Presence Of Gyrotactic Microorganisms Research Articles

Radiative bioconvective flow with non-uniform heat source and Soret and Dufour impacts

Background and objectiveThe stretched flow with heat transfer has pivotal role in geothermal energy system, oil extraction, continuous casting, metal spinning and electronic cooling. Owing to this fact, the current analysis focuses on non-linear thermal radiation effect in bio-convective stagnation point flow by a stretchable wedge. Darcy relation is used to discuss the porous space. Convective conditions are deliberated. Non-uniform heat source is addressed. Soret and Dufour outcomes are analyzed. Dissipation and magnetohydrodynamics are discussed. Presence of gyrotactic microorganisms along with chemical reaction is considered. MethodologyRelated non-linear partial differential equations (PDEs) are reduced into dimensionless ordinary differential equations (ODEs) through adequate transformations. Optimal homotopy analysis method (OHAM) is adopted for the computations of related nonlinear differential systems. ResultsFlow, microorganism field, concentration and temperature distribution are graphically explored. Numerical analysis for coefficient of skin friction, microorganism density number and Sherwood and Nusselt numbers against emerging parameters are discussed. It is noted that velocity and skin friction coefficient have similar scenario for modified Hartman number. Thermal transport rate and temperature have reverse trends for non-uniform heat source variable. An augmentation in thermal distribution is seen through thermal Biot number. Larger Dufour number has increasing trend for temperature. An increasing trend for solutal Biot number for concentration is noticed. Larger Soret number leads to concentration enhancement. Microorganism field and motile density number against Peclet number have opposite response. There is reduction for bio-convective Lewis number in motile density number.

Bioconvection heat and mass transfer across a nonlinear stretching sheet with hybrid nanofluids, joule dissipation, and entropy generation

AbstractNanofluids plays a crucial role in enhancing heat transfer characteristics of ordinary fluids such as oil, water and many more. Nanoliquids possess numerous applications in heat transport phenomenon in plethora of fields such as micro electronics, biomedicines, engine cooling thermal management, chiller and heat exchangers. Keeping in view of the above mentioned facts, the objective of the current work is to examine the heat and mass transportation characteristics of hybrid nanofluid (Cu‐/water) along with ohmic dissipation (Joule heating) in the presence of gyrotactic mirco‐organisms (flows under the effect of gravity) which causes bioconvection. The entropy produced by the conducting hybrid nanofluid is investigated in the permeable media in the current problem. Through similarity transformations, partial differential equations that represent the issue are transformed into ordinary differential equations. The BVP4C method is used to numerically solve the equations. The impacts of auxiliary variables on velocity, temperature , concentration of hybrid nanoparticles , and density of motile micro‐organisms () are plotted with those of the variation in bioconvection rayleigh number, Schmidt number, and Bioconvection Schmidt number and examined carefully in detail. Velocity of the flow decreases when porosity factor and bioconvection rayleigh number enlarges. Microbial velocity decreases for rising Prandtl number. Entropy generation and Bejan number rises for higher volume fraction values The current investigation also included entropy analysis, which revealed that hybrid nanofluids create less entropy than regular nanofluids. The potential for hybrid nanofluids to be employed in heat transfer applications in a more environmentally responsible and effective way is the relevance of this research. It looks at the interaction between heat transmission through nanofluids and the presence of gyrotactic microorganisms, which may cause bioconvection. Such a multiphysics method is quite new and complex.

Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model

Abstract This research delves into dynamics of magnetohydrodynamic second-grade fluid flow influenced by the presence of gyrotactic microorganisms on a stretching sheet. The study takes into account various factors such as thermal radiation, chemical reactivity, and activation energy, all of which contribute to the complex behavior of fluid flow in this system. The interaction between the magnetic field and the fluid, combined with the biological aspect introduced by gyrotactic microorganisms, adds complexity to the overall analysis. The mathematical model is presented in the form of partial differential equations (PDE)s. Using the similarity variables, the modeled PDEs are transformed into ordinary differential equations. Homotopy analysis method is used for the solution of the modeled equations. After a detailed insight into this investigation, it is established that the velocity distribution declined for growth in magnetic factor and second-grade fluid parameter. The thermal characteristics are augmented for the greater values of radiation, thermophoretic and Brownian motion factors, while these profiles are weakened for upsurge in thermal relaxation time factor and Prandtl number. The concentration characteristics declined with the enhancement in Schmidt number, mass relaxation time, chemical reaction, and Brownian motion factors, while they amplified with enhancement in activation energy and thermophoresis factors. The microorganisms’ profiles are the declining functions of bioconvection Lewis and Peclet numbers. This study included a comparative analysis, which aligns closely with existing research, demonstrating a strong concordance with established findings.

