Primary dendrite arm spacing(PDAS) of α phase in directionally solidified Pb-26%Bi(mass fraction) hypo-peritectic alloys was measured by considering the effect of melt convection in cylindrical samples with diffe...Primary dendrite arm spacing(PDAS) of α phase in directionally solidified Pb-26%Bi(mass fraction) hypo-peritectic alloys was measured by considering the effect of melt convection in cylindrical samples with different diameters.The experimental results show the measured PDAS increases with increasing diameter of the sample.At the growth velocity of 5 μm/s,its value changes from 161.5 μm for the sample with 1.8 mm in diameter to 240.4 μm for the sample with 7 mm in diameter.The strong melt convection in large diameter samples causes a high bulk alloy composition and a high concentration gradient in peritectic β phase,resulting in a larger PDAS.Simultaneously,the high concentration gradient could effectively promote the peritectic transformation,enhancing the dissolution of the thin α dendrite.展开更多
Using T106 numerical products, MM5 simulations in conjunction of Q-vector scheme-computed NCEP results, observations and satellite cloud images, study is undertaken for an exceptionally intense rainstorm event afflict...Using T106 numerical products, MM5 simulations in conjunction of Q-vector scheme-computed NCEP results, observations and satellite cloud images, study is undertaken for an exceptionally intense rainstorm event afflicting the Wenzhou region of Zhejiang province far away from the tropical storm center happening early on the morning of September 4, 1999 (TS9909 hereinafter). Evidence suggests that, like previously-studied typhoons landing in autumn south of Xiamen to the eastern part of Guangdong, TS9909 has an inverted trough in the central south of the coastal belt of Zhejiang province that produces the rainstorm from the meso convective complex (MCC) on the warm, moist shear inside; the time and order of the magnitude of the rainfall are bound up with the development of the pattern of strong Q-vector divergence gradients during the event for the study area; the NE - SW coastline and the unique topography of the Yandang mountains inside the region are favorable for air lifting are the major contributors to the torrential rains.展开更多
The hydrodynamic instabilities driven by an acid-base neutralization reaction, in contact along a plane interface, placed in a Hele-Shaw cell under the gravitational field are reported. The system consists of the heav...The hydrodynamic instabilities driven by an acid-base neutralization reaction, in contact along a plane interface, placed in a Hele-Shaw cell under the gravitational field are reported. The system consists of the heavier aqueous tetramethyle-ammonium hydroxide below the lighter layer of organic phase with propionic acid as reacting specie. The effect of chemical composition on hydrodynamic instabilities during interfacial mass transfer accompanied by a neutralization reaction is investigated. Depending on the initial concentration of the reacting species, Marangoni convection in the form of roll ceils or trains of waves is observed. Mach- Zehnder interferometer is used to measure the change in base concentration at the time of instability formation. The results show that the instabilities resulted from the convection flow are more efficient to the mechanism of mass transfer and can drastically alter pattern formation in the system.展开更多
In this work, the laminar convective heat transfer performance and the pressure drop of water-based nanofluids containing Al2O3, TiO2 and SiO2 nanoparticles flowing through a straight circular tube were experimentally...In this work, the laminar convective heat transfer performance and the pressure drop of water-based nanofluids containing Al2O3, TiO2 and SiO2 nanoparticles flowing through a straight circular tube were experimentally investigated. The experimental results showed that addition of small amounts of nano-sized Al2O3 and TiO2 particles to de-ionized water increased heat transfer coefficients considerably, while the SiO2 nanofluids showed the opposite behavior attracting the authors' interests. An average of 16% and 8.2% increase in heat transfer coefficient were observed with the average of 28% and 15% penalty in pressure drop for Al2O3 and TiO2 nanofluids.展开更多
A numerical investigation was carried out on the effect of carbon nanotube(CNT)-water-nanofluid-filled Trombe wall on heat transfer and fluid flow inside a 3 D typical room.Time depending governing equations are consi...A numerical investigation was carried out on the effect of carbon nanotube(CNT)-water-nanofluid-filled Trombe wall on heat transfer and fluid flow inside a 3 D typical room.Time depending governing equations are considered with applying hot temperature at the left surface(collector) of the Trombe wall.The left wall(glazing) of the room and a square part(window) at the right wall are considered at cold temperature.The effects of Rayleigh number and the nanofluid volume fractions and the Trombe wall height on the temperature field,flow structure and heat transfer rate,are studied.The results show that the addition of nanoparticles and the increase of the Trombe wall height,enhance the heat transfer considerably and affect the flow structure and the temperature field.展开更多
