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The purpose of this paper is to investigate the bioconvection flow in a porous square cavity saturated with both oxytactic microorganism and nanofluids.

The impacts of the effective parameters such as Rayleigh number, bioconvection number, Peclet number and thermophoretic force, Brownan motion and Lewis number reduces the flow strength in the cavity on the flow strength, oxygen density distribution, motile isoconcentrations and heat transfer performance are investigated using a finite volume approach.

The results obtained showed that the average Nusselt number is increased with Peclet number, Lewis number, Brownian motion and thermophoretic force. Also, the average Sherwood number increased with Brownian motion and Peclet number and decreased with thermophoretic force. It is concluded that the flow strength is pronounced with Rayleigh number, bioconvection number, Peclet number and thermophoretic force. Brownan motion and Lewis number reduce the flow strength in the cavity.

There is no published study in the literature about sensitivity analysis of Brownian motion and thermophoresis force effects on the bioconvection heat transfer in a square cavity filled by both nanofluid and oxytactic microorganisms.

In recent years, microfluidics has turned into a very important region of research because of its wide range of applications such as microheat exchanger, micromixers fuel cells, cooling systems for microelectronic devices, micropumps and microturbines. Therefore, in this paper, micropolar nanofluid flow through an inclined microchannel is numerically investigated in the presence of convective boundary conditions. Heat transport of fluid includes radiative heat, viscous and Joule heating phenomena.

Governing equations are nondimensionalized by using suitable dimensionless variables. The relevant dimensionless ordinary differential systems are solved by using variational finite element method. Detailed computations are done for velocity, microrotation and temperature functions. The influence of various parameters on entropy generation and the Bejan number is displayed and discussed.

It is established that the entropy generation rate increased with both Grashof number and Eckert number, while it decreased with nanoparticle volume fraction and material parameter. Temperature is decreased by increasing the volume fraction of Ag nanoparticle dispersed in water.

According to the literature survey and the best of the author’s knowledge, no similar studies have been executed on micropolar nanofluid flow through an inclined microchannel with effect of viscous dissipation, Joule heating and thermal radiation.

The purpose of this paper is to study the boundary layer flow and heat transfer of a power-law non-Newtonian nanofluid over a non-linearly stretching sheet.

The governing equations describing the problem are transformed into a nonlinear ordinary differential equations by suitable similarity transformations. The resulting equations for this investigation are solved numerically by using the variational finite element method.

It was found that the local Nusselt number increases by increasing the Prandtl number, stretching sheet parameter and decreases by increasing the power-law index, thermophoresis parameter and Lewis number. Increases in the stretching sheet parameter, Prandtl number and thermophoresis parameter decrease the local Sherwood number values. The effects of Brownian motion and Lewis number lead to increases in the local Sherwood number values.

The work is relatively original as very little work has been reported on non-Newtonian nanofluids.

The purpose of this paper is to analyze the mangnetohydrodynamic boundary layer flow of a viscous, incompressible and electrically conducting non-Newtonian nanofluid obeying power-law model over a non-linear stretching sheet under the influence of thermal radiation with heat source/sink.

The transverse magnetic field is applied normal to the sheet. The model used for the nanofluid incorporates the effects of Brownian motion with thermophoresis in the presence of thermal radiation. On this regard, thermophoresis effect on convective heat transfer on nanofluids are investigated simultaneously. The governing partial differential equations are reduced to ordinary differential equations by suitable similarity transformations which are solved numerically by variational finite element method.

The computations carried out for some values of the power-law index, magnetic parameter, radiation parameter, Brownian motion and thermophoresis. The effect of these parameters on the velocity, temperature and nanoparticle volume fraction distribution are presented graphically. The skin friction coefficient, Nusselt number and Sherwood number for various values of the flow parameters of the problem are also presented.

To the best of the authors’ knowledge, no investigations has been reported regarding the study of non-Newtonian nanofluids which obeying power-law model over a nonlinear stretching sheet. The principal aim of this paper is to study the boundary layer MHD flow of a non-Newtonian power-law model over a non-linear stretching sheet on a quotient viscous incompressible electrically conducting with a nanofluid.

The purpose of the study is to indicate a three-dimensional convective heat transfer properties evaluation of magnetohydrodynamics nanofluid flow, comprising motile oxytactic microorganisms and nanoparticles, passing through a rotating cone.

The imposed technique for solving the governing equations is the Runge–Kutta fifth-order method. The main point of this survey is to diagnosis the influence of diverse factors on velocity, temperature distributions and concentration profile. Furthermore, appending the magnetic field, thermal radiation and viscous dissipation in calculations; also, simultaneous involvement of heat absorption and excretion has been represented as novelties.

The results elucidate that by changing the Peclet number from 1 to 2, the dimensionless concentration of the microorganisms has been diminished by about 34.37%. In addition, variation of the magnetic parameter from 0 to 1 has been resulted in reducing the temperature distribution by about 3.11%.

Recently, attention has been absorbed to adding the motile microorganisms to nanofluid for enhancement of heat transfer and avoiding aggregation of particles. In this regard, the hydrothermal flow of microorganisms has been investigated in this study.

