes in liquid film take place at a regime of cycling mixing in the bulk of the film by the powerful waves. The existing Heat Transfer models of such phenomena do not take info account such intermittent mixing of fluid Materials and methods: The heat transfer and hydrodynamic processes that take place in down flowing film of water and sugar solutions at the regimes of evaporation from the interface have been studied. There were developed mathematical models, which then were compared with the result of direct experimentation of heat transfer in tubes at the regimes of solutions concentrations. Results and discussion: A mathematical model of heat transfer in laminar, heated to the saturation temperatures liquid films with the developed wavy structures on the free interface have been developed. The model takes into consideration cyclic relaxation of transient temperature field which happens right after the passage of a powerful big wave. The developed mathematical model describes the time history of the two dimensional temperature fields as a function of the Peclet number and the core characteristic of the wavy motion (the length of big waves). Based upon the proposed model a set of correlations have been obtained. These are proposed as a means for the generalization of heat transfer experimental data, obtained within the experimental studies of liquid films, heated to the saturation temperatures and evaporating from the interface. A generalized equation has been derived, which can be used for the calculations of Heat Transfer Coefficients (HTC) to the saturated sugar solutions liquid films. This equation contains wavy characteristics of down flowing films and valid within the range of parameters characteristic for the sugar industry evaporators, namely: concentrations – 0…70 % dry matter; liquid mass flow rate density–0.01×10-3…0.6×10-3 m 2 /sec, the Peclet number range – 400…25000. The mathematical model of the temperature field cyclic relaxation turned out efficient for generalization of heat transfer experimental data not only laminar, but turbulent liquid films either, despite of the fact that the transport equations do not contain turbulent characteristics. Conclusions: A correlation between the liquid film wavy structure with the heat transfer has been established. The correlation is based upon the model of temperature field cyclic relaxation after passage of big waves. The respective correlations have been presented.
Getting Git with Atlassian Stash - Choose Your Own Adventure - WEBINARServiceRocket
We conducted a webinar to discuss how software companies are using enterprise software training to grow their businesses. Training sometimes gets a bad wrap as a cost center when, in fact, it can be a strategic means for growing an early stage enterprise software company, especially those that are preparing to cross the chasm. Whether it is helping to drive qualified leads or directly adding revenue through training sales, software companies can build and run a training department that contributes to growth. This is a copy of the presentation slide used in the webinar.
Les divergences sociales en Europe après la criseFrance Stratégie
En contradiction avec l’objectif européen de convergence, un phénomène de divergences sociales et d’emploi est observé entre Etats membres, particulièrement de la zone euro, depuis la crise.
Solidification Simulation of Aluminum Alloy Casting – A Theoretical and Exper...IJMER
Aluminium alloy castings are extensively used in general engineering, automotive and
aerospace industries due to their excellent castability, machinability and high strength-to-weight ratio.
The major problem with aluminium castings is relatively high shrinkage of between 3.5 to 8.5% that
occurs during solidification. This study aims to theoretically analyze shrinkage behavior of cast
aluminium alloy and to conduct solidification simulation of casting using finite element technique based
on the experimental findings. A detailed finite element solidification simulation of A356 aluminum alloy
casting in sand mould is performed, and numerical simulations are carried out considering interface
resistance and with out interface resistance. Few test castings are poured with ordinary riser and
insulated riser, and time - temperature history is plotted with the help of thermocouples to verify the
results. It is observed that the results obtained by the solidification simulation are helpful in optimizing
casting yield, predicting shrinkage, reducing number of trials and rejections.
Porous media has two specifications: First its dissipation area is greater than the conventional fins that enhance heat convection. Second the irregular motion of the fluid flow around the individual beads mixes the fluid more effectively. Nanofluids are mixtures of base fluid with a very small amount of nanoparticles having dimensions from 1 to 100 nm, with very high thermal conductivities, so it would be the best convection heat transfer by using porous media and nanofluids. Thus studies need to be conducted involving nanofluids in porous media. For that, the purpose of this article is to summarize the published subjects respect to the enhancement of convective heat transfer using porous media and nanofluids and identifies opportunities for future research.
THE INFLUENCE OF SHAPE AND SPATIAL DISTRIBUTION OF METAL PARTICLES ON THE THE...IAEME Publication
In this paper, the effect of shape and spatial distribution of metal particles on the thermal conductivity of nickel-silicone composites is investigated to find out the optimum shape and spatial distribution of metal particles in polymer composites. Various finite element models with different particles shapes and arrangements are constructed to predict composite thermal conductivity.
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mechanical and civil engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mechanical and civil engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Film Condensation Behaviour of Steam on Isothermal Walls in Presence of Non-C...ijceronline
Numerical modelling of condensation had been a challenging task for the researchers for many years due to its time scale and rapidity. Present work deals with the characterization of condensation in presence of non-condensable gases on isothermal surfaces which is a common situation in many condensing devices. The investigation includes the effect of different flow parameters on condensation of saturated steam-air mixture using a numerical approach. The study uses wall condensation model through ANSYS CFX solver. The effect of mass fraction of steam, operating pressure and mass flow rate of mixture is studied. Investigation provides some key characteristics about film condensation which normally remain absent in condensation without non-condensable gas. The findings of this study will provide valuable insight in thermal design process of components incorporating this phenomenon.
