Motile Gyrotactic Microorganisms Research Articles

Darcy–Brinkman–Forchheimer Model for Nano-Bioconvection Stratified MHD Flow through an Elastic Surface: A Successive Relaxation Approach

The present study deals with the Darcy–Brinkman–Forchheimer model for bioconvection-stratified nanofluid flow through a porous elastic surface. The mathematical modeling for MHD nanofluid flow with motile gyrotactic microorganisms is formulated under the influence of an inclined magnetic field, Brownian motion, thermophoresis, viscous dissipation, Joule heating, and stratifi-cation. In addition, the momentum equation is formulated using the Darcy–Brinkman–Forchheimer model. Using similarity transforms, governing partial differential equations are reconstructed into ordinary differential equations. The spectral relaxation method (SRM) is used to solve the nonlinear coupled differential equations. The SRM is a straightforward technique to develop, because it is based on decoupling the system of equations and then integrating the coupled system using the Chebyshev pseudo-spectral method to obtain the required results. The numerical interpretation of SRM is admirable because it establishes a system of equations that sequentially solve by providing the results of the first equation into the next equation. The numerical results of temperature, velocity, concentration, and motile microorganism density profiles are presented with graphical curves and tables for all the governing parametric quantities. A numerical comparison of the SRM with the previously investigated work is also shown in tables, which demonstrate excellent agreement.

Bioconvection Reiner-Rivlin Nanofluid Flow between Rotating Circular Plates with Induced Magnetic Effects, Activation Energy and Squeezing Phenomena

This article deals with the unsteady flow in rotating circular plates located at a finite distance filled with Reiner-Rivlin nanofluid. The Reiner-Rivlin nanofluid is electrically conducting and incompressible. Furthermore, the nanofluid also accommodates motile gyrotactic microorganisms under the effect of activation energy and thermal radiation. The mathematical formulation is performed by employing the transformation variables. The finalized formulated equations are solved using a semi-numerical technique entitled Differential Transformation Method (DTM). Padé approximation is also used with DTM to present the solution of nonlinear coupled ordinary differential equations. Padé approximation helps to improve the accuracy and convergence of the obtained results. The impact of several physical parameters is discussed and gives analysis on velocity (axial and tangential), magnetic, temperature, concentration field, and motile gyrotactic microorganism functions. The impact of torque on the lower and upper plates are deliberated and presented through the tabular method. Furthermore, numerical values of Nusselt number, motile density number, and Sherwood number are given through tabular forms. It is worth mentioning here that the DTM-Padé is found to be a stable and accurate method. From a practical point of view, these flows can model cases arising in geophysics, oceanography, and in many industrial applications like turbomachinery.

Bioconvection in Magneto Hydrodynamics Casson Nanoliquid (Fe3O4-Sodium Alginate) With Gyrotactic Microorganisms Over an Exponential Stretching Sheet

The present investigation focuses on the influence of motile gyrotactic microorganisms and thermal heat flux on three-dimensional convective flow of a Casson nanoliquid over an elongated surface. The flow equations are modelled by using Tiwari-Das nanofluid model. Sodium alginate (SA) is considered as the base fluid together with Ferromagnetic oxide (Fe3O4) nanoparticles. The governing flow equations are changed into a system of ODEs with the aid of similarity variables and are then addressed computationally. Influence of various pertinent parameters on different physical quantities is examined graphically. The outcomes of present investigation is validated through comparison study and is found to be in good arrangement. It is noticed that the coefficient of heat transfer rises with growing radiation and Biot numbers. Also the mass transfer coefficient surges for higher values of Schmidt number and generative chemical reaction parameter.

Bidirectional non-linear stretched flow of Williamson nanofluid with swimming of motile gyrotactic microorganisms

