Dynamics of bioconvection flow of micropolar nanoparticles with Cattaneo-Christov expressions

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.

Bioconvection Cross Diffusion Effects on MHD Flow of Nanofluids over Three Different Geometries with Melting

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.

Effects of Viscous Dissipation on Unsteady MHD Thermo Bioconvection Boundary Layer Flow of a Nanofluid Containing Gyrotactic Microorganisms along a Stretching Sheet

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.

Numerical Simulation for Bioconvection of Unsteady Stagnation Point Flow of Oldroyd-B Nanofluid with Activation Energy and Temperature-Based Thermal Conductivity Past a Stretching Disk

A mathematical modeling is explored to scrutinize the unsteady stagnation point flow of Oldroyd-B nanofluid under the thermal conductivity and solutal diffusivity with bioconvection mechanism.Impacts of Joule heating and Arrhenius activation energy including convective boundary conditions are studied,and the specified surface temperature and constant temperature of wall(CTW)are discussed.The consequences of thermal conductivity and diffusivity are also taken into account.The flow is generated through stretchable disk geometry,and the behavior of non-linear thermal radiation is incorporated in energy equation.The partial differential equations governing the fluid flow in the structure is reduced into dimensionless nonlinear ODEs by applying suitable similarity variables.The obtained system of non-dimensional nonlinear ODEs is treated numerically with the help of bvp4c solver in Matlab under shooting algorithm.The impact of various prominent parameters on velocity profile,thermal profile,volumetric nanoparticle concentration and microorganism distribution is depicted in graphical form.The numerical outcomes for skin friction coefficient,heat transfer rate,Sherwood number as well as microorganism density number versus various parameters are listed in the tables.The results show that fluid velocity is reduced by increasing buoyancy ratio parameter,while the fluid flow increases with mixed convective parameter.The temperature profile is enhanced with the amount of nonlinear thermal radiation and temperature dependent thermal conductivity.Furthermore,concentration profiles of nanoparticles have opposite behavior for Brownian motion coefficient and thermophoresis diffusion parameter,and it is noticed that by varying Peclet number the microorganisms profile is declined.The proposed study is useful to control and optimize heat transfer in industrial applications.

Bioconvection in Casson nanofluid flow with Gyrotactic microorganisms and variable surface heat flux

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.

Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell

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.

Inclined magnetic field and variable viscosity effects on bioconvection of Casson nanofluid slip flow over non linearly stretching sheet

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.

Laminar MHD natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media

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.

Mixed convection in gravity-driven nano-liquid film containing both nanoparticles and gyrotactic microorganisms

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.

Bio-Marangoni convection flow of Casson nanoliquid through a porous medium in the presence of chemically reactive activation energy

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.

MHD Boundary Layer Flow of a Power-Law Nanofluid Containing Gyrotactic Microorganisms Over an Exponentially Stretching Surface

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.

Numerical Simulation of Reiner–Rivlin Nanofluid Flow under the Influence of Thermal Radiation and Activation Energy over a Rotating Disk

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.

Three-dimensional free bio-convection of nanofluid near stagnation point on general curved isothermal surface

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.

Insight into Dynamics of Hydromagnetic Flow of Micropolar Fluid Containing Nanoparticles and Gyrotactic Microorganisms at Weak and Strong Concentrations of Microelements: Homotopy Analysis Method

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.

Numerical study for bio-convection effects on MHD nano-fluid flow past a porous and extending wedge

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.