In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the bas...In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.展开更多
Marangoni convection and its influence on the mass transter in the liquid phase were investigated. Marangoni convection was visualized using laser Schlieren technique, Orderly polygonal convection patterns and random ...Marangoni convection and its influence on the mass transter in the liquid phase were investigated. Marangoni convection was visualized using laser Schlieren technique, Orderly polygonal convection patterns and random interfacial turbulence were observed. The effect of Marangoni convection on the mass transfer rate was studied by desorbing ethanol from aqneous solution in the falling film. The experimental results show that Marangoni convection can speed up the surface real and enhance the mass transfer rate in the liquid phase.The liquid mass transfer coefficient can be enhanced by as much as 3 folds. The corresponding empirical correlations are given in terms of the mass transfer enhancement factor. Furthermore, in considering the Marangoni effect, the conventional mass transfer correlation was modified, The differences between the values predicted by the correlation and the experimental data are within ±8.2% and the average difference is 4.2%.展开更多
Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifur...Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.展开更多
The volumetric overall mass transfer coefficients in a multistage column have been measured using axial dispersion model for toluene–acetone–water system. The effect of operating parameters on the volumetric overall...The volumetric overall mass transfer coefficients in a multistage column have been measured using axial dispersion model for toluene–acetone–water system. The effect of operating parameters on the volumetric overall mass transfer coefficients has been investigated for both mass transfer directions. The results show that the mass transfer performance is strongly dependent on rotor speed and mass transfer direction, although only slightly dependent on phase flow rates. In addition, empirical correlations to predict the overall mass transfer coefficients have been developed. The proposed correlations based on dimensionless numbers can be considered as a useful tool for the possible scale up of the multistage column extractor.展开更多
Thermodiffusion effects on stagnation point flow of a nanofuid towards a stretching surface with applied magnetic field is presented.Similarity transforms are applied to reduce the equations that govem the flow to a s...Thermodiffusion effects on stagnation point flow of a nanofuid towards a stretching surface with applied magnetic field is presented.Similarity transforms are applied to reduce the equations that govem the flow to a system of nonlinear ordinary differential equations.Runge-K utta-Fehlberg method is applied to solve the sy stem.Results are compared with existing solutions that are special cases to our problem.Concrete graphical analysis is carried out to study the effects of different emerging parameters such as stretching ratio A,mag netic infuence parameter M,Prandtl number Pr,Lewis number Le,Brownian motion parameter Nb,thermophoresis parameter Nr,nanofluid Lewis number Ln,modified Dufour parameter Nd and Dufour solutal number Ld coupled with comprehensive discussions.Numerical effects of local Nusselt number,local Sherwood number and nanofluid Sherwood number are also discussed.展开更多
This article studies effects of heat generation/absorption and chemical reaction on the unsteady magnetohydrodynamic(MHD)Casson fluid flow past over exponentially accelerated vertical plate embedded in porous medium.I...This article studies effects of heat generation/absorption and chemical reaction on the unsteady magnetohydrodynamic(MHD)Casson fluid flow past over exponentially accelerated vertical plate embedded in porous medium.It is assumed that the bounding plate has ramped temperature with ramped surface concentration and isothermal temperature with ramped surface concentration.This phenomenon is modeled in the form of system of partial differential equations with initial and boundary conditions.The goveming dimensionless equations are solved using Laplace transfom technique and expressions for velocity,temperature and concentration profiles are obtained.Expressions for skin friction,Nusselt number and Sherwood number are also derived and represented in tabular form.Effect of pertinent parameters on velocity,temperature and concentration profiles are presented through graphically.展开更多
The present paper is concerned with the study of flow,heat and mass transfer characteristics in the unsteady natural convective magneto hydrodynamics Casson fluid flow past over an oscillating vertical plate.The gover...The present paper is concerned with the study of flow,heat and mass transfer characteristics in the unsteady natural convective magneto hydrodynamics Casson fluid flow past over an oscillating vertical plate.The governing partial differential equations are solved analytically using Laplace transform technique and numerically using Matlab software.Expressions of skin friction,Nusselt number and Sherwood number are obtained.The features of the fluid flow,heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail.展开更多