Convective pore-fluid flow (CPFF) plays a critical role in generating mineral deposits and oil reservoirs within the deep Earth. Therefore, theoretical understanding and numerical modeling of the thermodynamic process...Convective pore-fluid flow (CPFF) plays a critical role in generating mineral deposits and oil reservoirs within the deep Earth. Therefore, theoretical understanding and numerical modeling of the thermodynamic process that triggers and controls the CPFF are extremely important for the exploration of new mineral deposits and underground oil resources. From the viewpoint of science, the CPFF within the upper crust can be treated as a kind of thermodynamic instability problem of pore-fluid in fluid-saturated porous media. The key issue of dealing with this kind of problem is to assess whether a nonlinear thermodynamic system under consideration is supercritical. To overcome limitations of using theoretical analysis and experimental methods in dealing with the CPFF problems within the upper crust, finite element modeling has been broadly employed for solving this kind of problem over the past two decades. The main purpose of this paper is to overview recent developments and applications of finite element modeling associated with solving the CPFF problems in large length-scale geological systems of complicated geometries and complex material distributions. In particular, two kinds of commonly-used finite element modeling approaches, namely the steady-state and transient-state approaches, and their advantages/disadvantages are thoroughly presented and discussed.展开更多
Bioconvection plays an inevitable role in introducing sustainable and environment-friendly fuel cell technologies.Bio-mathematical modelling of such designs needs continuous refinements to achieve strong agreements in...Bioconvection plays an inevitable role in introducing sustainable and environment-friendly fuel cell technologies.Bio-mathematical modelling of such designs needs continuous refinements to achieve strong agreements in experimental and computational results.Actually,microorganisms transport a miscellaneous palette of ingredients in manufacturing industrial goods particularly in fertilizer industries.Heat transfer characteristics of molecular structure are measured by a physical phenomenon which is allied with the transpiration of heat within matter.Motivated by bioinspired fuel cells involved in near-surface flow phenomena,in the present article,we examine the transverse swimming of motile gyrotactic microorganisms numerically in a rheological Jeffery fluid near a stretching wall.The leading physical model is converted in a nonlinear system of ODEs through proper similarity alterations.A numerical technique called shooting method with R-K Fehlberg is applied via mathematical software and graphical presentations are obtained.The influence of all relative physical constraints on velocity,temperature,concentration,and volume fraction of gyrotactic microorganisms is expressed geometrically.It is found that heat and mass flux at the surface as well as density of motile microorganism’s declines for Brownian motion and thermophoresis parameter.Comparison in tabular form is made with existing literature to validate the results for limiting cases with convective boundary conditions.展开更多
A three-dimensional numerical model was established to simulate the hydrodynamics within an octagonal tank of a recirculating aquaculture system. The realizable k-e turbulence model was applied to describe the flow, t...A three-dimensional numerical model was established to simulate the hydrodynamics within an octagonal tank of a recirculating aquaculture system. The realizable k-e turbulence model was applied to describe the flow, the discrete phase model (DPM) was applied to generate particle trajectories, and the governing equations are solved using the finite volume method. To validate this model, the numerical results were compared with data obtained from a full-scale physical model. The results show that: (1) the realizable k-e model applied for turbulence modeling describes well the flow pattern in octagonal tanks, giving an average relative error of velocities between simulated and measured values of 18% from contour maps of velocity magnitudes; (2) the DPM was applied to obtain particle trajectories and to simulate the rate of particle removal from the tank. The average relative error of the removal rates between simulated and measured values was 11%. The DPM can be used to assess the self-cleaning capability of an octagonal tank; (3) a comprehensive account of the hydrodynamics within an octagonal tank can be assessed from simulations. The velocity distribution was uniform with an average velocity of 15 cm/s; the velocity reached 0.8 m/s near the inlet pipe, which can result in energy losses and cause wall abrasion; the velocity in tank corners was more than 15 cm/s, which suggests good water mixing, and there was no particle sedimentation. The percentage of particle removal for octagonal tanks was 90% with the exception of a little accumulation of 〈5 mm particle in the area between the inlet pipe and the wall. This study demonstrated a consistent numerical model of the hydrodynamics within octagonal tanks that can be further used in their design and optimization as well as promote the wide use of computational fluid dynamics in aquaculture engineering.展开更多