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.
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.
Verification of johnson cook material model constants of aa2024-t3 for use in...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Computational model for multi alloy casting of aluminum rolling ingotsLOKESH BAVISKAR
The present model is useful in providing the insight on the thermo-fluid and solidification profile that can help in identifying appropriate process parameters. The development and validation of a steady-state computational fluid dynamics (CFD) model which appropriately treats heat transfer, fluid flow and solidification during multi alloy casting. Due to solidification shrinkage (density difference between the solid and liquid phase), the ingot contracts leading to the formation of an air gap between the ingot surface and the mold wall (air gap zone). In this zone, air gap gives rise to additional resistance to heat transfer from the ingot surface to the mold wall. To capture this phenomenon proposed a simplified approach for air gap predictions which is a combination of a one-dimensional air gap model with two dimensional CFD simulation for contact heat transfer coefficient when metal is in perfect contact with the mold surface.
Heat transfer studies were carried out in a laboratory scale gas-solid fluidized bed with 0.1m
ID x 1 m length column, using three sizes of local sand particles of 301, 454, and 560 µm. the bed
region was heated bya horizontal heat transfer probe. It was made of copper rod (15 mm ODx50 mm
long) and insulated at the ends by Teflon. A hole was drilled at the center of the rod to accommodate
a cartridge heater 200 W (6.5 mm OD x 42 mm long). Three bed inventories of sand 1.5 kg, 2.0 kg,
and 2.5 kg, four superficial air velocities of 1.0 m/s, 1.25 m/s, 1.5 m/s, 1.75 m/s were used. Three
heat fluxes of 1698.9, 2928.4, 4675.7 W m-2 were employed. The data obtained showed how the heat
transfer coefficient effected by the above operating parameters. The heat transfer coefficient is
directly proportional with air superficial velocity as well as the bed inventory and heat fluxes but
inversely proportional with sand particles size.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
Dhindaw al cu
1. Simulation of cooling of liquid Al–33 wt.% Cu droplet impinging
on a metallic substrate and its experimental validation
A. Kumar a
, S. Ghosh a,*, B.K. Dhindaw b
a
Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur 721302, India
b
Indian Institute of Technology Ropar (Punjab), Nangal Road, Rupnagar 140001, India
Received 20 June 2009; received in revised form 25 August 2009; accepted 28 August 2009
Available online 1 October 2009
Abstract
In the present work a model for heat transfer during collision of a falling liquid Al–33 wt.% Cu droplet on a 304 stainless steel sub-
strate has been developed on a FLUENT 6.3.16 platform. The model simultaneously takes into account the fluid flow and heat transfer
in the liquid droplet and the surrounding gas, and the heat transfer in the substrate. The liquid–gas interface was tracked using the vol-
ume of fluid method and the contact resistance between Al–33 wt.% Cu and the substrate was taken into account. The comprehensive
model correctly predicted the total spread in the droplet. As per the predicted transient thermal field, the solidification front speed
oscillated along the radius of the spread droplet. Based on the estimated front speeds at these locations and Jackson–Hunt plot for
Al–33 wt.% Cu, the variation of interlamellar spacing along the radial direction was found. It matched well with the variation of the
experimentally measured interlamellar spacing at different locations along the radius.
Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Eutectic; Alloy droplet; Substrate; Solidification; Modeling
1. Introduction
Spray forming or casting refers to the break-up of a
liquid metal stream into variously sized droplets, propelled
away from the atomization region by fast flowing atomiz-
ing gas to a substrate, where the droplets are deposited
[1–3]. The flight and deposition of the droplet are accompa-
nied by cooling and solidification, during which the cooling
rate determines the structural features at the mesoscale,
such as grain size, grain structure and eutectic spacing (in
the case of eutectic alloys). Thus, during the spray casting,
desired structural features can be obtained by controlling
the rate of cooling within the droplets.
The cooling rate within the droplets, in turn, depends on
the processing parameters such as superheat of liquid
metal, size of the droplet, velocity of impingement and
thermal diffusivity of the substrate material, and thus the
structure of solidified material can be controlled by con-
trolling these parameters. The processing condition for
achieving the desired structure can be identified by a vali-
dated comprehensive mathematical model that predicts
the flow and the thermal fields during the droplet deposi-
tion. However, due to interaction of several complex phe-
nomena, comprehensive modeling of the droplet
deposition is a challenging task. Further, the validation
of the model is complicated due to the small size of the
droplet and the high cooling rates involved.
In the past, mathematical models which simulate the
atomization and thermal history of gas atomized droplets
as a function of flight distance from the point of gas atom-
ization to the point of deposition [4–6] have been developed.
Gas atomization has been extensively modeled [7–13].
Zeoli and Gu [12] developed a numerical model to simulate
the critical droplet break-up during the atomization. In
this numerical model they coupled droplet break-up with
the flow field generated by high-pressure gas nozzle and
1359-6454/$36.00 Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2009.08.063
*
Corresponding author. Tel.: +91 3222283294; fax: +91 3222282280.
E-mail address: sudipto@metal.iitkgp.ernet.in (S. Ghosh).
www.elsevier.com/locate/actamat
Available online at www.sciencedirect.com
Acta Materialia 58 (2010) 122–133
2. reported that this numerical model can provide quantitative
assessment of the atomization process. Recently Zeoli and
Gu [13] developed an isentropic plug nozzle (IPN) to reduce
the shocks and maximize the kinetic energy being trans-
ferred from the gas in order to instablize the melt stream.
