This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid beh...This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid behavior. The flow is subjected to suction/blowing at the surface. Analysis is carded out in presence of thermal radiation and prescribed surface heat flux. In this study, an exponential order stretching velocity and prescribed exponential order surface heat flux are accorded with each other. The governing partial differential equations are first converted into nonlinear ordinary differential equations by using appropriate transformations and then solved numerically. The effect of increasing values of the Casson parameter is to suppress the velocity field. However the temperature is enhanced when Casson parameter increases. It is found that the skin-friction coefficient increases with increasing values of suction parameter. Temperature also increases for large values of power index n in both suction and blowing cases at the boundary. It is observed that the thermal radiation enhances the effective thermal diffusivity and hence the temperature rises.展开更多
This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comp...This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper （Cu）, Silver （Ag）, Alumina （A1203） and Titanium Oxide （TiO2）. Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.展开更多
This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of construc...This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of constructive and destructive chemical reactions are reported. Convergent solutions of the resulting differential systems are presented in series forms. Characteristics of various sundry parameters on the velocity, concentration, skin friction and local Sherwood number are analyzed and discussed.展开更多
In the present study,the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered.The similarity transformati...In the present study,the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered.The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations.Runge-Kutta-Fehlberg method is used to solve the governing problem.The effects of magnetic field parameter,local slip parameterλ,generalized Biot numberγ,Sisko fluid material parameter,Eckert number Ec,Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity,temperature,local entropy generation number N_(G) and Bejan number Be are inspected.Moreover,the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited.The current results are helpful in checking the entropy generation for Sisko-fluid.It is found that,an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity.For shear thinning fluids(n<1),the temperature dominates and the velocity rises.Local entropy generation number is more for larger generalized Biot number,magnetic field parameter and Brinkman number.The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases.The local Nusselt number decreases as magnetic field parameter,local slip parameter and Eckert number are increase,while it increases as material parameter,generalized Biot number and Prandtl number are increase.展开更多
This article gives a numerical report to two dimensional(2D)Darcy-Forchheimer flow of carbon-water nanofluid.Flow is instigated by exponential extending curved surface.Viscous liquid in permeable space is described by...This article gives a numerical report to two dimensional(2D)Darcy-Forchheimer flow of carbon-water nanofluid.Flow is instigated by exponential extending curved surface.Viscous liquid in permeable space is described by Darcy-Forchheimer.The subsequent arrangement of partial differential equations is changed into ordinary differential framework through proper transformations.Numerical arrangements of governing frameworks are set up by NDSolve procedure.Outcomes of different sundry parameters on temperature and velocity are examined.Skin friction and heat transfer rate are also shown and inspected.展开更多
A wide range of technological and industrial domains,including heating processors,electrical systems,mechanical systems,and others,are facing issues as a result of the recent developments in heat transmission.Nanoflui...A wide range of technological and industrial domains,including heating processors,electrical systems,mechanical systems,and others,are facing issues as a result of the recent developments in heat transmission.Nanofluids are a novel type of heat transfer fluid that has the potential to provide solutions that will improve energy transfer.The current study investigates the effect of a magnetic field on the two-dimensional flow of Williamson nanofluid over an exponentially inclined stretched sheet.This investigation takes into account the presence of multi-slip effects.We also consider the influence of viscous dissipation,thermal radiation,chemical reactions,and suction on the fluid’s velocity.We convert the nonlinear governing partial differential equations(PDEs)of the fluid flow problem into dimensionless ordinary differential equations(ODEs)through the utilization of similarity variables.We then use the homotopy analysis method(HAM)to numerically solve the resulting ordinary differential equations(ODEs).We demonstrate the effects of numerous elements on a variety of profiles through graphical and tabular representations.We observe a drop in the velocity profile whenever we increase either the magnetic number or the suction parameter.Higher values of the Williamson parameter lead to an increase in the thermal profile,while the momentum of the flow displays a trend in the opposite direction.The potential applications of this unique model include chemical and biomolecule detection,environmental cleansing,and the initiation of radiation-induced chemical processes like polymerization,sterilization,and chemical synthesis.展开更多
Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study ...Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.展开更多