The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial...The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial direction.In addition to that Stefan blowing is considered.The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit.The primitive mass conservation equation,radial,tangential and axial momentum,heat,nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall(disk surface)and free stream boundary conditions.This highly nonlinear,strongly coupled system of unsteady partial differential equations is normalized with the classical von Kármán and other transformations to render the boundary value problem into an ordinary differential system.The emerging 11th order system features an extensive range of dimensionless flow parameters,i.e.,disk stretching rate,Brownian motion,thermophoresis,bioconvection Lewis number,unsteadiness parameter,ordinary Lewis number,Prandtl number,mass convective Biot number,Péclet number and Stefan blowing parameter.Solutions of the system are obtained with developed semi-analytical technique,i.e.,Adomian decomposition method.Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique.展开更多
This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or u...This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.展开更多
This paper introduces to fluid state physics (fluid mechanics) a new interpretation of physical phenomena taking place in a fluid in motion. It introduces the base of a new theory claiming that every flow has its ow...This paper introduces to fluid state physics (fluid mechanics) a new interpretation of physical phenomena taking place in a fluid in motion. It introduces the base of a new theory claiming that every flow has its own internal structure of motion, which is definite organization of motion, rather than a "molecular chaos", known from the fluid statics. The paper introduces the new notion of structures vector fields of power and momentum and shows every Newtonian fluid flows are dual in character. It shows that the flow of Newtonian fluid has a dual character. It demonstrates on models and further in mathematical interpretation of physical phenomena. It introduces, on the one hand, the cycloidal motion model into the fluid mechanics, ad on the other hand an addition to the known, the classical model of Poiseuille laminar motion. The theory of dualism (double nature of physical phenomena) allows the description of selected characteristics of the flow, either by using the theory ofcycloidal motion (semicycloidal), or by using the supplemented theory of laminar motion. The dualism theory is useful to describe each type of flows both, laminar and turbulent. This paper is only an introduction to the theory. It has been assigned number 1. It has been granted a high priority, since it contains basic concepts that will be used in others, following papers of long cycle.展开更多
The intention of this investigation is to study the effects of heat transfer and inclined magnetic field on the peristaltic flow of Williamson fluid in an asymmetric channel through porous medium. The governing two-di...The intention of this investigation is to study the effects of heat transfer and inclined magnetic field on the peristaltic flow of Williamson fluid in an asymmetric channel through porous medium. The governing two-dimensional equations are simplified under the assumption of long wavelength approximation. The simplified equations are solved for the stream function, temperature, and axial pressure gradient by using a regular perturbation method. The expression for pressure rise is computed numerically. The profiles of velocity, pressure gradient, temperature, heat transfer coefficient and stream function are sketched and interpreted for various embedded parameters and also the behavior of stream function for various wave forms is discussed through graphs. It is observed that the peristaltic velocity increases from porous medium to non-porous medium, the magnetic effects have increasing effect on the temperature, and the size of the trapped bolus decreases with the increasing of magnetic effects while the trend is reversed with the increasing of Darcy number. Moreover, limiting solutions of our problem are in close agreement with the corresponding results of the Newtonian fluid model.展开更多
In this study,magneto-hydrodynamics (MHD) mixed convection effects of Al2O3-water nanofluid flow over a backward-facing step were investigated numerically for various electrical conductivity models of nanofluids.A uni...In this study,magneto-hydrodynamics (MHD) mixed convection effects of Al2O3-water nanofluid flow over a backward-facing step were investigated numerically for various electrical conductivity models of nanofluids.A uniform external magnetic field was applied to the flow and strength of magnetic field was varied with different values of dimensionless parameter Hartmann number (Ha=0,10,20,30,40).Three different electrical conductivity models were used to see the effects of MHD nanofluid flow.Besides,five different inclination angles between 0°-90° is used for the external magnetic field.The problem geometry is a backward-facing step which is used in many engineering applications where flow separation and reattachment phenomenon occurs.Mixed type convective heat transfer of backward-facing step was examined with various values of Richardson number (Ri=0.01,0.1,1,10) and four different nanoparticle volume fractions (Ф=0.01,0.015,0.020,0.025) considering different electrical conductivity models.Finite element method via commercial code COMSOL was used for computations.Results indicate that the addition of nanoparticles enhanced heat transfer significantly.Also increasing magnetic field strength and inclination angle increased heat transfer rate.Effects of different electrical conductivity models were also investigated and it was observed that they have significant effects on the fluid flow and heat transfer characteristics in the presence of magnetic field.展开更多