The performance of IPN was examined using a numerical
model which includes gas flow dynamics, droplet atomiza-
tion mechanism and particle tracking.
The in-flight thermal behavior during deposition over a
rotating substrate was modeled by Tinoco et al. [14]. The
calculations were performed by solving the momentum
and enthalpy equations for the gas. Ojha and coworkers
[15] studied solidification of undercooled droplets during
atomization process. The predicted cooling rate was com-
pared with the calculated cooling rate from the secondary
dendrite arm spacing measurement. Zeoli et al. [16]
described a numerical model which combines both cooling
and break-up in single computation (integrated model).
The dynamic history of droplets was solved as discrete
phase in Eulerian gas flow. The droplet solidification model
incorporated the detailed heat transfer mechanism of und-
ercooling, recalescence, peritectic and segregated solidifica-
tion during flight. The model establishes that the in-flight
distance is the major factor influencing the atomization
and solidification of droplets.
Several numerical models have been developed to simu-
late impact and solidification of molten droplets on a cold
substrate. Bennett and Poulikakos [17] and Kang et al. [18]
studied droplet deposition assuming that solidification
starts only after complete spreading of droplet in the form
of a disk. Theoretical and experimental studies done by
Bennett and Poulikakos [17] showed that the thermal con-
ductivity of the substrate significantly affects the cooling
rate of the splat. However, they did not incorporate the
convection.
Using numerical models and experiments, Zhao et al.
[19,20] studied heat transfer and fluid dynamics during
collision of a liquid droplet on a substrate. They extended
the earlier model of Fukai et al. [21] to account for the
relevant convection and conduction heat transfer phe-
nomena both in the droplet and in the substrate, in the
case when there is no solidification. Their results, there-
fore, are applicable to the pre-solidification stage of the
impact process. Liu et al. [22] used a one-dimensional
solidification model in conjunction with a two-phase flow
continuum technique to track the moving liquid–solid
boundary. The model, however, does not account for
the convection in the liquid and conduction in the
substrate.
Trapaga et al. [23] used a commercially available code,
FLOW-3D [24], to study the heat transfer and solidifica-
tion phenomena during droplet impact. They assumed
that the substrate was isothermal, and neglected any ther-
mal contact resistance at the liquid–solid interface. Ber-
tagnolii et al. [25] used a finite element approach with
an adaptive discretization technique to model the defor-
mation of the droplet and evolution of the thermal field
within the splat. Their model, however, does not take into
account the solidification and heat transfer to the sub-
strate. Waldvogel and Poulikakos [26] used a finite ele-
ment model to simulate spreading and solidification
during droplet impact.
A three-dimensional simulation of impingement of tin
droplet was carried out by Kamnis et al. [27]. This model
was based on a two-dimensional model of impact of tin
droplet on stainless steel using volume of fluid technique
(VOF) [28]. The VOF technique was employed along with
solidification to compute the tracking of dynamic impact,
spreading, solidification, splashing and air entrapment of
sequentially impinging droplets over the substrate. The
numerical model was validated with the results of high-
speed camera photography of the tin droplet, and excellent
agreement between simulation and experimental results
were reported. In particular the finger formation, which
cannot be predicted by an axisymmetric model, and air
entrapment could be predicted using the three-dimensional
model.
The heat transfer through the liquid metal substrate
contact will have significant influence on the cooling rate
of the impinging droplet. If the contact resistance is high
the cooling rate of the droplet will be low, even though
the substrate metal may have high conductivity and heat
capacity. Only a few investigators [27–32] have attempted
to estimate the contact resistance of the droplet–substrate
contact.
Simulation of the process of impingement and solidifica-
tion of a droplet by a comprehensive mathematical model
would incorporate the following:
1. cooling in the droplet during flight;
2. flow in the melt taking into account the surface tension;
3. coupled solidification, heat transfer to the surrounding
gaseous atmosphere and substrate;
4. solidification and undercooling;
5. variation of physical properties with temperature.
In the models of droplet deposition of liquid metals on a
solid substrate all these have not been simultaneously
incorporated. Most of the models have not taken into
account the contact thermal resistance between the liquid
droplet and substrate. Further, very few have attempted
validation of the model.
In the present study a comprehensive mathematical
model for impingement of liquid Al–33 wt.% Cu alloy on
a stainless grade 304 stainless steel substrate has been
developed. The model takes into account the coupled heat
transfer in the liquid droplet, surrounding gaseous med-
ium, solid substrate and the contact thermal resistance
between the droplet and substrate. It further takes into
account solidification, natural convection, flow in the drop-
let and the gaseous medium. The contact thermal resistance
between the liquid alloy droplet and a grade 304 stainless
steel substrate was estimated using an inverse approach.
The model was experimentally validated.
A. Kumar et al. / Acta Materialia 58 (2010) 122–133 123
3. 2. Mathematical modeling of droplet impingement
The present study aims at developing a mathematical
model of flow and heat transfer in a liquid metal which falls
freely through gaseous medium and finally impinges on a
cold substrate. The modeling of phenomena is complex
because it involves interactions among three phases, viz.,
liquid metal, solid substrate and gaseous medium. Further,
as the droplet falls under the action of gravity and impinges
on the substrate, its shape changes rapidly with time.
