Magnetohydrodynamic （MHD） bioconvection of an incompressible electrically conducting nanofluid near a vertical wavy surface saturated porous medium containing both nanoparticle and gyrotactic microorganisms is inves...Magnetohydrodynamic （MHD） bioconvection of an incompressible electrically conducting nanofluid near a vertical wavy surface saturated porous medium containing both nanoparticle and gyrotactic microorganisms is investigated. The nanofluid is represented by a model that includes both Brownian motion and thermophoresis effects. A suitable set of non-dimensional variables are used to transform the governing boundary layer equations into a dimensionless form. The resulting nonlinear system is mapped to the vertical flat plate domain, and a non-similar solution is used to the obtained equations. The obtained non-similar system is then solved numerically using the fourth-order Runge-Kutta method. The influence of various physical parameters on the local Nusselt number, the local Sherwood number, the local density number of the motile microorganisms, the dimensionless velocity, the dimensionless temperature, and the rescaled density of motile microorganisms is studied. It is found that the local Nusselt number, the local Sherwood number, and the local density number of the motile microorganisms decrease by increasing either the Grashof number or the magnetic field parameter.展开更多
基于趋旋性微生物和幂律流体模型,研究了在含有非 Newton 流体饱和多孔介质中生物对流的线性稳定性问题.利用 Galerkin 数值方法求解了该系统的控制方程,得到生物Rayleigh 数的数值解,讨论了非 Newton 流体的幂律指数对生物对流稳定性...基于趋旋性微生物和幂律流体模型,研究了在含有非 Newton 流体饱和多孔介质中生物对流的线性稳定性问题.利用 Galerkin 数值方法求解了该系统的控制方程,得到生物Rayleigh 数的数值解,讨论了非 Newton 流体的幂律指数对生物对流稳定性在假塑性流体和膨胀性流体间的变化规律.研究结果表明,随着幂律流体的速度增大,幂律指数对生物对流稳定性的影响会发生变化,并且这种变化会受到热Rayleigh 数和生物 Lewis 数的影响.另外,微生物趋旋性特征越明显,生物对流系统就越不稳定,而适当增大非 Newton 流体的幂律指数则有利于系统的稳定性.展开更多
Analysis of a gravity-induced film flow of a fluid containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is presented.The Buongiorno model is applied. Two kinds of bo...Analysis of a gravity-induced film flow of a fluid containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is presented.The Buongiorno model is applied. Two kinds of boundary conditions, the passive and the active boundary conditions, are considered to investigate this film flow phenomenon.Through a set of similarity variables, the ordinary differential equations that describe the conservation of the momentum, the thermal energy, the nanoparticles, and the microorganisms are derived and then solved numerically by an efficient finite difference technique.The effects of various physical parameters on the profiles of momentum, thermal energy,nanoparticles, microorganisms, local skin friction, local Nusselt number, local wall mass flux, and local wall motile microorganisms flux are investigated. It is expected that the passively controlled nanofluid model can be much more easily achieved and applied in real circumstances than the actively controlled model.展开更多
We explored the insinuations of bio-convection and thermal radiation on nanofluid transportation across stretching permeable wedge with magnetic force.Appropriate similarity transformation variables are utilized to ac...We explored the insinuations of bio-convection and thermal radiation on nanofluid transportation across stretching permeable wedge with magnetic force.Appropriate similarity transformation variables are utilized to achieve ordinary differential equations.In order to tackle the non-linearity of these equations,numerical procedure based on shooting technique and Range Kutta method are harnessed on MATLAB platform.Computational and devour is carried out to evaluate the influence of controlling limitations on temperature,velocity,concentration of nanofluids and micro-organisms density.The growing strength of thermophoresis and Brownian motion enhance the fluid temperature.The profile volume fraction show decline against higher values of parameters which are Lewis number,unsteadiness and Brownian motion but opposite trend noted against higher value of Williamson and thermophoresis parameters.The skin friction values rise with the growing values of parameter of wedge angle for the moving wedge.The motile organism profile exhibits decrease against growing strength of Peclet number,bioconvection Lewis number,temperature difference and unsteady parameters while opposite behavior has been noted against wedge angle parameter.展开更多