The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. Th...The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. The flow is generated due to exponentially stretching surface. The governing boundary layer equations are reduced into the ordinary differential equations. Series solutions are presented to analyze the velocity, temperature and nanoparticle concentration fields. Temperature and nanoparticle concentration fields decrease when the values of Casson parameter enhance. It is found that the Biot numbers arising due to thermal and concentration convective conditions yield an enhancement in the temperature and concentration fields. Further, we observed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. The effects of Brownian motion parameter on the temperature and nanoparticle concentration are reverse.展开更多
基金Project(50395100)supported by the National Natural Science Foundation of ChinaProject(NCET-07-0692)supported by the New Century Talents Program of the Ministry of Education,ChinaProject(34-TP-2009)supported by Open Project of State Key Laboratory of Solidification Processing,China
文摘Primary dendrite arm spacing(PDAS) of α phase in directionally solidified Pb-26%Bi(mass fraction) hypo-peritectic alloys was measured by considering the effect of melt convection in cylindrical samples with different diameters.The experimental results show the measured PDAS increases with increasing diameter of the sample.At the growth velocity of 5 μm/s,its value changes from 161.5 μm for the sample with 1.8 mm in diameter to 240.4 μm for the sample with 7 mm in diameter.The strong melt convection in large diameter samples causes a high bulk alloy composition and a high concentration gradient in peritectic β phase,resulting in a larger PDAS.Simultaneously,the high concentration gradient could effectively promote the peritectic transformation,enhancing the dissolution of the thin α dendrite.
基金sponsored jointly by the Natural Science Foundation of China (Grant 4040950009402050084)the Project of Planned National Key Basic Research/Development (2004CB418301)
文摘Using T106 numerical products, MM5 simulations in conjunction of Q-vector scheme-computed NCEP results, observations and satellite cloud images, study is undertaken for an exceptionally intense rainstorm event afflicting the Wenzhou region of Zhejiang province far away from the tropical storm center happening early on the morning of September 4, 1999 (TS9909 hereinafter). Evidence suggests that, like previously-studied typhoons landing in autumn south of Xiamen to the eastern part of Guangdong, TS9909 has an inverted trough in the central south of the coastal belt of Zhejiang province that produces the rainstorm from the meso convective complex (MCC) on the warm, moist shear inside; the time and order of the magnitude of the rainfall are bound up with the development of the pattern of strong Q-vector divergence gradients during the event for the study area; the NE - SW coastline and the unique topography of the Yandang mountains inside the region are favorable for air lifting are the major contributors to the torrential rains.
文摘The hydrodynamic instabilities driven by an acid-base neutralization reaction, in contact along a plane interface, placed in a Hele-Shaw cell under the gravitational field are reported. The system consists of the heavier aqueous tetramethyle-ammonium hydroxide below the lighter layer of organic phase with propionic acid as reacting specie. The effect of chemical composition on hydrodynamic instabilities during interfacial mass transfer accompanied by a neutralization reaction is investigated. Depending on the initial concentration of the reacting species, Marangoni convection in the form of roll ceils or trains of waves is observed. Mach- Zehnder interferometer is used to measure the change in base concentration at the time of instability formation. The results show that the instabilities resulted from the convection flow are more efficient to the mechanism of mass transfer and can drastically alter pattern formation in the system.
文摘In this work, the laminar convective heat transfer performance and the pressure drop of water-based nanofluids containing Al2O3, TiO2 and SiO2 nanoparticles flowing through a straight circular tube were experimentally investigated. The experimental results showed that addition of small amounts of nano-sized Al2O3 and TiO2 particles to de-ionized water increased heat transfer coefficients considerably, while the SiO2 nanofluids showed the opposite behavior attracting the authors' interests. An average of 16% and 8.2% increase in heat transfer coefficient were observed with the average of 28% and 15% penalty in pressure drop for Al2O3 and TiO2 nanofluids.
基金funded by Scientific Research Deanship at University of Ha ’ il-Saudi Arabia through project number BA-2019。
文摘A numerical investigation was carried out on the effect of carbon nanotube(CNT)-water-nanofluid-filled Trombe wall on heat transfer and fluid flow inside a 3 D typical room.Time depending governing equations are considered with applying hot temperature at the left surface(collector) of the Trombe wall.The left wall(glazing) of the room and a square part(window) at the right wall are considered at cold temperature.The effects of Rayleigh number and the nanofluid volume fractions and the Trombe wall height on the temperature field,flow structure and heat transfer rate,are studied.The results show that the addition of nanoparticles and the increase of the Trombe wall height,enhance the heat transfer considerably and affect the flow structure and the temperature field.