Fig. 1 is a schematic sketch of the phenomenon. A drop-
let, which is initially spherical, falls through gaseous med-
ium and impinges on a substrate. Since the initial shape
of the droplet is assumed to be spherical, the fluid flow
and the heat transfer are axisymmetric.
The following assumptions have been made while devel-
oping the model:
1. The droplet initially had spherical geometry.
2. The problem is axisymmetric about the axis shown in
Fig. 1.
3. Impinge velocity of the droplet is perpendicular to the
plane of the substrate and there is no rotation of drop-
let along the axis.
4. The flow of molten alloy and gas is laminar and incom-
pressible. The velocity of gaseous media at domain walls
is zero.
5. Walls of the domain (Fig. 1) are assumed to be at ambi-
ent temperature.
6. The heat transfer is dominated by convection and con-
duction modes. Therefore, radiation from the droplet
surface to the surroundings is ignored.
7. To estimate thermal contact resistance a special solid
material has been defined. The conductivity of the spe-
cial material is estimated from the measured value of
the contact resistance.
8. Initial velocity field is zero.
2.1. Governing equations
Numerical simulations of the axisymmetric droplet
deposition processes were conducted by solving the two-
dimensional (r–z) continuity, Navier–Stokes and energy
equations. The volume of fluid (VOF) approach [33] was
coupled with Navier–Stokes and energy equations to track
the surface of the impinging droplet on a fixed Eulerian
structured mesh.
The continuity or conservation of mass equation is given
by
1@
r@r
ðruÞ þ
@v
@z
¼ 0 ð1Þ
where u and v are velocity components in the r and z direc-
tions, respectively. The momentum conservation equations
in r and z directions are
@u
@t
þ u
@u
@r
þ v
@u
@z
¼ À
1
q
@P
@r
þ t
@2
u
@z2
þ
1
r
@
@r
r
@u
@r
À
u
r2
þ gr þ Sr ð2Þ
@v
@t
þu
@v
@r
þv
@v
@z
¼ À
1
q
@P
@z
þt
@2
v
@z2
þ
1
r
@
@r
r
@v
@r
þgz þSz
ð3Þ
where P, q, and t are pressure, density, and kinematic vis-
cosity of the fluid, respectively, g represents gravitational
force per unit mass and S represents any other source term
or body force term. The interfacial tension was incorpo-
rated in the Navier–Stokes equation as a body force term.
Enthalpy–porosity formulation [34] was incorporated in
the solution scheme in order to handle the effects of solid-
ification. The formulation is described below.
Solidification results in latent heat generation and a
modified form of the energy equation, incorporating latent
heat, was used. The modified energy equation is given by
@ðqHÞ
@t
þ r Á ðquHÞ ¼ r Á ðkrTÞ þ Sh ð4Þ
where H is the enthalpy per unit volume, k is thermal con-
ductivity and Sh is the rate of energy generation per unit
volume. The enthalpy of the material was computed as
the sum of the sensible enthalpy, h, and the latent heat,
DH. It is expressed as
H ¼ h þ DH ð5Þ
where
h ¼ href þ
Z T
Tref
cP dT ð6Þ
In Eq. (6) href is the sensible enthalpy at the reference tem-
perature and cP is the specific heat at constant pressure.
The liquid fraction, b, is defined as
b ¼ 0 if T Tsolidus
b ¼ 1 if T Tliquidus
b ¼ TÀTsolidus
TliquidusÀTsolidus
if Tsolidus T T liquidus
ð7Þ
Fig. 1. Schematic representation of the mathematical model of droplet
deposition.
124 A. Kumar et al. / Acta Materialia 58 (2010) 122–133
4. The latent heat content can be written in terms of the
latent heat of freezing, L:
DH ¼ bL ð8Þ
The source term appearing on the right-hand side of Eq.
(4) is given by
Sh ¼
@ðqDHÞ
@t
þ rðquDHÞ ð9Þ
Due to high temperature difference between the droplet
and substrate and the relatively low droplet velocity, vis-
cous dissipation of heat was negligible and thus not
included in the source term.
Solidification also results in phase change. Instead of
tracking the interface, Al–33 wt.% Cu was assumed to be
a single phase pseudo-porous medium whose porosity
was proportional to the liquid fraction. Thus the porosity
of this single phase pseudo-porous medium varied from
as low as 0 in the solidified region to maximum in the liquid
region. Since Al–33 wt.% Cu is a eutectic alloy a sudden
transition in the porosity is expected at the solidification
front. To avoid numerical difficulties associated with this
sudden transition, the solidification front was assumed to
be a narrow band and the porosity was varied from 0 to
the maximum value over this band. The effect of porosity
was incorporated in the momentum equations through a
momentum source terms (Eqs. (2) and (3)). The momen-
tum source term S is given by
S ¼
ð1 À bÞ
2
ðb3
þ eÞ
Amusht ð10Þ
where b denotes the liquid fraction, e is a small number
(0.001) to avoid divisionby zero, Amush is the mushy zone
constant, and t is the velocity term.