Numerical simulation of bio-magnetic nanofluid flow in the human circulatory system

The investigation of the rheological properties of bio-magnetic nanofluid in the human circulatory system has attracted the attention of biomedical engineers, medical professionals and researchers in recent days to explore the potential of utilizing magnetic field in the diagnosis of cancer cells, thrombosis and cardiovascular diseases. The Eyring-Powell fluid model was employed in this investigation because it accurately captures the non-Newtonian features of blood owing to its shear thinning and stress relaxation qualities. The present study illustrates the importance of the induced magnetic field on Eyring-Powell nanofluid flow across three distinct geometries (stagnation point, plate, and wedge) with the presence of gyrotactic microorganisms. The investigation of different geometries provides essential information regarding their practical applications, such as the development of targeted therapies for localized drug delivery, the dissolution of blood clots to promote clot breakdown, the enhancement of drug delivery to specific regions, the prevention of biofilm formation on vessel walls, the promotion of improved blood flow, and the reduction of plaque for arterial health. The conversion of fluid transport equations into ordinary differential equations has been achieved through the utilization of appropriate self-similarity variables. The resulting equations have been solved with the use of the Runge-Kutta-Fehlberg (RKF) approach. The characteristics of numerous dimensionless parameters such as magnetic Prandtl number ( M mp = 0.5 , 1.0 , 1.5 ) , magnetic parameter ( β mp = 0.2 , 0.4 , 0.6 ) , fluid parameters ( ε , δ = 0.0 , 0.5 , 1.0 ) , chemical reaction parameter ( Kr = 0.0 , 0.5 , 1.0 ) , Eckert number ( Ec = 1.0 , 2.0 , 3.2 ) , Thermophoresis ( N T = 0.3 , 0.6 , 0.9 ) , Brownian motion ( N B = 0.3 , 0.6 , 0.9 ) , Biot number ( Bi = 0.5 , 1.0 , 1.5 ) , bioconvective constant ( σ 1 = 0.0 , 1.0 , 2.0 ) , bioconvective Schmidt number ( Sb = 0.1 , 0.3 , 0.5 ) , Peclet number ( Pe = 0.1 , 0.3 , 0.5 ) , temperature ratio ( θ w = 1.0 , 2.0 , 3.0 ) , Radiation ( Rd = 0.0 , 1.0 , 1.5 ) , Schmidt number ( Sc = 1.0 , 2.0 , 3.0 ) , and non-dimensional activation energy ( E = 0.0 , 0.5 , 1.0 ) are analyzed. The magnetic Prandtl number and the magnetic parameter both show a decrease with an increase in the induced magnetic field. The magnitude of concentration increases with the elevation of both the Bio convective constant and the Peclet number. The skin friction coefficient is increased to the higher values of the fluid parameter in all three geometries. Nusselt number and Sherwood number both increase to the higher values of the thermophoresis parameter across the plate, wedge, and stagnation point. The Peclet and bioconvective numbers increase the concentration of motile organisms across the plate, wedge, and stagnation point geometries.

IMPACT OF AN ANISOTROPIC POROUS MEDIA ON THERMOBIOCONVECTION INSTABILITY IN THE PRESENCE OF GYROTACTICMICROORGANISMS AND HEATING FROM BELOW

The onset of thermobioconvection in a horizontal fluid layer saturated by gyrotactic microorganisms into an anisotropic porous medium is examined. The modeling of the governing equations considers heating from below, Darcy flow, and Boussinesq approximations along with the presence of gyrotactic microorganisms. The system of ordinary differential equations is obtained using linear stability analysis and the normal mode technique. The single-term Galerkin method casts the analytical solutions while the higher-order Galerkin technique is employed to compute the numerical solutions. The influence of the mechanical and thermal anisotropy parameters along with all bioconvection parameters on the onset of thermobioconvection are analytically as well as numerically discussed. It is perceived that bioconvection Rayleigh-Darcy number <i>Rb</i>, the gyrotactic number<i> G</i>, and Péclet number <i>Q</i> are to fast-forward the onset of convective motion. On the other hand, thermal anisotropy produces a stable system and acts to postpone the bioconvection pattern formulation. Mechanical anisotropy is found to have a destabilizing impact on the stability of the suspension and helps in the development of bioconvection. The enhancement of mechanical and thermal anisotropy is found to increase the size of bioconvective cells whereas the augmentation of the concentration of gyrotactic specie reduces the convective cell size.

