Motile Microorganisms Research Articles

Heat generation (absorption) in 3D bioconvection flow of Casson nanofluid via a convective heated stretchable surface

In the past few years, the bioconvection phenomenon has become increasingly important in various fields such as genetic systems, manufacturing, biotechnology, and ecological sciences. Bioconvection refers to the large-scale movement of fluid driven by a density gradient resulting from the collective spinning of microorganisms, like bacteria and algae. These self-propelled motile microorganisms increase the fluid's density as they swim in a coordinated direction, giving rise to the bioconvection phenomenon. The current study's goals are to investigate the characteristics of heat generation and absorption in a three-dimensional mixed bioconvection flow of Casson nanofluid inside a stretching cylinder. To analyze the system, a set of transformed nonlinear equations is numerically solved using the Runge-Kutta algorithm. The graphical representation helps explain the impact of different variables on physical properties. Notably, higher values of the Casson parameter are associated with increased viscosity and flow resistance, while a higher bioconvection Rayleigh number leads to elevated skin friction and motile density. Also, Skin friction is decreased by increasing the stretching and mixed convection characteristics. Heat generating processes achieve higher motile densities, Nusselt, and Sherwood amounts than heat absorbing processes.

Effect of electrostatic force and thermal radiation of viscoelastic nanofluid flow with motile microorganisms surrounded by PST and PHF: Bacillus anthracis in biological applications

Current studies have a significant application in various fields; motile microorganism, such as bacteria, can be used for targeted drug delivery. This is because they can be engineered to carry drugs to specific locations in the body. For example, bacteria can be modified to express genes that code for targeting ligands, which are molecules that bind to specific receptors on cells. This could help to prevent the bacteria from multiplying and causing disease. The main aim of the current work is to perform the numerical analysis of three-dimensional radiative, steady viscoelastic nanofluids flow towards an exponentially stretchable porous surface. The impact of nth-order chemical reaction and motile microbes are also disclosed looks at how multiple slips affect the Buongiorno model for magnetohydrodynamic viscoelastic nanofluids with radiation across a permeable stretched sheet. The appropriate suitable are used to transform nonlinear partial differential equations into ordinary differential equations. The numerical solution of the resulting system of equations is handled numerically by employing the bvp4c algorithm built-in MATLAB Software which comes of three-stage Lobatto IIIa formula. Dimensionless values such as temperature, concentration, velocity, and the non-Newtonian nano-fluid density profile are explored, as are non-dimensional numbers such as the local Nusselt, local friction coefficient, Sherwood, and motile microbe. Present results signifies enhancement in the temperature profiles as well as the thickness of the thermal boundary layer by increasing Brownian motion (Nb) and thermophoresis parameters (Nt), whereas decrement is noted against the viscoelastic parameter (K). As the value of the magnetic parameter ranges 0.0≤M≤ 0.2 the relative increment noted in skin friction coefficient is about 1.9 %, while decrement is found in curves of velocity field. Our findings are compared with the data available in the literature and found to be in good consensus.

Ternary Hybrid Nanofluids Containing Gyrotactic Microorganisms with Magnetohydrodynamics Effect over a Shrinking/Stretching of the Horizontal Plate

Nowadays, ternary hybrid nanofluids have been discovered by the researchers to play an important role in heat transfer systems. This study focuses on the study of heat and mass transfer of ternary hybrid nanofluids over a shrinking/stretching horizontal plate induced by gyrotactic microorganisms with the effects of magnetohydrodynamics (MHD). Motile microorganisms were added to a suspension of nanoparticles in a base fluid and mixed in most microsystems to the enhance the convectional properties of the nanofluids. This research uses water as the base fluid to investigate the effects of silver (Ag), Aluminium Oxide (AI203) and Copper (Cu) nanoparticles. The similarity transformation was used to reduce the partial differential governing equations into ordinary differential equations. The transformed nonlinear ordinary differential equations with appropriate transformed boundary conditions were solved numerically using the bvp4c procedure in the MATLAB software. The combination of the Tiwari and Das with Buongiorno model used in this mathematical equation. The results of the research are illustrated graphically and presented via tables to show the behaviour of velocity, temperature, concentration of nanoparticles, and microorganism density as well as the coefficients of skin friction, Nusselt number, Sherwood numbers, and motile microorganism density for the nanoparticles of the THNF. The results show that, for the shrinking case, the magnetic field parameter increases for skin friction and Sherwood number, while it decreases for the Nusselt number and density of motile microorganisms. The Brownian motion parameter and bioconvection Péclet number are shown to significantly increase the Sherwood Number and density motile microorganisms. Thermophoresis, however, has been proven to lower the Sherwood number and density of motile microorganisms. Then, THNF (water/Ag-AI2O3-Cu) is shown to better compared to nanofluids (water/AI2O3) and hybrid nanofluids (water/Ag-AI2O3) in both cases.