2.2. Boundary and initial conditions
2.2.1. Boundary conditions
Since the problem is axisymmetric, only half of the
domain shown in Fig. 1 was considered in the computation
domain. Axis of symmetry was like a free-slip wall. The
normal velocity was zero. The tangential velocity did not
have normal gradient. Thus along the axis of axisymmetry
u = 0 and ov/or = 0. At the other boundaries u = 0 and
v = 0. Since these boundaries are far away from the drop-
let, the temperature at these boundaries was set equal to the
ambient temperature, i.e., 300 K.
2.2.2. Initial conditions
All zones were initialized with a temperature of 300 K,
except the droplet. The droplet was given a pre-determined
higher temperature. The initial velocities at every point
inside the domain were zero, except within the droplet,
where it was set to ÀU0.
2.3. Discretization and the solution method
The above described model was simulated on a FLU-
ENT 6.3.16. FLUENT 6.3.16 solves the above described
equations using a control volume approach, which is fully
implicit in time and uses upwind differencing in space [35].
A segregated solution algorithm [36] with a control vol-
ume based technique was used in the numerical method.
The pressure and velocity were coupled with a semi-impli-
cit method for pressure linked equation (SIMPLE) algo-
rithm [37,38], which uses a guess-and-correct procedure
for the calculation of pressure on the staggered grid
arrangement.
3. Thermo-physical properties
Al–33 wt.% Cu alloy was selected as the alloy system for
two reasons. Firstly the thermo-physical properties of the
alloy are known, and secondly the Jackson–Hunt plot is
available for the comparison. The simulation was carried
out for Al–33 wt.% Cu liquid droplets sizes of 100–
1000 lm.
Table 1 gives the thermo-physical properties of the Al–
33 wt.% Cu alloy used in the present model [39].
The contact resistance between Al–33 wt.% Cu and the
grade 304 stainless steel substrate was determined to a first
approximation using an inverse approach, described in the
following section.
3.1. Determination of thermal contact resistance
In order to estimate the thermal contact resistance, two
chromel–alumel thermocouples were introduced in the
grade 304 stainless steel channel; one was placed at
the outer wall of the channel and the other was placed in
Table 1
Thermo-physical properties of Al–33 wt.% Cu alloy.
Properties of Al–33 wt.% Cu used in model Value
Thermal conductivity (W mÀ1
KÀ1
) Ks = 155
Kl = 71
Density (kg mÀ3
) qs = 3410
ql = 3240
Solidus temperature (K) 821
Liquidus temperature (K) 821
Melting heat (J kgÀ1
) 350,000
Specific heat (J kgÀ1
KÀ1
) Cs = 1070
Cl = 895
Viscosity*
(kg mÀ1
KÀ1
) At 943 K = 1.001 Â 10À3
[40]
At 973 K = 8.624 Â 10À4
[40]
At 1023 K = 5.65 Â 10À4
[40]
Surface tension (N mÀ1
) 0.868 [41]
s = solid; l = liquid.
*
Value of viscosity of Al–33 wt.% Cu has been calculated using Arrhenius
equation: g ¼ g0 exp À E
RT
À Á
up to the solidus temperature.
A. Kumar et al. / Acta Materialia 58 (2010) 122–133 125
5. the central position of the channel cavity as shown in
Fig. 2. Subsequently Al–33 wt.% Cu alloy was melted in
an electric resistance furnace and poured into the grade
304 stainless steel channel. Temperatures in the casting
were monitored using thermocouples connected to a data
acquisition system (DAS). The temperature data at the
two locations were used to estimate the thermal contact
resistance at the interface of the wall and the liquid metal
by matching them with the temperatures at the two posi-
tions obtained from simulation.
The computational domain for the simulation along
with the boundary conditions is shown in Fig. 3. The air
gap between Al–33 wt.% Cu and stainless grade 304 stain-
less steel channel has been assumed to be a solid layer with
equivalent thermal resistance.
3.2. Initial conditions
The input of initial conditions was taken from the
experiment:
Initia channel wall temperature = 398 K.
Liquid melt initial temperature = 956 K.
Ambient temperature = 300 K.
4. Experimental validation of the model
4.1. Uniform droplet deposition process
The master alloy was prepared from a 99.96% pure Al
and a 99.99% pure Cu by induction melting. The chemical
analysis was carried out to confirm the composition of the
master alloy. Fig. 4 shows the schematic diagram of droplet
deposition process. Al–33 wt.% Cu alloy was used for the
spray casting process. A metal charge of 50 g of master
alloy was heated in a crucible, under air atmosphere, to a
temperature above the liquidus temperature. The crucible
was made of quartz and was coated with alcohol soot to
avoid reaction between the melt and quartz crucible. The
diameter of the melt delivery nozzle was 3 mm. The cruci-
ble was fixed inside a resistance furnace. A graphite stopper
was placed on the delivery nozzle at the base of the cruci-
ble. A thermocouple in the center of the crucible and the
furnace insulation allowed continuous measurement of
temperature. When a pre-determined temperature was
reached, typically 150 °C above the alloy liquidus, the
graphite stopper rod was removed and the molten metal
flowed through the delivery nozzle. The molten metal
stream flowed into the deposition chamber in the form of
metal droplets which impinged upon the substrate and
were deposited.
The solidified droplets were prepared for metallographic
examination using standard metallographic procedure and
etched with Keller’s reagent. The microstructures were
studied using a JEOL JSM-6480LV scanning electron
microscope.