The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate...The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction.The buoyancy effects in terms of temperature and concentration differences are inserted in the x-momentum equation.The aspects of heat and mass transfer are studied using dimensionless thermophoresis,Schmidt and Brownian motion parameters.The governing coupled partial differential system(PDEs)is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations.The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c.Finally,the quantitative effects of emerging dimensionless quantities on the nondimensional velocity,temperature and mass concentration in the boundary layer are conferred graphically,and inferences are drawn that important quantities of interest are substantially affected by these parameters.It is concluded that non-similar modeling,in contrast to similar models,is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.展开更多
This paper studies stratified magnetohydrodynamic （MHD） flow of tan- gent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary cond...This paper studies stratified magnetohydrodynamic （MHD） flow of tan- gent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary conditions. The partial differential systems are reduced to ordinary differential systems using appropriate transformations. The reduced systems are solved for convergent series solutions. The velocity, temperature, and concentration fields are discussed for different physical parameters. The results indi- cate that the temperature and the thermal boundary layer thickness increase noticeably for large values of Brownian motion and thermophoresis effects. It is also observed that the buoyancy parameter strengthens the velocity field, showing a decreasing behavior of temperature and nanoparticle volume fraction profiles.展开更多
Present work reports chemically reacting Darcy-Forchheimer flow of nanotubes.Water is utilized as base liquid while carbon nanotubes are considered nanomaterial.An exponential stretchable curved surface flow is origin...Present work reports chemically reacting Darcy-Forchheimer flow of nanotubes.Water is utilized as base liquid while carbon nanotubes are considered nanomaterial.An exponential stretchable curved surface flow is originated.Heat source is present.Xue relation of nanoliquid is employed to explore the feature of CNTs (single and multi-wall).Transformation technique is adopted in order to achieve non-linear ordinary differential systems.The governing systems are solved numerically.Effects of involved parameters on flow,temperature,concentration,heat transfer rate (Nusselt number) with addition of skin friction coefficient are illustrated graphically.Decay in velocity is noted with an increment in Forchheimer number and porosity parameter while opposite impact is seen for temperature.Moreover,role of MWCNTs is prominent when compared with SWCNTs.展开更多
Nuclear magnetic resonance(NMR)measurements of water diffusion have been extensively used to probe microstructure in porous materials,such as biological tissue,however primarily using pulsed gradient spin echo(PGSE)me...Nuclear magnetic resonance(NMR)measurements of water diffusion have been extensively used to probe microstructure in porous materials,such as biological tissue,however primarily using pulsed gradient spin echo(PGSE)methods.Low-field single-sided NMR systems have built-in static gradients(SG)much stronger than typical PGSE maximum gradient strengths,which allows for the signal attenuation at extremely high b-values to be explored.Here,we perform SG spin echo(SGSE)and SG stimulated echo(SGSTE)diffusion measurements on biological cells,tissues,and gels.Measurements on fixed and live neonatal mouse spinal cord,lobster ventral nerve cord,and starved yeast cells all show multiexponential signal attenuation on a scale of b with significant signal fractions observed at b×Do>1 with b as high as 400 ms/um2.These persistent signal fractions trend with surface-to-volume ratios for these systems,as expected from porous media theory.An exception found for the case of fixed vs.live spinal cords was attributed to faster exchange or permeability in live spinal cords than in fixed spinal cords on the millisecond timescale.Data suggests the existence of multiple exchange processes in neural tissue,which may be relevant to the modeling of time-dependent diffusion in gray matter.The observed multi-exponential attenuation is from protons on water and not macromolecules because it remains proportional to the normalized signal when a specimen is washed with D20.The signal that persists to b×Do>1 is also drastically reduced after delipidation,indicating that it originates from lipid membranes that restrict water diffusion.The multiexponential or stretched exponential character of the signal attenuation at b×Do>1 appears mono-exponential when viewed on a scale of(b×Do)/3,suggesting it may originate from localization or motional averaging of water near membranes on sub-micron length scales.To try to disambiguate these two contributions,signal attenuation curves were compared at varying temperatures.While the curves align when normalizing them using the localization length scale,they separate on a motional averaging length scale.This supports localization as the source of non-Gaussian displacements,but this interpretation is still provisional due to the possible confounds of heterogeneity,exchange,and relaxation.Measurements on two types of gel phantoms designed to mimic extracellular matrix.one with charged functional groups synthesized from polyacrylic acid(PAC)and another with uncharged functional groups synthesized from polyacrylamide(PAM),both exhibit signal at b×Do>1,potentially due to water interacting with macromolecules.These preliminary finding motivate future research into contrast and attenuation mechanisms in tissue with low-field,high-gradient NMR。展开更多
The current work is being done to investigate the flow of nanofluids across a porous exponential stretching surface in the presence of a heat source/sink,thermophoretic particle deposition,and bioconvection.The collec...The current work is being done to investigate the flow of nanofluids across a porous exponential stretching surface in the presence of a heat source/sink,thermophoretic particle deposition,and bioconvection.The collection of PDEs(partial differential equations)that represent the fluid moment is converted to a system of ODEs(ordinary differential equations)with the use of suitable similarity variables,and these equations are then numerically solved using Runge Kutta Fehlberg and the shooting approach.For different physical limitations,the numerical results are visually represented.The results show that increasing the porosity characteristics reduces velocity.The mass transfer decreases as the thermophoretic limitation increases.Increases in the porosity parameter reduce skin friction,increases in the solid volume fraction improve the rate of thermal distribution,and increases in the thermophoretic parameter increase the rate of mass transfer.展开更多