The fields of material manufacture, graphic designing, information science, aerodynamics, plastic industry and biotechnology have been found to have a greater reliance on the phenomenon of fluid flow over three-dimensional realms. Consequently, this article has been focused to the study of Williamson nanofluid containing microorganisms over three-dimensional surface under the influence of magnetic field through bidirectional non-linearly stretched surface. To transform the set of nonlinear partial differential equations into ordinary differentials equations by using appropriate similarity transformation. These obtained fundamental ordinary differential equations are solved numerically by exploiting bvp4c process built-in MATLAB mathematical software. The presentation of the results has been made in form of graphs and tables to warrant the comparison between different scenarios. More specifically the parameters like temperature profile, velocity profile, motility of organisms, concentration profiles, Peclet numbers, Lewis number, Williamson parameters, material parameter, Brownian motion parameters, Rayleigh numbers and Prandtl number were presented as the graphical outcomes. The numerical data suggested that greater values of Schmidt number, thermophoresis parameters and Brownian motion reduce the coefficient of wall heat transfer. The study has its applications in transportation hypothesis that is utilized in many automotive and industrial processes. The field of industrial manufacturing has also many applications that consider flow over a bidirectional stretched surface. The current approach explores the cumulative effect of different physical features on the flow of Williamson fluid, and there is no such effort in the reviewed studies.

Thermo diffusion and diffusion thermo impacts on bioconvection Walter-B nanomaterial involving gyrotactic microorganisms

Here magnetohydrodynamic (MHD) bioconvection Walter-B nanofluid flow due to stretched sheet is considered. Significance of motile gyrotactic microorganisms and melting phenomena are scrutinized. Energy equation is assisted with Brownian motion, thermal radiation, Joule heating and thermophoresis diffusion. Diffusion-thermo and thermo diffusion impacts are also considered. Suitable transforms are used to reduce related expressions into ordinary differential systems. Non-linear ODEs are tackled through homotopy analysis method (HAM). Convergent series solutions are obtained. Impacts of melting parameter, Dufour number, bioconvection Lewis number, radiation parameter, Soret number, Brownian motion parameter, magnetic parameter, Prandtl number and Peclet number are addressed. Velocity intensifies with increase in melting and viscoelastic parameters while it decay against magnetic parameter. Decay in temperature in noted against melting and radiation parameters while it enhances for higher Brownian motion parameter and Prandtl number. Concentration increases against Brownian motion parameter while it decays against higher melting parameter. Microorganism field increases with Peclet number while it decays with bioconvection Lewis number.

Development of bioconvection flow of nanomaterial with melting effects

Here magnetohydrodynamic (MHD) bio-convective flow of nanomaterial due to stretched sheet is examined. Melting effects in the presence of motile gyrotactic microorganisms are addressed. Further effects of nonlinear radiation, Brownian motion, Joule heating and thermophoresis diffusion are considered in energy equation. Related expressions are transmitted into dimensionless differential system through appropriate variables. Homotopy analysis method is employed for solutions of nonlinear system. Convergence region of solutions are examined. Entropy optimization, Bejan number and other engineering quantities like Nusselt number, surface drag force, Sherwood and microorganism density numbers are elaborated. Graphical results showing the influence of various emerging parameters on microorganism concentration, fluid velocity, concentration and on temperature distribution are presented. Velocity intensifies with increasing in melting while it decays against magnetic parameter. An enhancement in temperature is noted against higher Brownian motion and Prandtl number while it decays for higher radiation and melting variables. Concentration decays against higher melting parameter while it enhances against higher Brownian motion parameter. Microorganism field increases with Peclet number while it decays against higher melting and bio-convection Lewis number.

A three-dimensional bioconvection Williamson nanofluid flow over bidirectional accelerated surface with activation energy and heat generation

The main focus of this research is to explore the consequences of motile gyrotactic microorganisms for unsteady Williamson nanofluid induced by bidirectional periodically accelerated surface. The combined features of magnetic and buoyancy forces with association of nanoparticles and swimming microorganisms developed the nanofluid bioconvection. Thermal radiation and heat generation aspects are considered to analyze the heat transportation phenomenon. The consequences of activation energy and chemical reaction are further explored for physical relevance. Appropriate transformations have been employed to transmute the formulated nonlinear equations into dimensionless form, and then analytically elucidated by homotopic technique. The effect of diverse dominant parameters on velocities, concentration, temperature, motile microorganisms as well as skin friction coefficients are deliberated through various graphs while the deviation in local Sherwood, Nusselt and motile density numbers have been deliberated by numerical data in tabular form. It is noticed that both velocity components periodically drop for augmentation in Williamson parameter. Current investigation accentuated that higher reaction rate leads to decay in concentration distribution, but impact of activation energy parameter is rather conflicting. Furthermore, the profile of motile microorganism leads to be intensified for higher magnetic parameter, while opposite trend is perceived for bioconvected Peclet and Lewis numbers.