Fig. 2. Schematic two-dimensional view of the experimental set-up for determination of contact resistance.
Fig. 3. Computational domain along with the boundary conditions for
computing the thermal field in the experimental set-up shown in Fig. 2.
126 A. Kumar et al. / Acta Materialia 58 (2010) 122–133
6. 5. Results and discussion
5.1. Determination of contact thermal resistance
The value of the effective conductivity of the gap region
and the thermal contact resistance were determined by
matching the computed temperatures at (i) a selected loca-
tion in the Al–33 wt.% Cu liquid melt (Location 1 in Fig. 2)
after it was poured on a grade 304 stainless steel channel
(Fig. 2), and (ii) a selected location in the stainless steel
channel (Location 2 in Fig. 1), with the experimentally
measured ones. For the value of thermal contact resistance
7 Â 10À4
m2
K WÀ1
the simulated temperature profile was
similar to the experimental profile as shown in Fig. 5.
Therefore, 7 Â 10À4
m2
K WÀ1
was considered a value of
the thermal contact resistance in the droplet deposition
model.
Fig. 4. Schematic drawing of the uniform droplet forming process.
Fig. 5. Computed and experimentally measured temperature at Locations
1 and 2 (Fig. 2).
Fig. 6. Phase profile of an impinging Al–33 wt.% Cu droplet on the substrate.
A. Kumar et al. / Acta Materialia 58 (2010) 122–133 127
7. 5.2. Simulation of droplet deposition
In the present study simulations were carried out for the
droplets, with diameters varying between 3.82 mm and
8.18 mm falling through a height of 50 cm on a grade 304
stainless steel substrate. As stated earlier, the shape of the
droplet impinging upon the substrate was assumed to be
spherical and the cooling of droplet in the gaseous medium
during the free fall was ignored. The assumption of insig-
nificant temperature drop during flight was reasonable, as
the temperature drop during the period of flight is expected
to be negligible compared to that during the spreading.
This was substantiated by an additional simulation of a
droplet during its free fall through a height of 50 cm. In this
simulation the Weber number was $312. The shape of the
Al–33 wt.% Cu droplets does not change significantly dur-
ing flight. The substrate thickness was taken as low as
1 mm in order to reduce the computational time. This will
not affect the accuracy of the prediction of the thermal field
because during the short duration of droplet spreading and
solidification the temperature rise did not take place
beyond a distance of 0.3 mm.
The computed velocity, temperature, liquid fraction and
phase (Al–33 wt.% Cu and air) fields after different periods
of time were plotted. Fig. 6 shows the phase contour of Al–
33 wt.% Cu droplet having a diameter of 8.18 mm in air. In
this case the velocity of impingement was 3.13 m sÀ1
, and
therefore the Weber number was 302. The spread of the
droplet occurred within a short time frame of 8 Â 10À3
s
and no disintegration due to the surface tension force
was observed. It can also be seen that the solidification
starts 10À2
s after the spread has taken place. Fig. 7 also
shows the velocity profile of Al–33 wt.% Cu/air system. It
can be noted from the figure that air adjacent to Al–
33 wt.% Cu is dragged in the direction of spread and a
re-circulating flow in air can be observed.
The evolution of the shape of liquid droplet impinging a
solid substrate is a complex phenomenon. However, this
has been studied by many investigators [28,42–47]. An
important parameter which decides upon the evolution of
shape of the liquid droplet is the Weber number, i.e., den-
sity, viscosity, impingement velocity and surface tension.
Depending on the Weber number, different types of shape
evolution are possible.
Fig. 7. Velocity profile of the Al–33 wt.% Cu/air system.
128 A. Kumar et al. / Acta Materialia 58 (2010) 122–133
8. The simulated evolution of droplet shape (Fig. 6) has
been reported earlier [46]. The bump near the edge has been
observed even when there is no cooling [42]. The physical
reasons for the bump formation are not fully clear
although surface tension and the existence of the bump
because of the maximum cooling near the edge (Fig. 8)
[46] could be suggested as two of the reasons.
The thermal contour in Fig. 8 shows convective cooling
at the top surface, where Al–33 wt.% Cu is colder than the
inner region. Similarly conductive cooling of Al–33 wt.%
Cu near the substrate can be seen along with heating up
of the substrate as shown in the temperature profile plotted
(Fig. 8). Fig. 9 shows the liquid fraction within Al–33 wt.%
Cu system.
Solidification front speed was estimated based on the
liquid fraction profile at 20 different locations, 7 of which
are shown in Fig. 10. Fig. 11a shows the variation of front
speed with the radial distance. Interestingly the experimen-
tally observed interlamellar spacing (Fig. 11b), which is
related to the front speed by Jackson–Hunt relationship,
also correlated with the radial distance in a similar manner.
Fig. 11c and d shows the microstructure at the marked
radial distance (Fig. 11b).
The variation front speed with the radial distance can
be explained in terms of variation of splat thickness with
the radial distance. Fig. 10 shows the different locations
in the splat along the radial direction. Fig. 11a shows
the growth rates at those locations. It can be observed
that the front speed is significantly less at thicker
locations (L3, L6, L12, L18, L19) and highest front
speeds can be observed only at the thinnest locations
(L9,L15).
Fig. 8. Temperature profile of an impinging Al–33 wt.% Cu droplet on the substrate.