A numerical simulation is presented to investigate the effect of an exponentially varying magnetic field on three dimensional flow of Zinc Oxide-Society of Automotive Engineers 50 nanolubricant(ZnO-SAE50nano-lubrican...A numerical simulation is presented to investigate the effect of an exponentially varying magnetic field on three dimensional flow of Zinc Oxide-Society of Automotive Engineers 50 nanolubricant(ZnO-SAE50nano-lubricant)past a stretching sheet.Subsequently the impact of homogenous and heterogeneous reactions on the flow of nanolubricant concerned has also taken into account.The study has been strengthened by introducing the convection mechanism and the effect of thermal radiation.Similarity transformations are employed to transform the set of partial governing equations into the set of ordinary differential equations.The suitable boundary conditions are used to obtain the numerical solution.The numerical results are simulated using Matlab bvp4c solver and validated with the existing results.The flow characteristics,thermal characteristics,nanoparticle concentration and some non-dimensional numbers are computed under the influence of the pertinent parameters.The valuable outcome of the current study is that augmented magnetic field strength is the root cause of diminishing axial as well as transverse velocities and growing trend of fluid temperature.Also,the coeffi-cients of homogenous and heterogeneous reactions are boons for ascending concentration boundary layer.展开更多
In this review the dielectric properties of relaxor ferroelectrics are discussed and compared withthe properties of normal dielectrics and ferroelectrics. We try to draw a general picture ofdielectric relaxation start...In this review the dielectric properties of relaxor ferroelectrics are discussed and compared withthe properties of normal dielectrics and ferroelectrics. We try to draw a general picture ofdielectric relaxation starting from a textbook review of the underlying concepts and pay attentionto common behavior of relaxors rather than to the features observed in specific materials. We hopethat this general approach is beneficial to those physicists, chemists, material scientists and deviceengineers who deal with relaxors. Based on the analysis of dielectric properties, a comprehensivedefinition of relaxors is proposed: relaxors are defined as ferroelectrics in which the maximum inthe temperature dependence of static susceptibility occurs within the temperature range ofdielectric relaxation, but does not coincide with the temperature of singularity of relaxation timeor soft mode frequency.展开更多
We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the lo...We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions.The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data.We also compute Value-at-Risk measures as well as mortality probabilities with our estimates.We also discuss the implications of our results and findings from the point of view of public health planning and modelling.展开更多
文摘This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid behavior. The flow is subjected to suction/blowing at the surface. Analysis is carded out in presence of thermal radiation and prescribed surface heat flux. In this study, an exponential order stretching velocity and prescribed exponential order surface heat flux are accorded with each other. The governing partial differential equations are first converted into nonlinear ordinary differential equations by using appropriate transformations and then solved numerically. The effect of increasing values of the Casson parameter is to suppress the velocity field. However the temperature is enhanced when Casson parameter increases. It is found that the skin-friction coefficient increases with increasing values of suction parameter. Temperature also increases for large values of power index n in both suction and blowing cases at the boundary. It is observed that the thermal radiation enhances the effective thermal diffusivity and hence the temperature rises.
基金supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia
文摘This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper （Cu）, Silver （Ag）, Alumina （A1203） and Titanium Oxide （TiO2）. Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.
文摘This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of constructive and destructive chemical reactions are reported. Convergent solutions of the resulting differential systems are presented in series forms. Characteristics of various sundry parameters on the velocity, concentration, skin friction and local Sherwood number are analyzed and discussed.
文摘In the present study,the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered.The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations.Runge-Kutta-Fehlberg method is used to solve the governing problem.The effects of magnetic field parameter,local slip parameterλ,generalized Biot numberγ,Sisko fluid material parameter,Eckert number Ec,Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity,temperature,local entropy generation number N_(G) and Bejan number Be are inspected.Moreover,the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited.The current results are helpful in checking the entropy generation for Sisko-fluid.It is found that,an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity.For shear thinning fluids(n<1),the temperature dominates and the velocity rises.Local entropy generation number is more for larger generalized Biot number,magnetic field parameter and Brinkman number.The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases.The local Nusselt number decreases as magnetic field parameter,local slip parameter and Eckert number are increase,while it increases as material parameter,generalized Biot number and Prandtl number are increase.