Bioconvection flow of Prandtl–Eyring nanofluid in the presence of gyrotactic microorganisms

AbstractThis work presents a theoretical numerical study of the bioconvection flow of Prandtl–Eyring nanofluid through a stretching cylinder with gyrotactic microorganisms. The mathematical model developed also incorporated the inclined magnetic field and heat generation effects. Further, stratification conditions are considered at the boundary of the stretched cylinder. The described flow problem conducting coupled high‐order partial differential equations (PDEs) is first reduced to the nonlinear system of ordinary differential equations (ODEs) by introducing suitable mathematical transformations. The resulting highly nonlinear flow equations are treated numerically by applying the shooting method. A comparison of the adapted method with previously reported data is also made to validate the presented results. The comparisons are in excellent agreement. The individual effect of controlling flow parameters/numbers on the flow profiles and physical quantities of engineering interest are represented graphically with physical descriptions. The significant results of the present analysis revealed that a rise in bioconvection Rayleigh number, thermal Grashof number, and angle of inclination boosts the velocity profile. The study shows that thermal stratification, mass stratification, and motile density stratification parameters diminish the temperature, concentration, and microorganism profiles, respectively. The nondimensional Sherwood number is decelerated significantly by thermophoresis and mass stratification parameters.

Onset of triply diffusive thermo-bio-convection in the presence of gyrotactic microorganisms and internal heating into an anisotropic porous medium: Oscillatory convection

This paper accentuates different aspects of an important and novel triply-diffusive thermo-bio-convection instability problem in the presence of inconsistent internal heating and the gyrotactic microorganism species into an anisotropic porous fluid layer. This instability study may be important from the application point of view in microfluidic devices, enhanced oil recovery, antibiotics, and many other areas. The normal mode analysis and linear stability analysis along with the weighted Galerkin method are used to establish the instability criteria in terms of the thermal Rayleigh number for both the oscillatory and non-oscillatory modes of convection as a secular equation among prominent parameters used in this study. It is perceived that the presence of internal heating and gyrotactic microorganism species destabilize the suspension and fast forward the triply-diffusive thermo-bio-convection. It is also established that the increment of mechanical anisotropy hastens the convection and advances the heat transfer in the porous medium while mounting thermal anisotropy and the concentration of solutes constitute a stable system that postpones the onset of triply-diffusive thermo-bio-convection.

Heat and mass transmission in a boundary layer flow due to swimming of motile gyrotactic microorganisms with variable wall temperature over a flat plate

Nanotechnology can significantly revolutionize several industries and technology domains, such as homeland security, food safety, information technology, healthcare, energy, transportation, and environmental research. Thus, a numerical study of boundary layer flow on a moving horizontal flat plate filled with nanofluid with variable temperature at the wall and viscous dissipation in the presence of gyrotactic microorganisms is presented. The partial differential equations governing flow phenomena are transformed into ordinary differential equations with the aid of appropriate similarity transformations. The transformed ordinary differential equations are solved numerically with the help of the built-in BVP4C scheme of MATLAB. After the validation of the scheme, numerical solutions are determined for the temperature, nanoparticle concentration, and motile microorganism profiles, along with physical quantities of interest. The outcomes of physical factors such as the variable temperature index, Prandtl number, Eckert number, Lewis number, Peclet number, plate moving parameter, thermophoresis motion, and Brownian parameters are examined and reported through graphs and tables. From the tables, it is clear that skin friction = 0 when the velocity parameter = 1, which shows that there is no resistance at the fluid-solid surface. It is concluded that by increasing the variable temperature, the temperature gradient rises, because of which the thickness of the thermal boundary layer reduces. Finally, more innovations are inevitable with the advancement of this interdisciplinary science. Moreover, the current investigation may help to efficiently enhance the viscosity, thermal conductivity, thermal diffusivity, and convective heat transmission linked to those base fluids, such as water and oil.