Confined run-and-tumble model with boundary aggregation: Long-time behavior and convergence to the confined Fokker–Planck model

The motile micro-organisms such as Escherichia coli, sperm, or some seaweed are usually modeled by self-propelled particles that move with the run-and-tumble process. Individual-based stochastic models are usually employed to model the aggregation phenomenon at the boundary, which is an active research field that has attracted a lot of biologists and biophysicists. Self-propelled particles at the microscale have complex behaviors, while characteristics at the population level are more important for practical applications but rely on individual behaviors. Kinetic PDE models that describe the time evolution of the probability density distribution of the motile micro-organisms are widely used. However, how to impose the appropriate boundary conditions that take into account the boundary aggregation phenomena is rarely studied. In this paper, we propose the boundary conditions for a 2D confined run-and-tumble model (CRTM) for self-propelled particle populations moving between two parallel plates with a run-and-tumble process. The proposed model satisfies the relative entropy inequality and thus long-time convergence. We establish the relation between CRTM and the confined Fokker–Planck model (CFPM) studied in [J. Fu, B. Perthame and M. Tang, Fokker–Plank system for movement of micro-organism population in confined environment, J. Statist. Phys. 184 (2021) 1–25]. We prove theoretically that when the tumble is highly forward peaked and frequent enough, CRTM converges asymptotically to the CFPM. A numerical comparison of the CRTM with aggregation and CFPM is given. The time evolution of both the deterministic PDE model and individual-based stochastic simulations are displayed, which match each other well.

Numerical assessment of bioconvection in MHD Prandtl nanofluid with gyrotactic motile microorganisms with bio-fuel applications

Due to the importance of bio-convection in biotechnology and various biological systems, scientists have made significant contributions in the current decade. This study intends to elaborate the investigation of the bio-convection flow in MHD Prandlt nanofluid with gyrotactic motile microorganism. Owing to engineering and industrial applications, the augmentation of dynamism by the insertion of nanoparticles is a prominent issue in the twenty-first period. The Arrhenius law and activation energy are also considered. The boundary layer approximations developed the governing flow equations such as momentum, energy, concentration and microorganisms equations. The non-linear coupled PDEs are converted to non-linear ODES with the help of similarity transformations. A couple of transmuted equations with modified boundary conditions are elucidated with the employ of the BVP4C via Matlab software. The behavior of different parameters on fluid motion, energy equation, concentration, and motile microorganisms are also discussed through graphical illustrations. It is analyzed that the heat transfer is improved by magnetic field while velocity field is diclines. Concentration and density performance improvises on thermophoretic and Brownian motion impact. Microorganisms field is decline with increasing the Peclet number and bioconvection Lewis number.

Permeation Dynamics of Active Swimmers Through Anisotropic Porous Walls

AbstractNatural habitats of most living microorganisms are distinguished by a complex structure often formed by a porous medium such as soil. The dynamics and transport properties of motile microorganisms are strongly affected by crowded and locally anisotropic environments. Using Chlamydomonas reinhardtii as a model system, we explore the permeation of active colloids through a structured wall of obstacles by tracking microswimmers' trajectories and analyzing their statistical properties. Employing micro‐labyrinths formed by cylindrical or elongated pillars, we demonstrate that the anisotropy of the pillar's form and orientation strongly affects the microswimmers' dynamics on different time scales. Furthermore, we discuss the kinetics of the microswimmer exchange between two compartments separated by an array of pillars.