基金Project(11272359)supported by the National Natural Science Foundation of China
文摘Convective pore-fluid flow (CPFF) plays a critical role in generating mineral deposits and oil reservoirs within the deep Earth. Therefore, theoretical understanding and numerical modeling of the thermodynamic process that triggers and controls the CPFF are extremely important for the exploration of new mineral deposits and underground oil resources. From the viewpoint of science, the CPFF within the upper crust can be treated as a kind of thermodynamic instability problem of pore-fluid in fluid-saturated porous media. The key issue of dealing with this kind of problem is to assess whether a nonlinear thermodynamic system under consideration is supercritical. To overcome limitations of using theoretical analysis and experimental methods in dealing with the CPFF problems within the upper crust, finite element modeling has been broadly employed for solving this kind of problem over the past two decades. The main purpose of this paper is to overview recent developments and applications of finite element modeling associated with solving the CPFF problems in large length-scale geological systems of complicated geometries and complex material distributions. In particular, two kinds of commonly-used finite element modeling approaches, namely the steady-state and transient-state approaches, and their advantages/disadvantages are thoroughly presented and discussed.
文摘Bioconvection plays an inevitable role in introducing sustainable and environment-friendly fuel cell technologies.Bio-mathematical modelling of such designs needs continuous refinements to achieve strong agreements in experimental and computational results.Actually,microorganisms transport a miscellaneous palette of ingredients in manufacturing industrial goods particularly in fertilizer industries.Heat transfer characteristics of molecular structure are measured by a physical phenomenon which is allied with the transpiration of heat within matter.Motivated by bioinspired fuel cells involved in near-surface flow phenomena,in the present article,we examine the transverse swimming of motile gyrotactic microorganisms numerically in a rheological Jeffery fluid near a stretching wall.The leading physical model is converted in a nonlinear system of ODEs through proper similarity alterations.A numerical technique called shooting method with R-K Fehlberg is applied via mathematical software and graphical presentations are obtained.The influence of all relative physical constraints on velocity,temperature,concentration,and volume fraction of gyrotactic microorganisms is expressed geometrically.It is found that heat and mass flux at the surface as well as density of motile microorganism’s declines for Brownian motion and thermophoresis parameter.Comparison in tabular form is made with existing literature to validate the results for limiting cases with convective boundary conditions.
基金Supported by the Application Research Project of Post-Doctoral Researchers in Qingdao(No.ZQ51201415037)the Modern Agriculture Industry System Construction of Special Funds(No.CARS-50-G10)+1 种基金the Special Project about Independent Innovation and Achievement Transformation of Shandong Province(No.2014ZZCX07102)the Key R&D Program of Jiangsu Province(No.BE2015328)
文摘A three-dimensional numerical model was established to simulate the hydrodynamics within an octagonal tank of a recirculating aquaculture system. The realizable k-e turbulence model was applied to describe the flow, the discrete phase model (DPM) was applied to generate particle trajectories, and the governing equations are solved using the finite volume method. To validate this model, the numerical results were compared with data obtained from a full-scale physical model. The results show that: (1) the realizable k-e model applied for turbulence modeling describes well the flow pattern in octagonal tanks, giving an average relative error of velocities between simulated and measured values of 18% from contour maps of velocity magnitudes; (2) the DPM was applied to obtain particle trajectories and to simulate the rate of particle removal from the tank. The average relative error of the removal rates between simulated and measured values was 11%. The DPM can be used to assess the self-cleaning capability of an octagonal tank; (3) a comprehensive account of the hydrodynamics within an octagonal tank can be assessed from simulations. The velocity distribution was uniform with an average velocity of 15 cm/s; the velocity reached 0.8 m/s near the inlet pipe, which can result in energy losses and cause wall abrasion; the velocity in tank corners was more than 15 cm/s, which suggests good water mixing, and there was no particle sedimentation. The percentage of particle removal for octagonal tanks was 90% with the exception of a little accumulation of 〈5 mm particle in the area between the inlet pipe and the wall. This study demonstrated a consistent numerical model of the hydrodynamics within octagonal tanks that can be further used in their design and optimization as well as promote the wide use of computational fluid dynamics in aquaculture engineering.