Buongiorno’s type nanofluid mass and heat transport appearances inside a cavity filled with gyrotactic microorganisms by captivating thermal radiation is analyzed in the present work. Finite element investigation is instigated to examine the converted momentum, temperature, concentration of microorganisms and concentration of nanofluid equations numerically.

Finite element investigation is instigated to examine the converted momentum, temperature, concentration of microorganisms and concentration of nanofluid equations numerically.

The sway of these influenced parameters on standard rates of heat transport, nanoparticles Sherwood number and Sherwood number of microorganisms is also illustrated through graphs. It is perceived that the rates of heat transport remarkably intensifies inside the cavity region with amplifying thermophoresis number values.

The research work carried out in this paper is original and no part is copied from others’ work.

The purpose of this paper is to consider heat and mass transfer on magnetohydrodynamics (MHD) Williamson fluid flow over a slendering stretching sheet with variable thickness in the presence of radiation and chemical reaction. All pertinent flow parameters are discussed and their influence on the hydrodynamics, thermal and concentration boundary layer are presented with the aid of the diagram.

The governing partial differential equations are reduced into a system of ordinary differential equations with the help of suitable similarity variables. A discrete version of the homotopy analysis method (HAM) called the spectral homotopy analysis method (SHAM) was used to solve the transformed equations. SHAM is efficient, and it converges faster than the HAM. The SHAM provides flexibility when solving linear ordinary differential equations with the use of the Chebyshev spectral collocation method.

The findings revealed that an increase in the variable thermal conductivity hike the temperature and the thermal boundary layer thickness, whereas the reverse is the case for velocity close to the wall.

The uniqueness of this paper is the exploration of combined effects of heat and mass transfer on MHD Williamson fluid flow over a slendering stretching sheet. The Williamson fluid term in the momentum equation is expressed as a linear function and the viscosity and thermal conductivity are considered to vary in the boundary layer.

This study aims to explore magnetohydrodynamic (MHD) thermo-bioconvection of oxytactic microorganisms in multi-physical directions addressing thermal gradient, lid motion, porous substance and magnetic field collectively using a typical differentially heated two-sided lid-driven cavity. The consequences of a range of pertinent parameters on the flow structure, temperature, oxygen isoconcentration and microorganisms’ isoconcentration are examined and explained in great detail.

Two-dimensional governing equations in a two-sided lid-driven porous cavity heated differentially and packed with oxytactic microorganisms under the influence of the magnetic field are solved numerically using the finite volume method-based computational fluid dynamics code. The evolved flow physics is analyzed assuming a steady laminar incompressible Newtonian flow within the validity of the Boussinesq approximation. The transport of oxytactic microorganisms is formulated by augmenting the continuum model.

The mechanisms involved with MHD-mixed thermo-bioconvection could have potential benefits for industrial exploitation. The distributions of fluid flow, temperature, oxygen and motile microorganisms are markedly modified with the change of convection regime. Both speed and direction of the translating walls significantly influence the concentration of the motile microorganisms. The concentration of oxygen and motile microorganisms is found to be higher at the upper portion of the cavity. The overall patterns of the fluid flow, temperature and the oxygen and microorganism distributions are markedly affected by the increase of magnetic field strength.

The concept of the present study could be extended to other areas of bioconvection in the presence of gravity, light or chemical attraction.

The findings of the present study could be used to multi-physical applications like biomicrosystems, pollutant dispersion in aquifers, chemical catalytic converters, geothermal energy usage, petroleum oil reservoirs, enhanced oil recovery, fuel cells, thermal energy storage and others.

The MHD-mixed thermo-bioconvection of oxytactic microorganisms is investigated under different parametric conditions. The effect of pertinent parameters on the heat and mass transfers are examined using the Nusselt number and Sherwood number.

The purpose of this study is to address magnetohydrodynamic (MHD) bioconvection caused by the swimming of oxytactic microorganisms in a linearly heated square cavity filled with porous media and Cu–water nanofluid. The effects of different multiphysical aspects are demonstrated using local distributions as well as global quantities for fluid flow, temperature, oxygen concentration and microorganisms population.

The coupled transport equations are converted into the nondimensional partial differential equations, which are solved numerically using a finite volume-based computing code. The flow of Cu–water nanofluid through the pores of porous media is formulated following the Brinkman–Forchheimer–Darcy model. The swimming of oxytactic microorganisms is handled following a continuum model.

The analysis of transport phenomena of bioconvection is performed in a linearly heated porous enclosure containing Cu–water nanofluid and oxytactic microorganisms under the influence of magnetic fields. The application of such a system could have potential impacts in diverse fields of engineering and science. The results show that the flow and temperature distribution along with the isoconcentrations of oxygen and microorganisms is markedly affected by the involved governing parameters.

Similar study of bioconvection could be extended further considering thermal radiation, chemical attraction, gravity and light.

The outcomes of this investigation could be used in diverse fields of multiphysical applications, such as in food industries, chemical processing equipment, fuel cell technology and enhanced oil recovery.

The insight of the linear heating profile reveals a special attribute of simultaneous heating and cooling zones along the heated side. With such an interesting feature, the MHD bioconvection of oxytactic microorganisms in nanofluid-filled porous substance is not reported so far.