Development of an intelligent computing system using neural networks for modeling bioconvection flow of second-grade nanofluid with gyrotactic microorganisms

Nanoparticles are carried in bioconvective fluid flow by convective motion caused by living tissues. This flow has important applications in cell and tissue engineering because it demonstrates the mechanics of particle transfer between cells and fluids. This type of flow is used in medicine delivery systems that particularly target cancer cells in real life. Nanofluids are crucial suspensions that allow nanomaterials to disperse and behave in a homogeneous and stable environment. The bioconvective second-grade nanofluid flow, on the other hand, is distinguished by a more complex process that permits nanoparticle motion to be controlled by external fields and pressures. This type of flow has numerous applications, including biology, the environment, and energy. It is particularly useful in medical imaging, cancer hyperthermia treatment, and nanodrug delivery systems. The primary purpose of this research is to use an artificial neural network to examine the rate of heat, mass, and motile microbe movement in the convective flow of magnetohydrodynamic second-grade nanofluid toward vertical surface. Suspended nanoparticles are effectively stabilized by the action of microorganisms, facilitated through bioconvection. This process is influenced by both nanoparticle attributes and buoyancy forces. In addition to thermophoretic dynamics and Brownian motion, the model considers radiation and Newtonian heating effects. Nonlinear equation systems are obtained using appropriate transformations. The non-linear simplified equations underwent numerical calculations utilizing the fourth-order Runge-Kutta shooting method. The Sherwood number, Nusselt number, and density of motile microorganism coefficient were determined using various parameters, and three distinct artificial neural networks were built employing the findings.

Peristaltic flow of bioconvective Ree–Eyring nanofluid through an inclined elastic channel with partial slip effects

Pharmaceutical fluid processing is a procedure of medication manufacturing, utilizing a particular kind of heat transfer in a biofluid designed to maintain the desired temperature for extended periods. Choosing a suitable fluid can have a positive effect on the operating efficacy of the system and lengthen the fluid’s and system’s life spans. As an outcome of this development, we investigate the influence of the partial slip and gyrotactic microorganisms on the peristaltic transport of a magnetohydrodynamic Ree–Eyring nanofluid via an aligned porous conduit with thermal radiation, energy generation, along with cross and double diffusion effects. By invoking suitable nondimensional parameters, the proposed dimensional governing equations are transformed into a system of dimensionless partial differential equations. The analytical solutions for the system of partial differential equations are obtained by incorporating the homotopy perturbation method. Further, tabular and graphical presentations are used to examine the characteristics of the various sundry parameters on the temperature, concentration, motile microorganism density, axial velocity, trapping, and other relevant flow quantities. The observations of this study indicate that the Darcy number and thermal Grashof number have the capability to enhance the velocity distribution of the Ree–Eyring nanofluid in the presence of bioconvection. The trapped bolus size and the skin friction coefficient increase noticeably because of an enhancement in the Ree–Eyring fluid parameter. Also, the Darcy number and the Hall current parameter increase the skin friction coefficient. Furthermore, validation of the results is carried out to examine the consistency between the current and the previous findings for some special cases and excellent agreements are found.

Multilayer neural networks for studying three-dimensional flow of non-Newtonian fluid flow with the impact of magnetic dipole and gyrotactic microorganisms

The current paper explores the three-dimensional flow of an Oldroyd-B liquid with the impact of a magnetic dipole that occurred by stretching a flat surface placed in the plane with a linear velocity variation in two directions containing motile gyrotactic microorganisms. Using proper similarity transformations, the governing equations are reduced into nonlinear coupled ordinary differential equations (ODEs). The ODEs are then solved using Runge–Kutta-Fehlberg (RKF) method. The training, testing, and validation processes are carried out in parallel to adapt neural networks and calculate an approximate solution for the considered model. This helps to reduce the mean square error (MSE) function by Levenberg–Marquardt backpropagation. The efficiency of the suggested backpropagated neural networks methodology has been demonstrated by utilizing outcomes such as MSE, error histograms, correlation and regression. Results reveal that the heat transport augments for increased Biot number values. The mass transport declines for improved chemical reaction rate parameter values. A higher Peclet number will result in a lower motile diffusivity and result in a decline in the micro-organism’s density profile. For the least value of Mu and gradient, better convergence of the findings can be achieved with better network testing and training.