The mathematical model of bioconvection flow of micropolar fluid through a vertical surface containing nanoparticles and gyrotactic microorganisms is presented in this study. In the study, weak and strong concentratio...The mathematical model of bioconvection flow of micropolar fluid through a vertical surface containing nanoparticles and gyrotactic microorganisms is presented in this study. In the study, weak and strong concentrations of microstructures are explored. In the energy and concentration equations, the Catteneo-Christov diffusion models are used to explain temperature and concentration diffusions with thermal and solutal relaxation durations, respectively. The governing equations describing the fluid flow are transformed and parameterized through similarity variables. The approximate analytical solution is obtained by using Homotopy Analysis Method (HAM). The impacts of relevant parameters on the various distributions are investigated and illustrated. It is discovered that increasing the value of the micropolar parameter results in an increase in the microrotation distribution for strong concentrations of microstructures while decreasing the microrotation distribution for weak concentrations of microstructures.展开更多
This paper presents a numerical study of the problem of unsteady thermo bioconvection boundary layer flow of a nanofluid containing gyrotactic microorganisms along a stretching sheet under the influence of magnetic fi...This paper presents a numerical study of the problem of unsteady thermo bioconvection boundary layer flow of a nanofluid containing gyrotactic microorganisms along a stretching sheet under the influence of magnetic field and viscous dissipation. With the help of usual transformation, the governing equations are transformed into unsteady nonlinear coupled partial differential equations. The numerical solution is obtained by using an explicit finite difference scheme. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. From the results it is found that both magnetic parameter and bioconvection Rayleigh number have positive effect on the dimensionless Nusselt number and density number of the motile microorgan-isms while the opposite behavior became clear in the case of Grashof number and Eckert number. The rescaled velocity, temperature, concentration and the density of motile microorganisms depend strongly on the governing parameters.展开更多
In this paper, the three-dimensional nanofluid bio-convection near a stagnation attachment is studied. With a set of similarity variables, the governing equations embodying the conservation of total mass, momentum, th...In this paper, the three-dimensional nanofluid bio-convection near a stagnation attachment is studied. With a set of similarity variables, the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticles and microorganisms are reduced to a set of fully coupled nonlinear differential equations. The homotopy analysis method （HAM）-finite difference method （FDM） technique is used to obtain exact solutions. The effect of various physical parameters on distribution of the motile microorganisms and the important physical quantities of practical interests are presented and discussed.展开更多
A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks.The consequences of the current flow problem are further extend...A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks.The consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis aspects.The energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass fluxes.The flow equations are converted into an ordinary differential model by employing the appropriate variables.The numerical solution is reported by using the MATLAB builtin bvp4c method.The consequences of engineering parameters on the flow velocity,the concentration,the microorganisms,and the temperature profiles are evaluated graphically.The numerical data for fascinating physical quantities,namely,the motile density number,the local Sherwood number,and the local Nusselt number,are calculated and executed against various parametric values.The microrotation magnitude reduces for increasing magnetic parameters.The intensity of the applied magnetic field may be utilized to reduce the angular rotation which occurs in the lubrication processes,especially in the suspension of flows.On the account of industrial applications,the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells.展开更多