A. Kumar et al. / Acta Materialia 58 (2010) 122–133 129
9. 5.3. Sensitivity of font speed to variation in contact
resistance and natural convection
In order to study the sensitivity of front speed to varia-
tion in contact resistance, the contact resistance was varied
from 6.3 Â 10À4
m2
K WÀ1
(10% less than experimentally
determined value) to 7.7 Â 10À4
m2
K WÀ1
(10% less than
experimentally determined value). At the thicker locations
the front speed was found to be insensitive to the contact
resistance. However, at locations L9 and L15, which are
the thinnest locations, front speed is sensitive to the contact
resistance. Thus it can be concluded that the variation in
the front speed along the radial direction is due to variation
in the splat thickness.
Simulation was carried out where natural convection in
both Al–33 wt.% Cu and air was suppressed. The results
suggest that natural convection did not play a significant
role as compared to the conduction through the substrate.
5.4. Effect of the initial temperature
Simulations were carried out for the two values of initial
temperature; viz., 875 K and 973 K. The initial temperature
had a strong influence on the extent of spreading. Fig. 12
shows the spread in diameter vs. time for 8.18 mm droplets
having initial temperature of 875 K and 973 K. It can be
seen that the spread increases with the increase in initial
temperature or the superheat. This is expected, as due to
Fig. 9. Liquid fraction profile of the Al–33 wt.% Cu/air system.
Fig. 10. Profile of the deformed droplet location for determination of the cooling rate at different positions.
130 A. Kumar et al. / Acta Materialia 58 (2010) 122–133
10. the rise in the initial temperature, both the fluidity and time
required for the initiation of solidification increases.
Experimental validation of the simulated spreading was
carried out for 8.18 mm droplet having an initial tempera-
ture of 973 K. 3.3 cm spread was observed in the droplet,
which matches reasonably well with the predicted spread
%3.7 cm.
The initial temperature of the droplet had a strong influ-
ence on the front velocity. The front velocity significantly
decreased with increase in the initial temperature. The aver-
age front speed (averaged over 7 locations, as shown in
Fig. 10) of 8.33 mm sÀ1
for initial droplet temperature of
875 K dropped to 6.05 mm sÀ1
when the initial droplet
temperature was increased to 973 K. Front speed is related
to the microstructure and thus appropriate interlamellar
spacing can be obtained by controlling the initial tempera-
ture of the droplet.
5.5. Effect of the droplet diameter
Droplet diameter had a significant effect on the time to
spread and front velocity. The time to spread increased
with increase in the initial diameter of the droplet. This is
as expected because the time to spread is expected to
increase with increase in the size of the droplet. Fig. 13
shows the effect of the initial diameter of drops on the
average solidification front speed for the initial droplet
Fig. 11. Variation of (a) front speed with radial distance of droplet for different value of contact resistance, (b) measured interlamellar spacing (k) (initial
temperature = 973 K, droplet diameter = 8.18 mm), (c) and (d) microstructure of splat at marked radial distance.
Fig. 12. Effect of initial temperature on the spread.
A. Kumar et al. / Acta Materialia 58 (2010) 122–133 131
11. temperature of 973 K. The front speed initially increases
with the diameter and then decreases.
5.6. Validation of the model
The present model is a comprehensive one that takes
into account the convective flows within and outside the
melt, solidification effects, conductive heat transfer through
the contact interface and the surface tension effects. As
mentioned earlier, Al–33 wt.% Cu was selected due to
availability of physical properties and also due to the fact
that the simulated results can be validated using J–H plot.
The experimental validation was carried out only for
droplet with 8.18 mm diameter having a superheat of
150 K (initial temperature = 973 K). The solidified droplet
was sectioned at seven different locations (Fig. 10) and the
sectioned pieces were metallographically prepared to char-
acterize the microstructure.
For validation, solidification front velocities in a droplet
of size 8.18 mm of Al–33 wt.% Cu alloy were calculated
using the model developed in the present work. These val-
ues were plugged in the Jackson–Hunt relationship
k2
V = 88 lm3
sÀ1
[48] for calculation of k from those veloc-
ities. Fig. 14 shows the experimental values obtained for
various sections as shown in Fig. 10 super imposed on
those calculated from this model. A very good correlation
is seen in the plot between experimental and simulated val-
ues within standard errors of experimental measurements.
6. Concluding remarks
1. Comprehensive CFD based modeling of droplet deposi-
tion on a cold substrate was developed on a FLUENT
6.3.16 platform.
2. The model predicted a rapid spread of droplet much
before the initiation of solidification. The spread was
found to depend on superheat and droplet diameter.
3. Front speed was estimated accurately from the liquid
fraction profile predictions at different time steps. It
was sensitive to the droplet size and superheat. It ini-
tially increased with droplet size and then decreased.
The front speed decreased with increase in the
superheat.
4. The front speed oscillated along radius of the splat. This
is consistent with the variation of the interlamellar spac-
ing along the radial distance.
5. The prediction of the model on droplet spreading
matched well with the experimental findings and so
did the prediction of the interlamellar spacings at differ-
ent locations of the splat.
References
[1] Gutierrez EM, Lavernia EJ, Trapaga GM, Szekely J. Int J Rapid
Solidif 1988;4:125.