Bioconvection has shown significant promise for environmentally friendly,sustainable“green”fuel cell technologies.The improved design of such systems requires continuous refinements in biomatheatical modeling in con...Bioconvection has shown significant promise for environmentally friendly,sustainable“green”fuel cell technologies.The improved design of such systems requires continuous refinements in biomatheatical modeling in conjunction with laboratory and fieldtesting.Motivated by exploring deeper the near-wall transport phenomena involved inbio-inspired fuel cells,in the present paper,we examine analytically and numericallythe combined free-forced convective steady boundary layer flow from a solid verticalflat plate embedded in a Darcian porous medium containing gyrotactic microorganisms.Gyrotaxis is one of the many taxes exhibited in biological microscale transport,andother examples include magneto-taxis,photo-taxis,chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field,light,chemical concentration orgravity,respectively). The bioconvection fuel cell also contains difusing oxygen specicswhich mimics the cathodic behavior in a proton exchange membrane(PEM) systei.Thevertical wall is maintained at isosolutal (constant oxygen volume fraction and motilemicroorganism density) and iso-thermal conditions. Wall values of these quantities aresustained at higher values than the ambient temperature and concentration of oxygenand biological microorganism specics.Similarity transformations are applied to renderthe governing partial differential equations for mass,momentum,energy,oxygen speciesand microorganism species density into a system of ordinary differential equations. Theemerging eight order nonlinear coupled,ordinary differential boundary value problemfeatures several important dimensionless control parameters,namely Lewis number(Le),buoyancy ratio paraneter i.e. ratio of oxygen species buoyancy force to thermal buoy-ancy force(Nr), bioconvection Rayleigh number(Rb), bioconvection Lewis number(Lb),bioconvection Peclet number(Pe) and the mixed convection parameter(e) spanning theentire range of free and forced convection. The transformed nonlinear system of equationswith boundary conditions is solved numerically by a finite difference met.hod with centraldifferencing,tridiagonal matrix manipulation and an iterative procedure.Computationsare validated with the symbolic Maple 14.0 software.The influence of buoyancy andbioconvection parameters on the dimensionless temperature,velocity,oxygen concentration and motile microorganism density distribution,Nusselt,Sherwood and gradient ofmotile microorganism density are studied. The work clearly shows the benefit of utilizingbiological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems.In particular,the deployment of gyrotacticmicroorganisns is shown to stimulate improved transport characteristics in heat andmormentum at the fuel cell wall.展开更多
This paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching sheet.Nanofluid model exhibiting Brownian motion and thermophoresis is used.Series solutions for a reduced system o...This paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching sheet.Nanofluid model exhibiting Brownian motion and thermophoresis is used.Series solutions for a reduced system of nonlinear ordinary differential equations are obtained by homotopy analysis method(HAM).Comparative study between the HAM solutions and previously published numerical results shows an excellent agreement.Velocity,temperature and mass fraction are displayed for various values of parameters.The local skin friction coefficient,the local Nusselt number and the local Sherwood number are computed.It is observed that the presence of nanoparticles enhances the thermal conductivity of base fluid.It is found that the convective heat transfer coefficient(Nusselt number)is decreased with an increase in concentration of nanoparticles whereas Sherwood number increases when concentration of nanoparticles in the base fluid is increased.展开更多
It is well documented that heat transfer is enhanced with addition of nanosized particles in fluid.But,in a mechanical system there are variety of factors influences the heat transfer.Some factors are significant whil...It is well documented that heat transfer is enhanced with addition of nanosized particles in fluid.But,in a mechanical system there are variety of factors influences the heat transfer.Some factors are significant while others are not.In this paper,authors will discuss sensitivity of different input parameters such as Le,Nt and Nb on output responses𝑁Nu_(x)and Sh_(x).To achieve this goal,the problem is modeled using basic conservation laws.The formulated model is a set of PDEs,which are converted to set of non-linear ODEs by using similarity transformation.Then these ODEs are solved numerically by using MATLAB built in package bvp4c and compared the numerical results with existing work and found good results.Sensitivity analysis is performed by employing RSM to determine the relationship between the input parameters such that 0.1≤Le≤1,0.1≤Nt≤1 and 0.1≤Nb≤1 and the output responses(Nu_(x)and Sh_(x)).ANOVA tables are generated by using RSM.By using the ANOVA tables the correlations between input parameters and output response are developed.To check the validity of correlated equations,the residuals are plotted graphically and show best correlations between input parameters and output responses.The high values of R^(2)=98.65 and AdjR^(2)=97.43 for Nu_(x)and R^(2)=97.83 and AdjR^(2)=95.88 for Sh_(x)demonstrates the high validity of ANOVA results to perform sensitivity analysis.Finally,we have conducted a sensitivity analysis of the responses and came to the important results that Nt and Nb is most sensitive to Nusselt number and Sherwood number respectively.展开更多
Investigation of the flow,heat and mass transfer of a nanofluid over a suddenly moved flat plate is presented using Buongiorno's model.This study is different from some of the previous studies as the effects of Br...Investigation of the flow,heat and mass transfer of a nanofluid over a suddenly moved flat plate is presented using Buongiorno's model.This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticles volume fraction are passively controlled on the boundary rather than actively.The partial differential equations governing the flow are reduced to a system of nonlinear ordinary differential equations.Viable similarity transforms are used for this purpose.A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations.Discussions on the effects of different emerging parameters is provided using graphical aid.A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers.The passive control model can be used to control the boundary layer thickness as well as the rate of mass transfer at the wall.展开更多
文摘In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.