文摘This article gives a numerical report to two dimensional(2D)Darcy-Forchheimer flow of carbon-water nanofluid.Flow is instigated by exponential extending curved surface.Viscous liquid in permeable space is described by Darcy-Forchheimer.The subsequent arrangement of partial differential equations is changed into ordinary differential framework through proper transformations.Numerical arrangements of governing frameworks are set up by NDSolve procedure.Outcomes of different sundry parameters on temperature and velocity are examined.Skin friction and heat transfer rate are also shown and inspected.
文摘A wide range of technological and industrial domains,including heating processors,electrical systems,mechanical systems,and others,are facing issues as a result of the recent developments in heat transmission.Nanofluids are a novel type of heat transfer fluid that has the potential to provide solutions that will improve energy transfer.The current study investigates the effect of a magnetic field on the two-dimensional flow of Williamson nanofluid over an exponentially inclined stretched sheet.This investigation takes into account the presence of multi-slip effects.We also consider the influence of viscous dissipation,thermal radiation,chemical reactions,and suction on the fluid’s velocity.We convert the nonlinear governing partial differential equations(PDEs)of the fluid flow problem into dimensionless ordinary differential equations(ODEs)through the utilization of similarity variables.We then use the homotopy analysis method(HAM)to numerically solve the resulting ordinary differential equations(ODEs).We demonstrate the effects of numerous elements on a variety of profiles through graphical and tabular representations.We observe a drop in the velocity profile whenever we increase either the magnetic number or the suction parameter.Higher values of the Williamson parameter lead to an increase in the thermal profile,while the momentum of the flow displays a trend in the opposite direction.The potential applications of this unique model include chemical and biomolecule detection,environmental cleansing,and the initiation of radiation-induced chemical processes like polymerization,sterilization,and chemical synthesis.
基金funded by King Mongkut’s University of Technology North Bangkok with Contract no.KMUTNB-Post-65-07。
文摘Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.
文摘The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction.The buoyancy effects in terms of temperature and concentration differences are inserted in the x-momentum equation.The aspects of heat and mass transfer are studied using dimensionless thermophoresis,Schmidt and Brownian motion parameters.The governing coupled partial differential system(PDEs)is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations.The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c.Finally,the quantitative effects of emerging dimensionless quantities on the nondimensional velocity,temperature and mass concentration in the boundary layer are conferred graphically,and inferences are drawn that important quantities of interest are substantially affected by these parameters.It is concluded that non-similar modeling,in contrast to similar models,is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.
文摘This paper studies stratified magnetohydrodynamic （MHD） flow of tan- gent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary conditions. The partial differential systems are reduced to ordinary differential systems using appropriate transformations. The reduced systems are solved for convergent series solutions. The velocity, temperature, and concentration fields are discussed for different physical parameters. The results indi- cate that the temperature and the thermal boundary layer thickness increase noticeably for large values of Brownian motion and thermophoresis effects. It is also observed that the buoyancy parameter strengthens the velocity field, showing a decreasing behavior of temperature and nanoparticle volume fraction profiles.
文摘Present work reports chemically reacting Darcy-Forchheimer flow of nanotubes.Water is utilized as base liquid while carbon nanotubes are considered nanomaterial.An exponential stretchable curved surface flow is originated.Heat source is present.Xue relation of nanoliquid is employed to explore the feature of CNTs (single and multi-wall).Transformation technique is adopted in order to achieve non-linear ordinary differential systems.The governing systems are solved numerically.Effects of involved parameters on flow,temperature,concentration,heat transfer rate (Nusselt number) with addition of skin friction coefficient are illustrated graphically.Decay in velocity is noted with an increment in Forchheimer number and porosity parameter while opposite impact is seen for temperature.Moreover,role of MWCNTs is prominent when compared with SWCNTs.
基金supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development.VJW acknowledges additional supported by NIGMS grant(K99 GM140338-01)for this work.