A novel model of non-linear radiative Williamson nanofluid flow along a vertical wavy cone in the presence of gyrotactic microorganisms

ABSTRACT A novel mathematical technique for an unsteady bioconvective flow of Williamson nanofluids over a vertical wavy cone in the presence of non-linear radiation and viscous dissipation impacts is investigated. The cone surface is described by a sinusoidal function while the components of the extra stress tensor are presented in terms of the dynamic viscosity. The irregular wavy surface is referred to the convective boundary conditions and nanoparticle passively controls conditions. The governing equations are presented in general forms then the condition and suitable transformations are used to map the wavy cone to regular domain. A fully implicit finite differences method (FDM) is applied to solve the converted system and wide ranges of independent variables are assumed. . The major outcomes disclosed that the increase in the Williamson number causes a reduction the nanofluid flow while the skin friction coefficient is rising. Further, there is an enhancement in the values of the Nusselt number up to 75% is obtained as Biot number is altered from 0.1 to 0.4. Also, the convective boundary conditions in presence of the non-linear radiations are recommended to enhance the velocity, temperature and rate of the heat transfer.

Second law analysis in Darcy‐Forchheimer flow of tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms

AbstractThis article investigates the creation of entropy and the thermal transport of fluids during hyperbolic tangent flow with Darcy‐Forchheimer flow over a stretching surface. Because of the role of shear‐thinning that the hyperbolic tangent fluid displays, the mechanics of the fluid are described with the assistance of a connected system of differential models that are constructed from a partial differential equation. The bvp4c routine, a three‐stage Lobatto‐IIIA method numerical analysis is utilized in the study. The effects of varying values of dimensionless parameters including Forchheimer number, inertia parameter, thermal radiation, Brownian motion, Prandtl number, Scimdth number, chemical reaction, Peclet number an Bioconvection Lewis number are simulated numerically. In addition, to this, the numerical values of the skin friction coefficient, the local Nusselt and Sherwood number and motile density are shown in the form of graphs and tables respectively. It has been discovered that increasing the value of the Fr and γ results in an upsurging velocity profile while a reverse trend is noted for the unsteady parameter. In addition to this, higher values of the radiation parameter Rd cause the operating fluid to be subjected to a greater quantity of heat, which results in an associated increase in the temperature profile.

Numerical simulation of nanofluid flow due to a stretchable rotating disk

In this study, a steady magnetohydrodynamic (MHD) flow due to stretchable rotating disk in the presence of gyrotactic microorganisms is investigated. The governing equations modeling the flow are solved numerically using the newly introduced simple iteration method (SIM) that seeks to linearize a system using relaxation technique that effectively decouples the system. To verify the convergence and accuracy of the method, solution error and residual error analysis are carried out, respectively. The obtained results suggest that the SIM is a highly efficient method that produces convergent and highly accurate solutions. The effects of various parameters as well as combined parameter effects on the solution profiles are also investigated. An increase in the Hall and permeability parameters leads to a corresponding rise in the microorganism?s density and nanoparticle volume fraction.

Entropy generation in bioconvection hydromagnetic flow with gyrotactic motile microorganisms.

Here, the magnetohydrodynamic bioconvective flow of a non-Newtonian nanomaterial over a stretched sheet is scrutinized. The characteristics of convective conditions are analyzed. Irreversibility analysis in the presence of gyrotactic micro-organisms is discussed. Energy expression is assisted with thermal radiation, heat generation and ohmic heating. Buongiorno's model is employed to discuss the characteristics of the nanoliquid through thermophoresis and random diffusions. Nonlinear expressions of the given model are transformed through adequate transformations. The obtained expressions have been computed by the Newton built in-shooting technique. Results of influential variables for velocity, concentration, microorganism field, temperature and entropy rate are graphically studied. Clearly, velocity reduction is witnessed for the bioconvection Rayleigh number and magnetic variable. A higher heat generation variable leads to augmentation of temperature. An increase in the magnetic variable results in entropy and temperature enhancement. A higher Peclet number results in microorganism field reduction. Temperature distribution rises for radiation and the thermal Biot number. A higher solutal Biot number intensifies the concentration. The entropy rate for radiation and diffusion variables is enhanced.

Energy and mass transport through hybrid nanofluid flow passing over an extended cylinder with the magnetic dipole using a computational approach

The objective of this research is to evaluate the heat and mass transfer in a water-based Darcy–Forchheimer hybrid nanofluid (HNF) flow across an expanding cylinder. The fluid flow has been studied under the influence of a magnetic field, viscous dissipation, heat source, thermal radiation, concentration stratification, and chemical reaction. Carbon nanotubes (CNTs) and iron ferrite (Fe3O4) nanoparticles (NPs) are added to the water, for the purpose of synthesizing the HNF. The fluid flow has been induced in the presence of gyrotactic microorganisms and the non-Fick’s model. Microorganisms are used to stabilize scattered nanoparticles through the hybrid nanofluid. The phenomena have been modeled in the form of a nonlinear system of partial differential equations (PDEs). The modeled equations are reduced to a dimensionless system of ODEs by using similarity substitution. The numerical solution of the derived sets of nonlinear differential equations is obtained by using the parametric continuation method. The impact of physical constraints on temperature, velocity, concentration, and microorganism profiles is presented through figures and tables. It has been observed that the heat and mass transport rates increase with the rising effect of the curvature parameter, while declining with the effect of the thermal stratification parameter.