基金Supported by National Natural Science Foundation of China(No.20136010).
文摘Marangoni convection and its influence on the mass transter in the liquid phase were investigated. Marangoni convection was visualized using laser Schlieren technique, Orderly polygonal convection patterns and random interfacial turbulence were observed. The effect of Marangoni convection on the mass transfer rate was studied by desorbing ethanol from aqneous solution in the falling film. The experimental results show that Marangoni convection can speed up the surface real and enhance the mass transfer rate in the liquid phase.The liquid mass transfer coefficient can be enhanced by as much as 3 folds. The corresponding empirical correlations are given in terms of the mass transfer enhancement factor. Furthermore, in considering the Marangoni effect, the conventional mass transfer correlation was modified, The differences between the values predicted by the correlation and the experimental data are within ±8.2% and the average difference is 4.2%.
基金the University Grants Commission (UGC), New Delhi, India for supporting her research work with a Rajiv Gandhi National Fellowship
文摘Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.
文摘The volumetric overall mass transfer coefficients in a multistage column have been measured using axial dispersion model for toluene–acetone–water system. The effect of operating parameters on the volumetric overall mass transfer coefficients has been investigated for both mass transfer directions. The results show that the mass transfer performance is strongly dependent on rotor speed and mass transfer direction, although only slightly dependent on phase flow rates. In addition, empirical correlations to predict the overall mass transfer coefficients have been developed. The proposed correlations based on dimensionless numbers can be considered as a useful tool for the possible scale up of the multistage column extractor.
文摘Thermodiffusion effects on stagnation point flow of a nanofuid towards a stretching surface with applied magnetic field is presented.Similarity transforms are applied to reduce the equations that govem the flow to a system of nonlinear ordinary differential equations.Runge-K utta-Fehlberg method is applied to solve the sy stem.Results are compared with existing solutions that are special cases to our problem.Concrete graphical analysis is carried out to study the effects of different emerging parameters such as stretching ratio A,mag netic infuence parameter M,Prandtl number Pr,Lewis number Le,Brownian motion parameter Nb,thermophoresis parameter Nr,nanofluid Lewis number Ln,modified Dufour parameter Nd and Dufour solutal number Ld coupled with comprehensive discussions.Numerical effects of local Nusselt number,local Sherwood number and nanofluid Sherwood number are also discussed.
文摘This article studies effects of heat generation/absorption and chemical reaction on the unsteady magnetohydrodynamic(MHD)Casson fluid flow past over exponentially accelerated vertical plate embedded in porous medium.It is assumed that the bounding plate has ramped temperature with ramped surface concentration and isothermal temperature with ramped surface concentration.This phenomenon is modeled in the form of system of partial differential equations with initial and boundary conditions.The goveming dimensionless equations are solved using Laplace transfom technique and expressions for velocity,temperature and concentration profiles are obtained.Expressions for skin friction,Nusselt number and Sherwood number are also derived and represented in tabular form.Effect of pertinent parameters on velocity,temperature and concentration profiles are presented through graphically.
文摘The present paper is concerned with the study of flow,heat and mass transfer characteristics in the unsteady natural convective magneto hydrodynamics Casson fluid flow past over an oscillating vertical plate.The governing partial differential equations are solved analytically using Laplace transform technique and numerically using Matlab software.Expressions of skin friction,Nusselt number and Sherwood number are obtained.The features of the fluid flow,heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail.