Biological transmission in a magnetized reactive Casson–Maxwell nanofluid over a tilted stretchy cylinder in an entropy framework

Biological transmission (or bioconvection) offers a huge room for studying the interplay between microorganisms and fluid dynamics. The understanding of bioconvection is relevant for studying microbial ecology, population dynamics and exploring the behaviour of microorganisms in complex environments. The objective of this research work is to delve into the physical and biochemical aspects of bioconvection in a magnetized Casson–Maxwell nanofluid containing gyrotactic microorganisms. The investigation is conducted on a tilted elongated cylindrical surface, taking into account the presence of entropy generation. Arrhenius activation energy and slip and convective boundary conditions are novel aspects of this research. The current model invokes the impacts of thermophoresis diffusion, and Brownian motion impacts using the Buongiorno model. The Casson–Maxwell fluid model is employed to expound the rheological behaviour of non-Newtonian nanofluids with the migration of gyrotactic microorganisms. The similarity functions are used to convert the model equations and the related boundary conditions into dimensionless form. The insightful numerical results are developed by implementing the ND Solver in Mathematica, providing valuable insights into the velocity, thermal, concentration, and microorganism fields, as well as the rate of entropy generation and other engineering quantities. Outcomes are presented as graphs and tables for further analysis and discussion. The computational findings unravel several significant contributions of influential model parameters. The Lorentz force and porosity are found to create a drag force that deters the fluid pace, while the reverse trend holds for the fluid temperature. Higher activation energy results in a growth in the concentration field. A larger Peclet number leads to a decline in microorganism density. Furthermore, motile microorganisms’ density and swimming speed significantly influence entropy inflation. A 10% increase in magnetic strength results in a 1.47% increase in skin friction for the Casson fluid model and a 1.32% increase in skin friction for the Casson–Maxwell fluid model. This study contributes to understanding bioconvection in reactive Casson–Maxwell nanofluids with gyrotactic microorganisms and sheds light on entropy production in biological systems.

A hybrid machine learning algorithm for studying magnetized nanofluid flow containing gyrotactic microorganisms via a vertically inclined stretching surface.

The novelty of the present work is to acquire continuous functions as solutions rather than the discrete ones that traditional numerical methods generally produce and to minimize simulation times and higher computation costs that are the fundamental barriers to employing any numerical method. In this study, a novel hybrid finite element-based machine learning algorithm utilizing the Levenberg-Marquardt scheme with backpropagation in a neural network (LMBNN) is presented to analyze the nanofluid flow in the presence of magnetohydrodynamics and gyrotactic microorganisms through a vertically inclined stretching surface in a porous medium. Finite Element Method is used to generate the minimum reference dataset for LMBNN by varying six flow parameters in the form of six scenarios. Surface plots are utilized to understand how these scenarios affect velocity, temperature, concentration of nanoparticles, and density of motile microorganisms. Regression analysis, error histogram analysis, and fitness curves based on mean square error all support the LMBNN's effectiveness and dependability. Results reveal that temperature increases with the rise in Brownian motion and thermophoresis parameter, whereas the reverse trend has been noticed for Prandtl number. The motile microorganism density number decreases with the rise in Prandtl numbers but improves with the porosity parameter.