Three‐dimensional magnetohydrodynamic non‐Newtonian bioconvective nanofluid flow influenced by gyrotactic microorganisms over stretching sheet

AbstractThe current manuscript deals with MHD Casson nanofluid flow in presence of gyrotactic microorganisms and convective conditions. Initially, partial differential equations are converted into first‐order ordinary differential equations (ODEs) by using similarity variables, and then these ODEs are solved by applying mathematical simulation due to the highly nonlinear behavior of resulting equations. Runge–Kutta–Fehlberg technique is employed by following the shooting method and results are symbolically calculated in MATLAB software. The motive behind solving this model is to calculate the influence of various crucial fluid parameters, namely, Casson fluid parameter β (0.1 ≤ β ≤ 0.5), magnetic parameter M (1 ≤ M ≤ 5), Biot numbers (a (0.1 ≤ a ≤ 2.1), b (1 ≤ b ≤ 9), and d (0.5 ≤ d ≤ 2.5)), Brownian motion Nb (1 ≤ Nb ≤ 21), thermophoresis Nt (1.0 ≤ Nt ≤ 3.0), Peclet number Pe (1 ≤ Pe ≤ 5), bioconvective constant σ (1 ≤ σ ≤ 5), Lewis number Le (10 ≤ Le ≤ 50), bioconvective Lewis number Lb (1 ≤ Lb ≤ 5). It is inferred that thermal Biot number enhances temperature distribution and nanoparticle concentration declines with inclination in chemical reaction.

Study of Buongiorno’s nanofluid model for flow due to stretching disks in presence of gyrotactic microorganisms

Owing to the widespread practical significances of nanoparticles in thermal engineering and industrial processes, scientists are devoted to explore the more fundamental thermal aspects of such nano-materials. Recently, the nanoparticles show extensive applications in heat transfer improvement, energy production, cooling and heating processes, refrigeration, thermal extrusion processes, thermoelectric devices, bio-medical applications like cancer treatment, brain tumors and many more. Moreover, the phenomenon of bioconvection utilize interesting applications in bio-technology, bio-fuels, enzymes, fertilizes etc. Keeping such motivations in mind, this research presents the bioconvection flow of nanofluid induced by two stretchable disks separated at confined distance. The Buongiorno nanofluid model is employed to examine the Brownian motion and thermophoresis aspects. The equations govern for the flow of the nanofluid, heat transfer; nanoparticles concentration and density of motile microorganisms’ fields are simplified with the help of similarity transformation. The resultant form of nonlinear equations is solved by using homotopy analysis method. The influence of significantly participating parameters on velocity, nanofluid temperature, concentration and density of motile microorganisms profiles are observed with relevant physical significances. The convergence of solution for velocity, temperature, concentration and motile microorganisms profiles are examined carefully. The simulations are compared with already declared numerical data and found a convincible accuracy. It is noticed that the temperature profile enhances up to specified range and then start decline due to larger values of values of Brownian motion and thermophoresis parameters. A dual nature of velocity profiles for higher the value of stretching parameter has been observed. The concentration profile declines with increasing Brownian motion constant and Lewis number. The motile microorganisms profile decreases due to enhancement of bio-convection Peclet number, Reynolds number and Schmidt number.

Varying wall temperature and thermal radiation effects on MHD boundary layer liquid flow containing gyrotactic microorganisms

Nanofluid dynamics and magnetohydrodynamics have tremendously contributed to industrial applications. The presence of nanoparticles in base fluids enhances the specific chemical and physical properties. This study intends to examine the combined impacts of magnetic field and convective boundary state on bioconvection of a Casson fluid and concentration of nanoparticles in presence of gyrotactic microorganisms over a straight extending sheet. To simplify the governing equations comprising momentums, temperature, and concentration of nanoparticles, and microorganisms, the similarity transformations are employed. Emerged system of coupled nonlinear differential equations is solved by the differential transformation method and MATHEMATICA software. The impacts of the Brownian motion parameter, thermophoresis parameter, Casson fluid parameter, radiation parameter, suction or mass flux parameter, magnetic field, Prandtl number, Lewis number, Peclet number, and bioconvection parameter on dimensionless velocity, temperature, nanoparticles concentration, and microorganisms density profile are interpreted through graphs. The present bioconvection analysis is most relevant to the study of bioproducts.