This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic(MHD)and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero na...This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic(MHD)and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero nanoparticle mass flux and convective heating.The nonlinear system of the governing equations is transformed and solved by Runge-Kutta-Fehlberg method.The impacts of the transverse magnetic field,bioconvection parameters,Lewis number,nanofluid parameters,Prandtl number and power-law index on the velocity,temperature,nanoparticle volume fraction,density of motile microorganism profiles is explored.In addition,the impacts of these parameters on local skin-friction coefficient,local Nusselt,local Sherwood numbers and local density number of the motile microorganisms are discussed.The results reveal that the power law index is considered an important factor in this study.Due to neglecting the buoyancy force term,the bioconvection and nanofluid parameters have slight effects on the velocity profiles.The resultant Lorentz force,from increasing the magnetic field parameter,try to decrease the velocity profiles and increase the rescaled density of motile microorganisms,temperature and nanoparticle volume fraction profiles.Physically,an augmentation of power-law index drops the reduced local skin-friction and reduced Sherwood number,while it increases reduced Nusselt number and reduced local density number of motile microorganisms.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
In this study,we considered the three-dimensional flow of a rotating viscous,incompressible electrically conducting nanofluid with oxytactic microorganisms and an insulated plate floating in the fluid.Three scenarios ...In this study,we considered the three-dimensional flow of a rotating viscous,incompressible electrically conducting nanofluid with oxytactic microorganisms and an insulated plate floating in the fluid.Three scenarios were considered in this study.The first case is when the fluid drags the plate,the second is when the plate drags the fluid and the third is when the plate floats on the fluid at the same velocity.The denser microorganisms create the bioconvection as they swim to the top following an oxygen gradient within the fluid.The velocity ratio parameter plays a key role in the dynamics for this flow.Varying the parameter below and above a critical value alters the dynamics of the flow.The Hartmann number,buoyancy ratio and radiation parameter have a reverse effect on the secondary velocity for values of the velocity ratio above and below the critical value.The Hall parameter on the other hand has a reverse effect on the primary velocity for values of velocity ratio above and below the critical value.The bioconvection Rayleigh number decreases the primary velocity.The secondary velocity increases with increasing values of the bioconvection Rayleigh number and is positive for velocity ratio values below 0.5.For values of the velocity ratio parameter above 0.5,the secondary velocity is negative for small values of bioconvection Rayleigh number and as the values increase,the flow is reversed and becomes positive.展开更多
Currently,nanofluid is a hot area of interest for researchers.The nanofluid with bioconvection phenomenon attracted the researchers owing to its numerous applications in the field of nanotechnology,microbiology,nuclea...Currently,nanofluid is a hot area of interest for researchers.The nanofluid with bioconvection phenomenon attracted the researchers owing to its numerous applications in the field of nanotechnology,microbiology,nuclear science,heat storage devices,biosensors,biotechnology,hydrogen bomb,engine of motors,cancer treatment,the atomic reactor,cooling of devices,and in many more.This article presents the bioconvection cross-diffusion effects on the magnetohydrodynamic flow of nanofluids on three different geometries(cone,wedge,and plate)with mixed convection.The temperature-dependent thermal conductivity,thermal diffusivity,and Arrhenius activation energy applications are considered on the fluid flow with melting phenomenon.The flow is analyzed under thermal and solutal Robin’s conditions.The problem is formulated in the mathematical formulation of partial differential equations(PDEs).The similarity transformations are applied to diminish the governing nonlinear coupled boundary value problems into higher-order non-linear ordinary differential equations(ODEs).The resulting expressions/equation numerically tackled utilizing the famous bvp4c package by MATLAB for various interesting parameters.The results were physically and numerically calculated through graphics and tables for the velocity field,energy distribution,nanoparticles concentration,and microorganisms profile for numerous parameters.From the obtained results,we discern that the transfer of heat and mass coefficient is high over a plate and cone in the flow,respectively.The velocity profile is reduced via a larger magnetic parameter.Temperaturedependent thermal conductivity enhances the thermal field.Larger thermophoresis enhanced the concentration of nanoparticles.The microorganisms’Biot number boosts the microorganism’s profile.展开更多