Role of nanolayer on the dynamics of tri-hybrid nanofluid subject to gyrotactic microorganisms and nanoparticles morphology vis two porous disks

This paper investigates the simultaneous heat and mass transfer phenomena in nanolayers induced by morphology, motile microorganisms, and magnetohydrodynamics (MHD). The study also discusses the crucial role of viscous dissipation resulting from joule heating effects in the flow of ternary hybrid nanofluids, considering both model thermal conductivity and nanolayer thermal conductivity. The influence of various types of nanoparticles on thermal conductivity (TC) and nanolayer thermal conductivity (NTC) is examined, with a focus on the significance of chemical reactions and concentration equations. To solve the nonlinear system of ordinary differential equations, a stable and accurate numerical method is employed. The study provides valuable engineering insights, summarizing key parameters such as skin friction coefficient, Nusselt number, Sherwood number, and motile number. Several nondimensional parameter effects like Re, Pr, β, Pe,α,h,r,γ, and Sc are shown in graphical and tabulation form for both porous disks. The addition of nanolayer thermal conductivity of ternary nanoparticles at a level of 5% enhances the heat transfer rate. When the values of the radius of nanoparticles and nanolayer thickness increase, the flow of tri-hybrid nanofluid's nanolayer thermal conductivity behaves oppositely.

Radiative ternary nanoliquid flow over an exponentially stretching sheet with motile oxytactic microorganisms

This article examines the mixed convection ternary nanoliquid flow containing a suspension of oxytactic microorganisms under the impact of nonlinear thermal radiation. The potential applications include microbiology, biotechnology, biosensors, cell therapy, medication release system, and protein expression. The governing equations that handle the problem are partial differential equations, they are dimensional, nonlinear in nature, and are nondimensionalized by using nonsimilar transformations. Further, for the computation of mathematical analysis, the Quasilinearization technique and numerical method such as the implicit finite difference scheme are used. The impacts of varying relevant factors on velocity, temperature, and microbe density are thoroughly examined. Results designate that the radiation factor favorably affects the velocity and temperature profiles. The rate of mass transport of liquid oxygen rises by about 45% when the Schmidt number grows from 1 to 2. The coefficient of skin friction is found to be more for ternary nanofluid than hybrid nanoliquid and nanoliquid. The current analysis compares the solution to earlier literature and finds that there is a good agreement.

Homotopic simulation of MHD bioconvective flow of water-based hybrid nanofluid over a thermal convective exponential stretching surface

PurposeWhilst a modest number of investigations have been undertaken concerning nanofluids (NFs), the exploration of fluid flow under exponentially stretching velocities using NFs remains comparatively uncharted territory. This work presents a distinctive contribution through the comprehensive examination of heat and mass transfer phenomena in the NF ND–Cu/H2O under the influence of an exponentially stretching velocity. Moreover, the investigation delves into the intriguing interplay of gyrotactic microorganisms and convective boundary conditions within the system.Design/methodology/approachSimilarity transformations have been used on PDEs to convert them into dimensionless ODEs. The solution is derived by using the homotopy analysis method (HAM). The pictorial notations have been prepared for sundry flow parameters. Furthermore, some engineering quantities are calculated in terms of the density of motile microbes, Nusselt and Sherwood numbers and skin friction, which are presented in tabular form.FindingsThe mixed convection effect associated with the combined effect of the buoyancy ratio, bioconvection Rayleigh constant and the resistivity due to the magnetization property gives rise to attenuating the velocity distribution significantly in the case of hybrid nanoliquid. The parameters involved in the profile of motile microorganisms attenuate the profile significantly.Practical implicationsThe current simulations have uncovered fascinating discoveries about how metallic NFs behave near a stretched surface. These insights give us valuable information about the characteristics of the boundary layer close to the surface under exponential stretching.Originality/valueThe novelty of the current investigation is the analysis of NF ND–Cu/H2O along with an exponentially stretching velocity in a system with gyrotactic microorganisms. The investigation of fluid flow at an exponentially stretching velocity using NFs is still relatively unexplored.