Unsteady Mixed Bioconvection Flow of Eyring–Powell Nanofluid with Motile Gyrotactic Microorganisms Past Stretching Surface

The provided mathematical analysis aims to scrutinize the behavior of gyrotactic microorganisms to depict their role in heat and mass transfer in an unsteady mixed convection stretched flow of special Eyring–Powell nanofluid loaded by nanoparticles and gyrotactic microorganisms with simultaneous impact of Lorentz forces and zero nanoparticle flux condition at boundary. A two-phase type is presented for modeling the nanofluid. Thought of microorganisms is adopted just to stabilize the pendant nanoparticles due to bioconvection which has been promoted by combined impacts of both buoyancy and magnetic field forces. The controlling highly nonlinear partial differential equations with the auxiliary conditions have been mutated into ordinary differential equations via a convenient similarity approach. Governing mutated equations have been solved computationally by means of fifth-order Runge–Kutta–Fehlberg scheme with 10−6 tolerance level, the numerical calculations were presented. Further, our computations illustrate that a significant impact of unsteady parameter by examining the factor values of skin friction and the local density numbers. While A parameter leads to weaken skin friction, it boosts the local density number. The coefficient of heat and motile microorganism transfer rates strengthen, when mixed convection parameter λ improves. While base fluid parameter ϵ weakens the rate of heat transfer, it enhances the local density number. In addition, comparison was provided between Newtonian and non-Newtonian Powell–Eyring fluid on velocity and temperature distributions to confirm the methodology. Comparison with given results for special conditions is presented and seen to be highly satisfactory.

Bioconvection of Nanofluid Due to Motile Gyrotactic Micro-Organisms with Ohmic Heating Effects Saturated in Porous Medium

Bioconvection of Nanofluid Due to Motile Gyrotactic Micro-Organisms with Ohmic Heating Effects Saturated in Porous Medium

The onset of Marangoni bio-thermal convection in a layer of fluid containing gyrotactic microorganisms

<abstract><p>The problem of the onset of Marangoni bio-thermal convection is investigated for a horizontal layer of fluid containing motile gyrotactic microorganisms. The fluid layer is assumed to rest on a rigid surface with fixed temperature and the top boundary of the layer is assumed to be a free non deformable surface. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau numerical method. The critical values of the thermal Marangoni number are calculated for several values of the bioconvection Péclet number, bioconvection Marangoni number, bioconvection Lewis number and gyrotaxis number. The results of this study showed that the existence of gyrotactic microorganisms increases the critical thermal Marangoni numbers. Moreover, the critical eigenvalues obtained were real-valued indicating that the mode of instability is via a stationary mode, however oscillatory mode is possible for some ranges of the parameters values.</p></abstract>

Thermosolutal Marangoni Impact on Bioconvection in Suspension of Gyrotactic Microorganisms Over an Inclined Stretching Sheet

Abstract Microorganism cells movement in the fluid is universal and affects many ecological and biological processes, including infection, reproduction, and marine life ecosystem. There are many biological and medical applications that require an understanding of the transport process in nanofluids containing a suspension of microorganism. The present problem deals with the bioconvection of Casson nanofluid containing a suspension of motile gyrotactic microorganisms over an inclined stretching sheet in the presence of thermal radiation, viscous dissipation, and chemical reaction and magnetic field. At the surface, the influence of the thermosolutal Marangoni convection and suction/injection impact are considered. The governing equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg method with shooting technique. The impact of the major pertinent parameters on the velocity, temperature, nanoparticles concentration, and density of the motile microorganism is illustrated graphically. Finally, the correlations of various crucial parameters on skin friction, local Nusselt number, Sherwood number, and local motile microorganism density number are displayed through the graphs and tables.