文摘Bioconvection has shown significant promise for environmentally friendly,sustainable“green”fuel cell technologies.The improved design of such systems requires continuous refinements in biomatheatical modeling in conjunction with laboratory and fieldtesting.Motivated by exploring deeper the near-wall transport phenomena involved inbio-inspired fuel cells,in the present paper,we examine analytically and numericallythe combined free-forced convective steady boundary layer flow from a solid verticalflat plate embedded in a Darcian porous medium containing gyrotactic microorganisms.Gyrotaxis is one of the many taxes exhibited in biological microscale transport,andother examples include magneto-taxis,photo-taxis,chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field,light,chemical concentration orgravity,respectively). The bioconvection fuel cell also contains difusing oxygen specicswhich mimics the cathodic behavior in a proton exchange membrane(PEM) systei.Thevertical wall is maintained at isosolutal (constant oxygen volume fraction and motilemicroorganism density) and iso-thermal conditions. Wall values of these quantities aresustained at higher values than the ambient temperature and concentration of oxygenand biological microorganism specics.Similarity transformations are applied to renderthe governing partial differential equations for mass,momentum,energy,oxygen speciesand microorganism species density into a system of ordinary differential equations. Theemerging eight order nonlinear coupled,ordinary differential boundary value problemfeatures several important dimensionless control parameters,namely Lewis number(Le),buoyancy ratio paraneter i.e. ratio of oxygen species buoyancy force to thermal buoy-ancy force(Nr), bioconvection Rayleigh number(Rb), bioconvection Lewis number(Lb),bioconvection Peclet number(Pe) and the mixed convection parameter(e) spanning theentire range of free and forced convection. The transformed nonlinear system of equationswith boundary conditions is solved numerically by a finite difference met.hod with centraldifferencing,tridiagonal matrix manipulation and an iterative procedure.Computationsare validated with the symbolic Maple 14.0 software.The influence of buoyancy andbioconvection parameters on the dimensionless temperature,velocity,oxygen concentration and motile microorganism density distribution,Nusselt,Sherwood and gradient ofmotile microorganism density are studied. The work clearly shows the benefit of utilizingbiological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems.In particular,the deployment of gyrotacticmicroorganisns is shown to stimulate improved transport characteristics in heat andmormentum at the fuel cell wall.
文摘This paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching sheet.Nanofluid model exhibiting Brownian motion and thermophoresis is used.Series solutions for a reduced system of nonlinear ordinary differential equations are obtained by homotopy analysis method(HAM).Comparative study between the HAM solutions and previously published numerical results shows an excellent agreement.Velocity,temperature and mass fraction are displayed for various values of parameters.The local skin friction coefficient,the local Nusselt number and the local Sherwood number are computed.It is observed that the presence of nanoparticles enhances the thermal conductivity of base fluid.It is found that the convective heat transfer coefficient(Nusselt number)is decreased with an increase in concentration of nanoparticles whereas Sherwood number increases when concentration of nanoparticles in the base fluid is increased.
基金Researchers supporting project number(RSPD2023 R535),King Saud University,Riyadh,Saudi Arabia.
文摘It is well documented that heat transfer is enhanced with addition of nanosized particles in fluid.But,in a mechanical system there are variety of factors influences the heat transfer.Some factors are significant while others are not.In this paper,authors will discuss sensitivity of different input parameters such as Le,Nt and Nb on output responses𝑁Nu_(x)and Sh_(x).To achieve this goal,the problem is modeled using basic conservation laws.The formulated model is a set of PDEs,which are converted to set of non-linear ODEs by using similarity transformation.Then these ODEs are solved numerically by using MATLAB built in package bvp4c and compared the numerical results with existing work and found good results.Sensitivity analysis is performed by employing RSM to determine the relationship between the input parameters such that 0.1≤Le≤1,0.1≤Nt≤1 and 0.1≤Nb≤1 and the output responses(Nu_(x)and Sh_(x)).ANOVA tables are generated by using RSM.By using the ANOVA tables the correlations between input parameters and output response are developed.To check the validity of correlated equations,the residuals are plotted graphically and show best correlations between input parameters and output responses.The high values of R^(2)=98.65 and AdjR^(2)=97.43 for Nu_(x)and R^(2)=97.83 and AdjR^(2)=95.88 for Sh_(x)demonstrates the high validity of ANOVA results to perform sensitivity analysis.Finally,we have conducted a sensitivity analysis of the responses and came to the important results that Nt and Nb is most sensitive to Nusselt number and Sherwood number respectively.
文摘Investigation of the flow,heat and mass transfer of a nanofluid over a suddenly moved flat plate is presented using Buongiorno's model.This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticles volume fraction are passively controlled on the boundary rather than actively.The partial differential equations governing the flow are reduced to a system of nonlinear ordinary differential equations.Viable similarity transforms are used for this purpose.A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations.Discussions on the effects of different emerging parameters is provided using graphical aid.A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers.The passive control model can be used to control the boundary layer thickness as well as the rate of mass transfer at the wall.