[2] Lavernia EJ, Gutierrez EM, Szekely J, Grant NJ. Int J Rapid Solidif
1988;4:89.
[3] Grant PS, Cantor B. Acta Metall 1995;43:913.
[4] Mathur P, Apelian D, Lawly A. Acta Metall 1989;37:429.
[5] Lavernia EJ, Guttirez GM, Szekely J, Grant NJ. Int J Rapid Solidif
1998;4:89.
[6] Grant PS, Cantor B, Katgerman L. Acta Metall Mater 1993;41:1097.
[7] Antipas G, Lekakou C, Tsakiropoulos P. In: Proceedings of 2nd
international conference on spray forming ICSF-2, Swansea, Sep-
tember 13–15; 1993. p. 15.
[8] Grant PS. Prog Mater Sci 1995;39:497.
[9] Sadhal SS, Ayyaswamy PS, Chung JN. Transport phenomena with
drops and bubbles. Berlin: Springer; 1997. p. 311.
[10] Lee CS, Reitz RD. Atom Sprays 2001;11:1.
[11] Antipas GSE. Comput Mater Sci 2006;35:416.
[12] Zeoli N, Gu S. Comput Mater Sci 2006;38:282.
[13] Zeoli N, Gu S. Comput Mater Sci 2008;42(2):245.
[14] Tinoco J, Widell B, Fredriksson H, Fuchs L. Mater Sci Eng A
2004;365:302.
[15] Shukla P, Mandal RK, Ojha SN. Bull Mater Sci Indian Acad Sci
2001;24:547.
Fig. 13. Growth velocity vs. diameter of the droplets.
Fig. 14. Interlamellar spacing vs. growth velocity.
132 A. Kumar et al. / Acta Materialia 58 (2010) 122–133
12. [16] Zeoli N, Gu S, Kamnis S. Int J Heat Mass Transfer 2008;
51(15–16):4121.
[17] Bennett T, Poulikakos D. J Mater Sci 1994;29:2025.
[18] Kang B, Zhao Z, PouLikakos D. ASME J Heat Transfer
1994;116:445.
[19] Zhao Z, Poulikakos D, Fukai J. Int J Heat Mass Transfer
1996;39:2791.
[20] Zhao Z, Poulikakos D, Fukai J. Int J Heat Mass Transfer
1996;39:2771.
[21] Fukai J, Zhao Z, Poulikakos D, Megaxidis CM, Miyatake O. Phys
Fluids A 1993;5:2588.
[22] Liu H, Lavernia EJ, Rangel RH. J Phys D: Appl Phys 1993;26:1900.
[23] Trapaga G, Matthys EF, Valencia JJ, Szekely J. Met Trans B
1992;23:701.
[24] FLOW-3D. Report No. FSI-88-00-1, vols. 1–4. Los Alamos, NM:
Flow Science Inc.; 1988.
[25] Bertagnolii M, Marchese M, Jacucci G. J Therm Spray Technol
1995;4:41.
[26] Waldvogel JM, Poulikakos D. Int J Heat Mass Transfer 1997;40:295.
[27] Kamnis S, Gu S, Lu TJ, Chen C. J Phys D: Appl Phys
2008;41(16):165303.
[28] Kamnis S, Gu S. J Phys D: Appl Phys 2005;38:3664.
[29] Liu W, Wang GX, Int MatthysEF. J Heat Mass Transfer
1995;38:1387.
[30] Wang GX, Matthys EF. J Heat Transfer 1996;118:157.
[31] Chung M, Rangel RH. Numer Heat Transfer, Part A 2000;37:201.
[32] Shakeri S, Chandra S. Int J Heat Mass Transfer 2002;45:4561.
[33] Sussman M, Smereka P, Osher S. J Comput Phys 1994;114:
146.
[34] Voller VR, Prakash C. J Heat Mass Transfer 1987;30(8):1709.
[35] Patankar SV. Numerical heat transfer and fluid flow. New
York: McGraw-Hill; 1980. p. 59.
[36] Van Doormat JP, Raithby GD, McDonald BH. ASME J Turbomach
1987;109:268.
[37] Peric M. Heat Transfer Part B: Fund 1990;17:63.
[38] Raithby GD, Schneider GE. Numer Heat Transfer 1979;2:417.
[39] Toloukian YS. Thermophysical properties of matter, vol. 1. New
York: IFI/Plenum; 1970.
[40] Korolkov AM. Trans. from Russian, Consultants Bureau. New York;
1960 [p. 65].
[41] Lang G. Aluminium 1974;50(11):731.
[42] Sikalo S, Ganic EN. Exp Therm Fluid Sci 2006;31:97.
[43] Fukumoto M, Nishikola E, Matsubara T. Surf Coat Technol
1999;120–121:131.
[44] Zhang H. Int J Heat Mass Transfer 1999;42:2499.
[45] Chung MO, Rangel RH. Int J Heat Mass Transfer 2001;44:605.
[46] Fukai J, Ozaki T, Asami H, Miyatake O. J Chem Eng Jpn
2000;34(4):630.
[47] Pasandideh-Fard M, Chandra S, Mostaghimi J. Int J Heat Mass
Transfer 2002;45:2229.
[48] Jones H. Rapid solidification of metals and alloys. London: Institute
of Metallurgists; 1982.
A. Kumar et al. / Acta Materialia 58 (2010) 122–133 133