In pursuit of improved thermal transportation,the slip flow of Casson nanofluid is considered in the existence of an inclined magnetic field and radiative heat flux flow over a nonlinear stretching sheet.The viscosity...In pursuit of improved thermal transportation,the slip flow of Casson nanofluid is considered in the existence of an inclined magnetic field and radiative heat flux flow over a nonlinear stretching sheet.The viscosity of the fluid is considered as a function of temperature along with the convective thermal boundary condition.Numerical solutions are obtained via Runge-Kutta along with the shooting technique method for the chosen boundary values problem.To see the physical insights of the problem,some graphs are plotted for various flow and embedded parameters on temperature function,micro-organism distribution,velocity,and volume fraction of nanoparticles.A decline is observed in the velocity and the temperature for Casson fluid.Thermophoresis and Brownian motion incremented the temperature profile.It is also found that thermal transportation can be enhanced in the presence of nanoparticles and the bioconvection of microorganisms.Present results are useful in the various sectors of engineering and for heat exchangers working in various technological processors.The main findings of the problem are validated and compared with those in the existing literature as a limiting case.展开更多
Bioconvection research is primarily focused on the augmentation of energy and mass species,which has implications in the processes intensification,mechanical,civil,electronics,and chemical engineering branches.Advance...Bioconvection research is primarily focused on the augmentation of energy and mass species,which has implications in the processes intensification,mechanical,civil,electronics,and chemical engineering branches.Advanced bioconvection technology sectors include cooling systems for electronic devices,building insulation,and geothermal nuclear waste disposal.Hence,the present investigation is mainly discoursing the impact of Marangoni convention Casson nanoliquid flow under gyrotactic microorganisms over the porous sheet.The partial differential equations(PDEs)are re-structured into ordinary differential equations(ODEs)via suitable similar variables.These ODEs are numerically solved with the help of the spectral relaxation method(SRM).The numerical outcomes are illustrated graphically for various parameters over velocity,temperature,concentration,and bioconvection profiles.Three-dimensional(3 D)views of important engineering parameters are illustrated for various parameters.The velocity of the Casson nanoliquid increases with increasing the Marangoni parameter but decreases against higher porosity parameter.The surface drag force enhances for enhancement in the Marangoni number.The rate of mass transmission is higher for reaction rate constraint but diminishes for activation energy parameter.The higher radiative values augment the rate of heat transmission.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
In current study,the numerical computations of Reiner–Rivlin nanofluid flow through a rotational disk under the influence of thermal radiation and Arrhenius activation energy is considered.For innovative physical sit...In current study,the numerical computations of Reiner–Rivlin nanofluid flow through a rotational disk under the influence of thermal radiation and Arrhenius activation energy is considered.For innovative physical situations,the motile microorganisms are incorporated too.The multiple slip effects are considered in the boundary conditions.The bioconvection of motile microorganism is utilized alongside nanofluids to provide stability to enhanced thermal transportation.The Bioconvection pattern in various nanoparticles accredits novel applications of biotechnology like the synthesis of biological polymers,biosensors,fuel cells,petroleum engineering,and the natural environment.By deploying some suitable similarity transformation functions,the governing partial differential equations(PDEs)of the flow problem are rehabilitated into dimensionless forms.The accomplished ordinary differential equations(ODEs)are solved numerically through the bvp4c scheme via a built-in function in computational MATLAB software.The upshots of some prominent physical and bioconvection parameters including wall slip parameters,thermophoresis parameter,Brownian motion parameter,Reiner–Revlin nanofluid parameter,Prandtl number,Peclet number,Lewis number,bioconvection Lewis number,and the mixed convection parameter against velocity,temperature,nanoparticles concentration,and density of motile microorganism profiles are dichotomized and pondered through graphs and tables.The presented computations show that the velocity profiles are de-escalated by the wall slip parameters while the thermal and solutal fields are upgraded with augmentation in thermophoresis number and wall slip parameters.The presence of thermal radiation enhances the temperature profile of nanofluid.The concentration profile of nanoparticles is boosted by intensification in activation energy.Furthermore,the increasing values of bioconvection Lewis number and Peclet number decay the motile microorganisms’field.展开更多