Analysis of Arrhenius Kinetics on Multiphase Flow between a Pair of Rotating Circular Plates

In this study, we aim to deal with the flow behavior betwixt a pair of rotating circular plates filled with Carreau fluid under the suspension of nanoparticles and motile gyrotactic microorganisms in the presence of generalized magnetic Reynolds number. The activation energy is also contemplated with the nanoparticle concentration equation. The appropriate similarity transformations are used to formulate the proposed mathematical modeling in the three dimensions. The outcomes of the torque on both plates, i.e., the fix and the moving plate, are also contemplated. A well-known differential transform method (DTM) with a combination of Padé approximation will be implemented to get solutions to the coupled nonlinear ordinary differential equations (ODEs). The impact of different nondimensional physical aspects on velocity profile, temperature, concentration, and motile gyrotactic microorganism functions is discussed. The shear-thinning fluid viscosity decreases with shear strain due to its high velocity compared to the Newtonian and shear-thickening case. The impact of Carreau fluid velocity for shear-thinning n < 1 , Newtonian case n = 0 , and shear-thickening n > 1 cases on axial velocity distribution f ′ λ has been discussed in tabular form and graphical figures. For the validation of the current methodology, a comparison is made between DTM-Padé and the numerical shooting scheme.

MHD Darcy-Forchheimer flow due to gyrotactic microorganisms of Casson nanoparticles over a stretched surface with convective boundary conditions

In the current article, the augmentation of heat transmission for non-Newtonian Casson nanoparticles is investigated with motile gyrotactic microorganisms, magnetohydrodynamic (MHD), and thermal radiation upon a stretched sheet. An extended Darcy-Forchheimer model along with convective boundary conditions is also applied to the flow system. To convert these coupled nonlinear fluid flow expressions into ordinary differential expression, the concept of similarity transformation is employed. The modified coupled nonlinear set of differential expression is solved analytically by employing the HAM technique. The mathematical program Mathematica is used to manage the complexities of computations. It is established in this study that the velocity distribution is reducing the function of the inertial, porosity, and magnetic parameters. Additionally, the motile density of microorganisms displays diminishing conduct for developing estimations of bioconvection Lewis and Peclet numbers. It is further established in this study that there is an augmentation in Nusselt number and skin friction coefficient with a corresponding increase in nonlinear radiation and magnetic parameters. In order to ensure the validity of the HAM solution, we have determined numerical solutions for modeled equations with the help of boundary conditions by using ND-Solve in Mathematica-10. It is established that there is pretty fine concurrence between both solutions that ensure the validity of our solution by HAM.

MHD bioconvection Darcy‐Forchheimer flow of Casson nanofluid over a rotating disk with entropy optimization

AbstractIn this paper, we analyzed Darcy‐Forchheimer three‐dimensional bioconvection Casson nanofluid flow due to a rotating disk with entropy generation. The flow is considered with the outcome of thermal radiation and Arrhenius activation energy. For nondimensionality, we utilized the similarity transformations to deal with the problem equations. The homotopy analysis method is applied for the re‐creation of the modeled equations. The biothermal framework is investigated for all the implanted parameters whose impacts are observed through various graphs. There exist intriguing outcomes due to the impacts of various parameters on various distributions. Nanoparticles' concentration diminishes with expansion of the Schmidt parameter and Brownian motion constraint, whereas motile gyrotactic microorganisms' distribution diminishes with expansion of bioconvection Peclet and Lewis numbers. The entropy generation rate increases with the increase of the Brinkman number, Casson fluid parameters, and magnetic parameters. Enrichment in the Reynolds number () leads to a decrease in the entropy generation rate. Moreover, Bejan number reduces with escalating values of the magnetic parameter, Brinkman number, and Casson fluid parameters. Bejan number () is higher for larger Reynolds numbers and temperature difference parameter.

New Insight into Gyrotactic Microorganisms in Anti-Infection Agents Through Wavy Deformable Catheter/Endoscope with Non-Linear Thermal Radiation: Numerical Study

The reason for this work is to assess the impact of the peristaltic flow of Jeffery nanofluid containing motile gyrotactic microorganisms. This problem can be considered a numerical depiction of the fluid move through an endoscope or catheter tube. Where the catheter is covered with a blend of anti-infection agents and nanoparticles to oppose the formation of vital membranes. The effects of non-linear thermal radiation, viscous dissipation, and magnetic field are taken into consideration. Both inward and the external cylinders have sinusoidal waves traveling along their walls since there is a coupling between the occlusion of the external cylinder and the radius ratio. For long wavelength and low Reynolds number, a numerical study by using the Rung-Kutta-Merson method with Newton iteration in a shooting and matching technique is performed. The effect of physical implanted parameters is represented through a lot of charts for velocity, temperature, nanoparticle concentration, the density of motile microorganisms, shear stress, pressure rise, and pressure gradient.