文摘Nuclear magnetic resonance(NMR)measurements of water diffusion have been extensively used to probe microstructure in porous materials,such as biological tissue,however primarily using pulsed gradient spin echo(PGSE)methods.Low-field single-sided NMR systems have built-in static gradients(SG)much stronger than typical PGSE maximum gradient strengths,which allows for the signal attenuation at extremely high b-values to be explored.Here,we perform SG spin echo(SGSE)and SG stimulated echo(SGSTE)diffusion measurements on biological cells,tissues,and gels.Measurements on fixed and live neonatal mouse spinal cord,lobster ventral nerve cord,and starved yeast cells all show multiexponential signal attenuation on a scale of b with significant signal fractions observed at b×Do>1 with b as high as 400 ms/um2.These persistent signal fractions trend with surface-to-volume ratios for these systems,as expected from porous media theory.An exception found for the case of fixed vs.live spinal cords was attributed to faster exchange or permeability in live spinal cords than in fixed spinal cords on the millisecond timescale.Data suggests the existence of multiple exchange processes in neural tissue,which may be relevant to the modeling of time-dependent diffusion in gray matter.The observed multi-exponential attenuation is from protons on water and not macromolecules because it remains proportional to the normalized signal when a specimen is washed with D20.The signal that persists to b×Do>1 is also drastically reduced after delipidation,indicating that it originates from lipid membranes that restrict water diffusion.The multiexponential or stretched exponential character of the signal attenuation at b×Do>1 appears mono-exponential when viewed on a scale of(b×Do)/3,suggesting it may originate from localization or motional averaging of water near membranes on sub-micron length scales.To try to disambiguate these two contributions,signal attenuation curves were compared at varying temperatures.While the curves align when normalizing them using the localization length scale,they separate on a motional averaging length scale.This supports localization as the source of non-Gaussian displacements,but this interpretation is still provisional due to the possible confounds of heterogeneity,exchange,and relaxation.Measurements on two types of gel phantoms designed to mimic extracellular matrix.one with charged functional groups synthesized from polyacrylic acid(PAC)and another with uncharged functional groups synthesized from polyacrylamide(PAM),both exhibit signal at b×Do>1,potentially due to water interacting with macromolecules.These preliminary finding motivate future research into contrast and attenuation mechanisms in tissue with low-field,high-gradient NMR。
文摘The current work is being done to investigate the flow of nanofluids across a porous exponential stretching surface in the presence of a heat source/sink,thermophoretic particle deposition,and bioconvection.The collection of PDEs(partial differential equations)that represent the fluid moment is converted to a system of ODEs(ordinary differential equations)with the use of suitable similarity variables,and these equations are then numerically solved using Runge Kutta Fehlberg and the shooting approach.For different physical limitations,the numerical results are visually represented.The results show that increasing the porosity characteristics reduces velocity.The mass transfer decreases as the thermophoretic limitation increases.Increases in the porosity parameter reduce skin friction,increases in the solid volume fraction improve the rate of thermal distribution,and increases in the thermophoretic parameter increase the rate of mass transfer.
文摘A numerical simulation is presented to investigate the effect of an exponentially varying magnetic field on three dimensional flow of Zinc Oxide-Society of Automotive Engineers 50 nanolubricant(ZnO-SAE50nano-lubricant)past a stretching sheet.Subsequently the impact of homogenous and heterogeneous reactions on the flow of nanolubricant concerned has also taken into account.The study has been strengthened by introducing the convection mechanism and the effect of thermal radiation.Similarity transformations are employed to transform the set of partial governing equations into the set of ordinary differential equations.The suitable boundary conditions are used to obtain the numerical solution.The numerical results are simulated using Matlab bvp4c solver and validated with the existing results.The flow characteristics,thermal characteristics,nanoparticle concentration and some non-dimensional numbers are computed under the influence of the pertinent parameters.The valuable outcome of the current study is that augmented magnetic field strength is the root cause of diminishing axial as well as transverse velocities and growing trend of fluid temperature.Also,the coeffi-cients of homogenous and heterogeneous reactions are boons for ascending concentration boundary layer.
文摘In this review the dielectric properties of relaxor ferroelectrics are discussed and compared withthe properties of normal dielectrics and ferroelectrics. We try to draw a general picture ofdielectric relaxation starting from a textbook review of the underlying concepts and pay attentionto common behavior of relaxors rather than to the features observed in specific materials. We hopethat this general approach is beneficial to those physicists, chemists, material scientists and deviceengineers who deal with relaxors. Based on the analysis of dielectric properties, a comprehensivedefinition of relaxors is proposed: relaxors are defined as ferroelectrics in which the maximum inthe temperature dependence of static susceptibility occurs within the temperature range ofdielectric relaxation, but does not coincide with the temperature of singularity of relaxation timeor soft mode frequency.
基金supported by the Spanish Ministerio de Ciencia e Innovaciòn(PID 2020-112773 GB-I00)by Gobierno de Aragòn(ADETRE Reference GroupS39_20R).
文摘We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions.The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data.We also compute Value-at-Risk measures as well as mortality probabilities with our estimates.We also discuss the implications of our results and findings from the point of view of public health planning and modelling.