The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bio- convection and mixed convection on the steady bo...The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bio- convection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conser- vation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative anal- ysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence beat, mass and motile micro-organism transfer rates.展开更多
This paper presents a two-dimensional unsteady laminar boundary layer mixed convection flow heat and mass transfer along a vertical plate filled with Casson nanofluid located in a porous quiescent medium that contains...This paper presents a two-dimensional unsteady laminar boundary layer mixed convection flow heat and mass transfer along a vertical plate filled with Casson nanofluid located in a porous quiescent medium that contains both nanoparticles and gyrotactic microorganisms. This permeable vertical plate is assumed to be moving in the same direction as the free stream velocity. The flow is subject to a variable heat flux, a zero nanoparticle flux and a constant density of motile microorganisms on the surface. The free stream velocity is time-dependent resulting in a non-similar solution. The transport equations are solved using the bivariate spectral quasilinearization method. A grid independence test for the validity of the result is given. The significance of the inclusion of motile microorganisms to heat transfer processes is discussed. We show, inter alia, that introducing motile microorganisms into the flow reduces the skin friction coefficient and that the random motion of the nanoparticles improves the rate of transfer of the motile microorganisms.展开更多
文摘Magnetohydrodynamic （MHD） bioconvection of an incompressible electrically conducting nanofluid near a vertical wavy surface saturated porous medium containing both nanoparticle and gyrotactic microorganisms is investigated. The nanofluid is represented by a model that includes both Brownian motion and thermophoresis effects. A suitable set of non-dimensional variables are used to transform the governing boundary layer equations into a dimensionless form. The resulting nonlinear system is mapped to the vertical flat plate domain, and a non-similar solution is used to the obtained equations. The obtained non-similar system is then solved numerically using the fourth-order Runge-Kutta method. The influence of various physical parameters on the local Nusselt number, the local Sherwood number, the local density number of the motile microorganisms, the dimensionless velocity, the dimensionless temperature, and the rescaled density of motile microorganisms is studied. It is found that the local Nusselt number, the local Sherwood number, and the local density number of the motile microorganisms decrease by increasing either the Grashof number or the magnetic field parameter.
文摘基于趋旋性微生物和幂律流体模型,研究了在含有非 Newton 流体饱和多孔介质中生物对流的线性稳定性问题.利用 Galerkin 数值方法求解了该系统的控制方程,得到生物Rayleigh 数的数值解,讨论了非 Newton 流体的幂律指数对生物对流稳定性在假塑性流体和膨胀性流体间的变化规律.研究结果表明,随着幂律流体的速度增大,幂律指数对生物对流稳定性的影响会发生变化,并且这种变化会受到热Rayleigh 数和生物 Lewis 数的影响.另外,微生物趋旋性特征越明显,生物对流系统就越不稳定,而适当增大非 Newton 流体的幂律指数则有利于系统的稳定性.
基金Project supported by the Program for New Century Excellent Talents in University(No.NCET-12-0347)
文摘Analysis of a gravity-induced film flow of a fluid containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is presented.The Buongiorno model is applied. Two kinds of boundary conditions, the passive and the active boundary conditions, are considered to investigate this film flow phenomenon.Through a set of similarity variables, the ordinary differential equations that describe the conservation of the momentum, the thermal energy, the nanoparticles, and the microorganisms are derived and then solved numerically by an efficient finite difference technique.The effects of various physical parameters on the profiles of momentum, thermal energy,nanoparticles, microorganisms, local skin friction, local Nusselt number, local wall mass flux, and local wall motile microorganisms flux are investigated. It is expected that the passively controlled nanofluid model can be much more easily achieved and applied in real circumstances than the actively controlled model.
基金This work was supported by the National Natural Science Foundation of China(No.52106004)for which the authors are thankful.