Enhanced thermal and mass transfer of harnessing microbial mediation in electrically conducting Oldroyd-B nanofluid flow: Eukaryotes microorganisms in biological applications

In bioremediation, pollutants are broken down or detached from an atmosphere using microorganisms like bacteria or fungus. These bacteria can either ingest contaminants or be enzymatically converted into innocuous molecules. Bioremediation can be enhanced by several techniques, such as bioaugmentation (the introduction of specific microorganisms), biostimulator (the provision of nutrients to stimulate microbial activity), and bioventing (the provision of air or oxygen to encourage microbial growth). The creation and dissipation of heat in a convective non-Newtonian Oldroyd-B fluid flow across a nonlinear stretching sheet in a three-dimensional boundary layer is examined in this study. The boundary layer flow's highly nonlinear partial differential equations are transformed into ordinary differential equations in the study via similarity transformations. The bvp4c technique of MATLAB is then used to resolve these equations. The study looks at some variables, including as temperature, concentration, the presence of microorganisms, velocity, heat transfer rate, and shear stress. These parameters are evaluated graphically and presented in tabular form, with a focus on the local Deborah numbers (β₁ and β₂), the local buoyancy parameters (λ₁ and λ₂), the Prandtl number (Pr), the Schmidt number (Sc), the Bio-convection Schmidt number (Sb), and the Peclet number (Pe). The results show that raising the local buoyancy parameter improves the boundary layer flow's velocity field and rate of heat transfer. Visual representations of the effects of non-dimensional factors on non-dimensional velocity, concentration, motile microorganism, and temperature profiles help to comprehend the underlying physical properties clearly.

Bio-Convective Hartmann Flow of Couple Stress Hybrid Nanofluid Between Two Dilating Parallel Walls with Heat and Mass Transfer

The study of bio-convective flow of hybrid nanofluid attracted many researchers because of tremendous applications in the fields of biofuel biotechnology, enzyme-based biosensors and biomedical science. The present work addresses a comparative study of CuO/Al2O3-water and CuO-water nanoparticles on heat and mass transfer characteristics of the squeezing flow of MHD couple stress fluid between two parallel plates by suspending motile micro-organisms. An approximated numerical technique (Shooting method along with Runge-Kutta 4th order scheme) have been employed to analyse the system of coupled nonlinear ordinary differential equations. The above numerical investigations were carried out for various governing parameters such as couple stress parameter, Hartmann number, bioconvection Peclet number, squeezing parameter etc. The effects of these physical parameters are illustrated graphically over velocity components, temperature distribution, diffusion of concentration and density of motile microorganisms. In addition to this the numerical values of skin friction, the local Nusselt number and local Sherwood number are tabulated at the upper plate for CuO-water and CuO–Al2O3-water at the expanding and squeezing cases. The numerical results for temperature profiles are in good consistency with earlier research.

Exploring the dynamics of active swimmers microorganisms with electromagnetically conducting stretching through endothermic heat generation/assimilation flow: Observational and computational study

Enhancements brought about by motile gyrotactic microorganisms encompass improved mixing, efficient oxygen and nutrient transfer, environmental sensing, and reactions, as well as potential applications in bioremediation, contributing to the advancement of knowledge in fluid dynamics and biological locomotion. These microorganisms find utility in various fields such as biotechnology, environmental engineering, and fluid dynamics research, among others, playing a pivotal role in numerous ecological processes. The present study places its focus on the investigation of the effects associated with mass and heat transport in a fluid flow scenario featuring the presence of a heat source or sink. Specifically, the study aims to examine the impact of nanoparticles on Powell-Eyring fluid flow in the presence of a magnetic field (MHD) across a stretched sheet, taking into account factors such as activation energy, heat sources, and thermal radiation. Furthermore, the study explores the influence of motile gyrotactic microorganisms on various parameters. Recognizing the dearth of research in the realm of polymer extrusion processes, this study strives to bridge this research gap. Its primary objective is to develop a mathematical formulation employing a boundary layer approach, which encompasses the consideration of the interrelated effects of mass and heat transport in Eyring-Powell fluid flow across a stretched sheet in the presence of thermal radiation and chemical reactions from figure it shows that temperature profile rises as result of radiation parameter's increasing values (0.1<Rd<0.4). The impact of Lb is also showed with the help of graph. Greater diffusive mixing is implied by higher Lb for (0.1<Lb<0.4), which tends to distribute the microbes more equally throughout the fluid. This research study serves as an inspiration for the innovation of endogenous heat generation/consumption within the flow of motile organisms exhibiting gyro-taxis in the presence of magnetic flux density on a stretching sheet. To address the complexity of the problem, the renowned BVP4C package, a computational software tool in MATLAB, is utilized for solving a set of highly intricate and nonlinear coupled differential equations. The nonlinear nature of these equations poses significant challenges, necessitating the application of specialized numerical methods to ensure accurate and efficient solutions.