文摘The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial direction.In addition to that Stefan blowing is considered.The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit.The primitive mass conservation equation,radial,tangential and axial momentum,heat,nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall(disk surface)and free stream boundary conditions.This highly nonlinear,strongly coupled system of unsteady partial differential equations is normalized with the classical von Kármán and other transformations to render the boundary value problem into an ordinary differential system.The emerging 11th order system features an extensive range of dimensionless flow parameters,i.e.,disk stretching rate,Brownian motion,thermophoresis,bioconvection Lewis number,unsteadiness parameter,ordinary Lewis number,Prandtl number,mass convective Biot number,Péclet number and Stefan blowing parameter.Solutions of the system are obtained with developed semi-analytical technique,i.e.,Adomian decomposition method.Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique.
文摘This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.
文摘This paper introduces to fluid state physics (fluid mechanics) a new interpretation of physical phenomena taking place in a fluid in motion. It introduces the base of a new theory claiming that every flow has its own internal structure of motion, which is definite organization of motion, rather than a "molecular chaos", known from the fluid statics. The paper introduces the new notion of structures vector fields of power and momentum and shows every Newtonian fluid flows are dual in character. It shows that the flow of Newtonian fluid has a dual character. It demonstrates on models and further in mathematical interpretation of physical phenomena. It introduces, on the one hand, the cycloidal motion model into the fluid mechanics, ad on the other hand an addition to the known, the classical model of Poiseuille laminar motion. The theory of dualism (double nature of physical phenomena) allows the description of selected characteristics of the flow, either by using the theory ofcycloidal motion (semicycloidal), or by using the supplemented theory of laminar motion. The dualism theory is useful to describe each type of flows both, laminar and turbulent. This paper is only an introduction to the theory. It has been assigned number 1. It has been granted a high priority, since it contains basic concepts that will be used in others, following papers of long cycle.
文摘The intention of this investigation is to study the effects of heat transfer and inclined magnetic field on the peristaltic flow of Williamson fluid in an asymmetric channel through porous medium. The governing two-dimensional equations are simplified under the assumption of long wavelength approximation. The simplified equations are solved for the stream function, temperature, and axial pressure gradient by using a regular perturbation method. The expression for pressure rise is computed numerically. The profiles of velocity, pressure gradient, temperature, heat transfer coefficient and stream function are sketched and interpreted for various embedded parameters and also the behavior of stream function for various wave forms is discussed through graphs. It is observed that the peristaltic velocity increases from porous medium to non-porous medium, the magnetic effects have increasing effect on the temperature, and the size of the trapped bolus decreases with the increasing of magnetic effects while the trend is reversed with the increasing of Darcy number. Moreover, limiting solutions of our problem are in close agreement with the corresponding results of the Newtonian fluid model.
文摘In this study,magneto-hydrodynamics (MHD) mixed convection effects of Al2O3-water nanofluid flow over a backward-facing step were investigated numerically for various electrical conductivity models of nanofluids.A uniform external magnetic field was applied to the flow and strength of magnetic field was varied with different values of dimensionless parameter Hartmann number (Ha=0,10,20,30,40).Three different electrical conductivity models were used to see the effects of MHD nanofluid flow.Besides,five different inclination angles between 0°-90° is used for the external magnetic field.The problem geometry is a backward-facing step which is used in many engineering applications where flow separation and reattachment phenomenon occurs.Mixed type convective heat transfer of backward-facing step was examined with various values of Richardson number (Ri=0.01,0.1,1,10) and four different nanoparticle volume fractions (Ф=0.01,0.015,0.020,0.025) considering different electrical conductivity models.Finite element method via commercial code COMSOL was used for computations.Results indicate that the addition of nanoparticles enhanced heat transfer significantly.Also increasing magnetic field strength and inclination angle increased heat transfer rate.Effects of different electrical conductivity models were also investigated and it was observed that they have significant effects on the fluid flow and heat transfer characteristics in the presence of magnetic field.
文摘The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. The flow is generated due to exponentially stretching surface. The governing boundary layer equations are reduced into the ordinary differential equations. Series solutions are presented to analyze the velocity, temperature and nanoparticle concentration fields. Temperature and nanoparticle concentration fields decrease when the values of Casson parameter enhance. It is found that the Biot numbers arising due to thermal and concentration convective conditions yield an enhancement in the temperature and concentration fields. Further, we observed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. The effects of Brownian motion parameter on the temperature and nanoparticle concentration are reverse.