Analysis of Heat and Mass Transfer Features of Hybrid Casson Nanofluid Flow with the Magnetic Dipole Past a Stretched Cylinder

The main purpose of this research is to scrutinize the heat and mass transfer in the Casson hybrid nanofluid flow over an extending cylinder in the presence of a magnetic dipole and double stratification. The nanofluid contained chemically reactive hybrid nanoparticles (Ag, MgO) in the conventional fluids (water). The effects of viscous dissipation, radiation, and concentration stratification were taken into consideration. In the presence of gyrotactic microorganisms and the Non-Ficks Model, the flow was induced. Incorporating microorganisms into a hybrid nanofluid flow is thought to help stabilize the dispersed nanoparticles. For viscosity and thermal conductivity, experimental relations with related dependence on nanoparticle concentration were used. To acquire the nonlinear model from the boundary layer set of equations, suitable similarity transformations were employed. The built-in function bvp4c of Matlab software was utilized to solve the transformed equation numerically. The graphical results were obtained for temperature, velocity, concentration, and microorganism distribution for various parameters. The numerical amounts of drag friction, heat transport rate, and motile density number for different parameters are presented through tables. It is seen that the fluid velocity is augmented by the increase of the curvature parameter, while a decrease occurs in the fluid velocity with an increase in the magnetic and slips parameters. The comparison of the present study with previously available studies is discussed, which shows a good agreement with published results.

Entropy analysis of unsteady MHD three‐dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

AbstractThis article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well‐known scheme, namely the shooting method along with the Runge‐Kutta‐Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non‐Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.

Homotopy perturbation method solution of magneto-polymer nanofluid containing gyrotactic microorganisms over the permeable sheet with Cattaneo–Christov heat and mass flux model

Many non-Newtonian materials behave as a polymeric solution and this type of materials is used in various industrial and physical applications such as polymer extraction, manufacturing processes, various geophysical systems, and glass production. Especially the gyrotactic microorganisms have widely used for the production of biodiesel, hydrogen, an essential sustainable energy source and in water treatment plants. This study intends to examine the impacts of magnetic field, convective boundary state on bioconvection of a tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms over a porous stretching surface with a Cattaneo–Christov heat and mass flux model. Appropriate self-similarity variables are implemented to transform the fluid transport equations into ordinary differential equations that have been resolved using the homotopy perturbation method. The influences of effective parameters on transport properties of the fluid are represented with graphs and tables. This model forecast the shear-thinning attitude significantly and exactly describes the flow of fluids. It is noted from the obtained results that the velocity profile declines with raising the Weissenberg number and buoyancy ratio parameter. It also observed that the temperature profile rises with a growth in the radiation and thermal relaxation parameters. The higher values of the stagnation parameter increase the rate of heat transfer while it is opposite nature in the mixed convection parameter. Microorganisms density uplifts with an increase in Peclet number, while it decreases for the microorganism concentration difference. Microorganisms density increases with an enlargement in bioconvection Schmidt number.

Numerical Simulation of Jeffrey Hamel Flow of Nanofluid in the Presence of Gyrotactic Microorganisms

The nonlinear differential equations play a prominent role in mathematically describing many phenomena that occur in our world. A similar set of equations appear in this paper that govern the nanofluid flow between two non-parallel walls in the presence of gyrotactic microorganisms that are responsible for bioconvection. These microorganisms ensure the safety of the appliance by avoiding the accumulation of nanoparticles and the movement of these nanoparticles within the fluid experiences major slip mechanisms as discussed by Buongiorno. Further, the orientation of the channel is described by the parameter β and based on this parameter channel is said to be converging if and the channel is diverging if . The case when corresponds to a channel with parallel walls, hence this case is ignored. Following these assumptions, the set of governing equations thus formed are made dimensionless and further solved by the Differential Transformation Method (DTM) and the outcomes are discussed through graphs. The analysis is performed for both converging and diverging orientation of the channel. The results indicate that the temperature and the concentration profiles increase with the increase in Brownian motion parameters in both divergent and convergent channels. Meanwhile, the increase in Reynolds number decreases the temperature of the nanofluid. Through the simulation, it was observed that the heat flow is taking place along the isothermal planes in the case of the diverging channel but it was uniform in the domain of the converging channel.