文摘We explored the insinuations of bio-convection and thermal radiation on nanofluid transportation across stretching permeable wedge with magnetic force.Appropriate similarity transformation variables are utilized to achieve ordinary differential equations.In order to tackle the non-linearity of these equations,numerical procedure based on shooting technique and Range Kutta method are harnessed on MATLAB platform.Computational and devour is carried out to evaluate the influence of controlling limitations on temperature,velocity,concentration of nanofluids and micro-organisms density.The growing strength of thermophoresis and Brownian motion enhance the fluid temperature.The profile volume fraction show decline against higher values of parameters which are Lewis number,unsteadiness and Brownian motion but opposite trend noted against higher value of Williamson and thermophoresis parameters.The skin friction values rise with the growing values of parameter of wedge angle for the moving wedge.The motile organism profile exhibits decrease against growing strength of Peclet number,bioconvection Lewis number,temperature difference and unsteady parameters while opposite behavior has been noted against wedge angle parameter.
文摘The mathematical model of bioconvection flow of micropolar fluid through a vertical surface containing nanoparticles and gyrotactic microorganisms is presented in this study. In the study, weak and strong concentrations of microstructures are explored. In the energy and concentration equations, the Catteneo-Christov diffusion models are used to explain temperature and concentration diffusions with thermal and solutal relaxation durations, respectively. The governing equations describing the fluid flow are transformed and parameterized through similarity variables. The approximate analytical solution is obtained by using Homotopy Analysis Method (HAM). The impacts of relevant parameters on the various distributions are investigated and illustrated. It is discovered that increasing the value of the micropolar parameter results in an increase in the microrotation distribution for strong concentrations of microstructures while decreasing the microrotation distribution for weak concentrations of microstructures.
文摘This paper presents a numerical study of the problem of unsteady thermo bioconvection boundary layer flow of a nanofluid containing gyrotactic microorganisms along a stretching sheet under the influence of magnetic field and viscous dissipation. With the help of usual transformation, the governing equations are transformed into unsteady nonlinear coupled partial differential equations. The numerical solution is obtained by using an explicit finite difference scheme. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. From the results it is found that both magnetic parameter and bioconvection Rayleigh number have positive effect on the dimensionless Nusselt number and density number of the motile microorgan-isms while the opposite behavior became clear in the case of Grashof number and Eckert number. The rescaled velocity, temperature, concentration and the density of motile microorganisms depend strongly on the governing parameters.
基金supported by the Program for New Century Excellent Talents in University of China(No.NCET-12-0347)
文摘In this paper, the three-dimensional nanofluid bio-convection near a stagnation attachment is studied. With a set of similarity variables, the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticles and microorganisms are reduced to a set of fully coupled nonlinear differential equations. The homotopy analysis method （HAM）-finite difference method （FDM） technique is used to obtain exact solutions. The effect of various physical parameters on distribution of the motile microorganisms and the important physical quantities of practical interests are presented and discussed.
文摘A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks.The consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis aspects.The energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass fluxes.The flow equations are converted into an ordinary differential model by employing the appropriate variables.The numerical solution is reported by using the MATLAB builtin bvp4c method.The consequences of engineering parameters on the flow velocity,the concentration,the microorganisms,and the temperature profiles are evaluated graphically.The numerical data for fascinating physical quantities,namely,the motile density number,the local Sherwood number,and the local Nusselt number,are calculated and executed against various parametric values.The microrotation magnitude reduces for increasing magnetic parameters.The intensity of the applied magnetic field may be utilized to reduce the angular rotation which occurs in the lubrication processes,especially in the suspension of flows.On the account of industrial applications,the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells.
基金the Deanship of Scientific Research at King Khalid University for funding this work through Big Group Research Project under grant number(R.G.P2/16/40).
文摘This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic(MHD)and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero nanoparticle mass flux and convective heating.The nonlinear system of the governing equations is transformed and solved by Runge-Kutta-Fehlberg method.The impacts of the transverse magnetic field,bioconvection parameters,Lewis number,nanofluid parameters,Prandtl number and power-law index on the velocity,temperature,nanoparticle volume fraction,density of motile microorganism profiles is explored.In addition,the impacts of these parameters on local skin-friction coefficient,local Nusselt,local Sherwood numbers and local density number of the motile microorganisms are discussed.The results reveal that the power law index is considered an important factor in this study.Due to neglecting the buoyancy force term,the bioconvection and nanofluid parameters have slight effects on the velocity profiles.The resultant Lorentz force,from increasing the magnetic field parameter,try to decrease the velocity profiles and increase the rescaled density of motile microorganisms,temperature and nanoparticle volume fraction profiles.Physically,an augmentation of power-law index drops the reduced local skin-friction and reduced Sherwood number,while it increases reduced Nusselt number and reduced local density number of motile microorganisms.