Bioconvective flow of fourth-grade nanofluid via a stretchable porous surface with microbial activity and activation energy

The current work scrutinizes electro-magnetized mixed convective flow of radiative fourth-grade nanofluid over a stretchable surface with bioconvection mechanism, thermophoretic body force, Brownian motion and activation energy for both nanoparticles (NPs) and motile microorganisms. Also, features of viscous dissipation, fluctuating fluid viscosity, Joule heating, suction/injection, heat source/sink and convective heat-mass-microbial conditions are included in the flow model. By employing suitable dimensionless variables, the set of model equations has been transformed into non-dimensional ordinary differential equations, which are subsequently tackled using quasilinearization-based spectral collocation approach applied in overlapping grids. For different flow parameters, numerical results of flow profiles and quantities of engineering intrigue are discussed. The results reveal that the inclusion of Biot numbers for heat, mass and microbes transfer helps to enhance flow profiles along with quantities of engineering interest. The material parameters enhance the magnitude of velocity, which is also higher for the fourth-grade nanomaterial model. Better heat transfer attributes can be achieved through strong thermophoretic force, thermal radiation, heat generation, viscous dissipation and NP Brownian motion. Activation energy increases NP concentration, while a decreasing trend is notable for higher chemical reaction and NP Brownian diffusion parameters. Bioconvection parameters reduce the motile microbes concentration, while enhancing the rate of motile microbes transfer. Microbial Brownian motion and microbial reaction play a crucial role in the dynamics of microorganisms, and that is confirmed by their noticeable effect on the flow properties.

Bioconvective MHD flow of Williamson nanofluid past an expandable Riga wedge in the presence of activation energy, mass suction and velocity slip

The aim of this work is to investigate MHD bioconvectional unsteady Williamson nanofluid flow across an expandable Riga wedge near a stagnation point containing activation energy, motile microorganisms and velocity slip. Using similarity transformations, the PDEs are converted to ODEs, which have a similarity solution. To find approximate solutions to the ODEs, the RK-4 procedure with shooting technique is used. The velocity is increased by increasing the magnetic field parameter, wedge angle parameter, and modified Hartmann number. The heat transfer rate is improved by increasing the magnetic field parameter, Prandtl number, Biot number, and heat source parameter. Increasing the magnetic field parameter from 0 to 1 increases the velocity by 13.77%, the skin friction factor by 36.27%, the Nusselt number by 0.22%, the Sherwood number by 3.10%, and the motile density factor by 5.31%. Decreasing the heat source parameter from 1.0 to 0.0 increases the temperature by 16.78%.

Comparative Numerical Analysis for the Error Estimation of the Fluid Flow over an Inclined Axisymmetric Cylinder with a Gyrotactic Microbe

The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of heat sources/sinks. Through proper transformation, all partial differential equations are transformed into a non-linear ODE scheme. A new set of variables is presented in the directive to get the first-order convectional equations and then solved numerically using bvp4c MATLAB, embedded in the function. The proposed model is validated after calculating the error estimation and obtaining the residual error. The influence of various factors on the velocity, energy, concentration, and density of motile microorganisms is examined and studied. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number, the density of motile microorganisms, and Nusselt number. To validate the present study, a comparison is conducted with previous studies, and excellent correspondence is found. In addition, the ND-Solve approach is utilized to confirm the bvp4c. The mathematical model is confirmed through error analysis. This study provides the platform for industrial applications such as cooling capacity polymers, heat exchange, and chemical production sectors.