Radiation and Partial Slip Effects on Magnetohydrodynamic Jeffrey Nanofluid Containing Gyrotactic Microorganisms Over a Stretching Surface

Abstract In this study, the impact of thermal radiation and partial slip on magnetohydrodynamic flow of the Jeffrey nanofluid comprising motile gyrotactic microorganisms via vertical stretching surface is analyzed. The governing partial differential equations are reformed to a system of coupled ordinary differential equations by utilizing the similarity transformations. The transformed equations are of order four, which are complex to solve analytically and hence, the coupled system is solved computationally by using the shooting technique along the Runge–Kutta integrated scheme. The ramifications of different thermophysical parameters on the density of gyrotactic microorganisms, Jeffrey nanofluid velocity, nanoparticles concentration, temperature, Sherwood number, and Nusselt number are illustrated graphically. Comparing this study with the results already published favors the validity of this study. It is established that the Nusselt number is boosted on enhancing the thermal radiation parameter, and the reverse trend has been observed on increasing the Richardson number, whereas the gyrotactic microorganisms density is more in case of viscous nanofluid compared to the Jeffrey nanofluid.

Gyrotactic mixed bioconvection flow of a nanofluid over a stretching wedge embedded in a porous media in the presence of binary chemical reaction and activation energy

A mathematical analysis has been performed to study numerically bioconvection flow of nanofluid containing gyrotactic microorganisms over a stretching wedge embedded in a porous medium in the presence of binary chemical reaction (as a function of temperature) and Arrhenius activation energy. Nonlinear thermal radiation and suction effects have also been considered in this study. The governing partial differential equations are solved numerically by Runge–Kutta–Felhberg method. Profiles of velocity, temperature, nanoparticle concentration and density of gyrotactic microorganism profiles are drawn for some important physical and bioconvection parameters to analyse the behaviour of nanofluid in the presence of motile gyrotactic microorganisms. It is seen that the rate of decrease of the velocity profiles of the nanofluid is more in the presence of motile gyrotactic microorganisms than in the absence of motile gyrotactic microorganisms by increasing the values of inverse Darcy number and suction parameter into the flow. Further, the nanoparticle concentration profiles increase in the presence of activation energy. Also, the increment of the temperature distribution is higher for nonlinear thermal radiation than those of with linear thermal radiation.

Investigation of cross-fluid flow containing motile gyrotactic microorganisms and nanoparticles over a three-dimensional cylinder

Due to the variation in fluid flow behavior in various physical conditions, the presented study have been performed an investigation of cross-fluid flow containing gyrotactic microorganisms and nanoparticles on a horizontal and three-dimensional cylinder considering viscous dissipation and magnetic field. The governing equations of the problem have been solved by the Runge-Kutta fifth-order method. The aim of this study is to inspect the effects of cross fluid, microorganisms, and magnetic field, on velocity, temperature, and concentration profiles. Also, Heat flux and mass flux values for nanoparticles and microorganisms have been calculated in tabular form. In this research, the simultaneous utilization of nanoparticles with motile microorganisms in cross fluid, and three-dimensional assessment on the cylinder has been proposed as an innovation. The results show that, when the Brownian motion parameter varies from 0.1 to 0.4 and at η=4, the concentration of nanoparticle deduces about 80.43%. Furthermore, with the change of bioconvection Lewis number from 0.2 to 0.5, it was observed that the concentration of the microorganisms reduced about 78.38%.

Heat and mass transmission of an Oldroyd-B nanofluid flow through a stratified medium with swimming of motile gyrotactic microorganisms and nanoparticles

This paper focuses on the research of motile microorganism rates in the bioconvective Oldroyd-B nanoliquid flow over a vertical stretching sheet with mixed convection and inclined magnetic field. Additionally, interesting characteristics of thermophoresis, Brownian motion, viscous dissipation, Joule heating, and stratification are examined. Similarity transformations are employed to reduce the mathematical model to higher-order ODE. The convergent serious solution is applied to solve the nonlinear differential system. The analysis of temperature, velocity, motile microorganisms’ density, and nanoparticle concentration are represented through graphs. Local Nusselt number, density number of motile microorganisms, and Sherwood number are examined via contour plots.

Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.