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.
文摘In this study,we considered the three-dimensional flow of a rotating viscous,incompressible electrically conducting nanofluid with oxytactic microorganisms and an insulated plate floating in the fluid.Three scenarios were considered in this study.The first case is when the fluid drags the plate,the second is when the plate drags the fluid and the third is when the plate floats on the fluid at the same velocity.The denser microorganisms create the bioconvection as they swim to the top following an oxygen gradient within the fluid.The velocity ratio parameter plays a key role in the dynamics for this flow.Varying the parameter below and above a critical value alters the dynamics of the flow.The Hartmann number,buoyancy ratio and radiation parameter have a reverse effect on the secondary velocity for values of the velocity ratio above and below the critical value.The Hall parameter on the other hand has a reverse effect on the primary velocity for values of velocity ratio above and below the critical value.The bioconvection Rayleigh number decreases the primary velocity.The secondary velocity increases with increasing values of the bioconvection Rayleigh number and is positive for velocity ratio values below 0.5.For values of the velocity ratio parameter above 0.5,the secondary velocity is negative for small values of bioconvection Rayleigh number and as the values increase,the flow is reversed and becomes positive.
基金This work is financially supported by the Government College University,Faisalabad and Higher Education Commission,Pakistan.
文摘Currently,nanofluid is a hot area of interest for researchers.The nanofluid with bioconvection phenomenon attracted the researchers owing to its numerous applications in the field of nanotechnology,microbiology,nuclear science,heat storage devices,biosensors,biotechnology,hydrogen bomb,engine of motors,cancer treatment,the atomic reactor,cooling of devices,and in many more.This article presents the bioconvection cross-diffusion effects on the magnetohydrodynamic flow of nanofluids on three different geometries(cone,wedge,and plate)with mixed convection.The temperature-dependent thermal conductivity,thermal diffusivity,and Arrhenius activation energy applications are considered on the fluid flow with melting phenomenon.The flow is analyzed under thermal and solutal Robin’s conditions.The problem is formulated in the mathematical formulation of partial differential equations(PDEs).The similarity transformations are applied to diminish the governing nonlinear coupled boundary value problems into higher-order non-linear ordinary differential equations(ODEs).The resulting expressions/equation numerically tackled utilizing the famous bvp4c package by MATLAB for various interesting parameters.The results were physically and numerically calculated through graphics and tables for the velocity field,energy distribution,nanoparticles concentration,and microorganisms profile for numerous parameters.From the obtained results,we discern that the transfer of heat and mass coefficient is high over a plate and cone in the flow,respectively.The velocity profile is reduced via a larger magnetic parameter.Temperaturedependent thermal conductivity enhances the thermal field.Larger thermophoresis enhanced the concentration of nanoparticles.The microorganisms’Biot number boosts the microorganism’s profile.
基金the University of Management and Technology Lahore,Pakistan for facilitating and affirming this research study.
文摘In pursuit of improved thermal transportation,the slip flow of Casson nanofluid is considered in the existence of an inclined magnetic field and radiative heat flux flow over a nonlinear stretching sheet.The viscosity of the fluid is considered as a function of temperature along with the convective thermal boundary condition.Numerical solutions are obtained via Runge-Kutta along with the shooting technique method for the chosen boundary values problem.To see the physical insights of the problem,some graphs are plotted for various flow and embedded parameters on temperature function,micro-organism distribution,velocity,and volume fraction of nanoparticles.A decline is observed in the velocity and the temperature for Casson fluid.Thermophoresis and Brownian motion incremented the temperature profile.It is also found that thermal transportation can be enhanced in the presence of nanoparticles and the bioconvection of microorganisms.Present results are useful in the various sectors of engineering and for heat exchangers working in various technological processors.The main findings of the problem are validated and compared with those in the existing literature as a limiting case.
文摘Bioconvection research is primarily focused on the augmentation of energy and mass species,which has implications in the processes intensification,mechanical,civil,electronics,and chemical engineering branches.Advanced bioconvection technology sectors include cooling systems for electronic devices,building insulation,and geothermal nuclear waste disposal.Hence,the present investigation is mainly discoursing the impact of Marangoni convention Casson nanoliquid flow under gyrotactic microorganisms over the porous sheet.The partial differential equations(PDEs)are re-structured into ordinary differential equations(ODEs)via suitable similar variables.These ODEs are numerically solved with the help of the spectral relaxation method(SRM).The numerical outcomes are illustrated graphically for various parameters over velocity,temperature,concentration,and bioconvection profiles.Three-dimensional(3 D)views of important engineering parameters are illustrated for various parameters.The velocity of the Casson nanoliquid increases with increasing the Marangoni parameter but decreases against higher porosity parameter.The surface drag force enhances for enhancement in the Marangoni number.The rate of mass transmission is higher for reaction rate constraint but diminishes for activation energy parameter.The higher radiative values augment the rate of heat transmission.
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.
基金supported by the Government College University,Faisalabad,and Higher Education Commission,Pakistan.
文摘In current study,the numerical computations of Reiner–Rivlin nanofluid flow through a rotational disk under the influence of thermal radiation and Arrhenius activation energy is considered.For innovative physical situations,the motile microorganisms are incorporated too.The multiple slip effects are considered in the boundary conditions.The bioconvection of motile microorganism is utilized alongside nanofluids to provide stability to enhanced thermal transportation.The Bioconvection pattern in various nanoparticles accredits novel applications of biotechnology like the synthesis of biological polymers,biosensors,fuel cells,petroleum engineering,and the natural environment.By deploying some suitable similarity transformation functions,the governing partial differential equations(PDEs)of the flow problem are rehabilitated into dimensionless forms.The accomplished ordinary differential equations(ODEs)are solved numerically through the bvp4c scheme via a built-in function in computational MATLAB software.The upshots of some prominent physical and bioconvection parameters including wall slip parameters,thermophoresis parameter,Brownian motion parameter,Reiner–Revlin nanofluid parameter,Prandtl number,Peclet number,Lewis number,bioconvection Lewis number,and the mixed convection parameter against velocity,temperature,nanoparticles concentration,and density of motile microorganism profiles are dichotomized and pondered through graphs and tables.The presented computations show that the velocity profiles are de-escalated by the wall slip parameters while the thermal and solutal fields are upgraded with augmentation in thermophoresis number and wall slip parameters.The presence of thermal radiation enhances the temperature profile of nanofluid.The concentration profile of nanoparticles is boosted by intensification in activation energy.Furthermore,the increasing values of bioconvection Lewis number and Peclet number decay the motile microorganisms’field.
文摘The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bio- convection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conser- vation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative anal- ysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence beat, mass and motile micro-organism transfer rates.
文摘This paper presents a two-dimensional unsteady laminar boundary layer mixed convection flow heat and mass transfer along a vertical plate filled with Casson nanofluid located in a porous quiescent medium that contains both nanoparticles and gyrotactic microorganisms. This permeable vertical plate is assumed to be moving in the same direction as the free stream velocity. The flow is subject to a variable heat flux, a zero nanoparticle flux and a constant density of motile microorganisms on the surface. The free stream velocity is time-dependent resulting in a non-similar solution. The transport equations are solved using the bivariate spectral quasilinearization method. A grid independence test for the validity of the result is given. The significance of the inclusion of motile microorganisms to heat transfer processes is discussed. We show, inter alia, that introducing motile microorganisms into the flow reduces the skin friction coefficient and that the random motion of the nanoparticles improves the rate of transfer of the motile microorganisms.
