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This study aims to focuse on the flow behavior of a specific nanofluid composed of blood-based iron oxide nanoparticles, combined with motile gyrotactic microorganisms, in a ciliated channel with electroosmosis.

This study applies a powerful mathematical model to examine the combined impacts of bio convection and electrokinetic forces on nanofluid flow. The presence of cilia, which are described as wave-like motions on the channel walls, promotes fluid propulsion, which improves mixing and mass transport. The velocity and dispersion of nanoparticles and microbes are modified by the inclusion of electroosmosis, which is stimulated by an applied electric field. This adds a significant level of complexity.

To ascertain their impact on flow characteristics, important factors such as bio convection Rayleigh number, Grashoff number, Peclet number and Lewis number are varied. The results demonstrate that while the gyrotactic activity of microorganisms contributes to the stability and homogeneity of the nanofluid distribution, electroosmotic forces significantly enhance fluid mixing and nanoparticle dispersion. This thorough study clarifies how to take advantage of electroosmosis and bio convection in ciliated micro channels to optimize nanofluid-based biomedical applications, such as targeted drug administration and improved diagnostic processes.

First paper discussed “Numerical Computation of Cilia Transport of Prandtl Nanofluid (Blood-Fe₃O₄) Enhancing Convective Heat Transfer along Micro Organisms under Electroosmotic effects in Wavy Capillaries”.

This paper aims to study the fluid flow and heat transfer within the Casson nanofluid confined between disk and cone both rotating with distinct velocities. For a comprehensive investigation, two distinct nano-size particles, namely, silicon dioxide and silicon carbide, are submerged in ethanol taken as the base fluid.

This paper explores the disk and cone contraption mostly encountered for viscosity measurement in various industrial applications such as lubrication industry, hydraulic brakes, pharmaceutical industry, petroleum and gas industry and chemical industry.

It is worth mentioning here that the radially varying temperature profile at the disk surface is taken into the account. The effect of prominent emerging parameters on velocity fields and temperature distribution are studied graphically, while bar graphs are drawn to examine the physical quantities of industrial interest such as surface drag force and heat transfer rate at disk and cone.

To the best of the authors’ knowledge, no study in literature exists that discusses the thermal enhancement of nano-fluidic transport confined between disk and cone both rotating with distinct angular velocities with heat transfer.

This paper aims to optimize bioconvective heat transfer for magnetohydrodynamics Eyring–Powell nanofluids containing motile microorganisms with variable viscosity and porous media in ciliated microchannels.

The flow problem is first modeled in the two-dimensional frame and then simplified under low Reynolds number and long wavelength approximations. The numerical method is used to examine the impact of thermal radiation, temperature-dependent viscosity, mixed convection, magnetic fields, Ohmic heating and porous media for velocity, temperature, concentration and motile microorganisms. Graphical results are presented to observe the impact of physical parameters on pressure rise, pressure gradient and streamlines.

It is observed that the temperature of nanofluid decreases with higher values of the viscosity parameter. It is absolutely in accordance with the physical expectation as the radiation parameter increases, the heat transfer rate at the boundary decreases. Nanoparticle concentration increases by increasing the values of bioconvection Rayleigh number. The density of motile microorganisms decreases when bioconvection Peclet number is increased. The velocity of the nanofluid decreases with higher value of Darcy number. With increase in the value of bioconvection parameter, the flow of nanofluid is increased.

The bioconvective peristaltic movement of magnetohydrodynamic nanofluid in ciliated media is proposed. The non-Newtonian behavior of the fluid is described by using an Eyring–Powell fluid model.

Sheet processing of magnetic nanomaterials is emerging as a new branch of smart materials’ manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve the understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, this study aims to develop a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet.

This study developed a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant-strength magnetic field is applied transversely to the stretching flow plane. The Buongiorno nanofluid model is used to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo–Christov) model is used to simulate thermal conduction effects, of which the Fourier model is a special case when thermal relaxation effects are neglected.

The governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth-order Runge–Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters, e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nanoparticle concentration distributions, is investigated.

A strong elevation in temperature accompanies an increase in Brownian motion parameter, whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nanoparticle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter, whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values, i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model.

The purpose of this paper is to discuss free convection peristaltic flow in an asymmetric channel with nanofluid containing gyrotactic microorganism.

The governing equations for proposed model are simplified using “long wavelength and low Reynolds number approximation.” Numerical solutions have been presented for “velocity, pressure gradient, the solid volume fraction nanoparticles, temperature profile and density of motile microorganisms.” The effects of various flow parameters, i.e Hartmann number, the solid volume fraction of the nanoparticles amplitude ratio, Prandtl number, bioconvection Péclet number, bioconvection constant, bioconvection Rayleigh number are presented.

The author finds that the pressure rise increases with an increase in Hartmann number, Grashof number bioconvection, Rayleigh number and buoyancy ratio in the peristaltic pumping section.

The peristaltic flow nanofluid containing gyrotactic microorganism is explored in the literature for the first time.

The purpose of this paper is to study the effects of temperature‐dependent viscosity on the peristaltic flow of Jeffrey fluid through the gap between two coaxial horizontal tubes.

The inner tube is maintained at a temperature T₀0 and the outer tube has sinusoidal wave travelling down its wall and it is exposed to temperature T₁. The governing problem is simplified using longwave length and low Reynold number approximations. Regular perturbation in terms of small viscosity parameter is used to obtain the expressions for the temperature and velocity for Reynold' s models of viscosity. The numerical solution of the problem has also been computed by shooting method and an agreement of numerical solutions and analytical solutions had been presented. The expressions for pressure rise and friction force are calculated numerically.

Graphical results and trapping phenomenon are presented at the end of the paper to see the physical behaviour of different parameters.

The paper is a new and original work on the subject of peristaltic flows and heat transfer in Jeffrey fluid.

The purpose of this study is to examine the effects of heat and mass transfer on the peristaltic flow of Eyring‐Powell fluid in a diverging tube.

The governing equations for Eyring‐Powell are modelled in cylindrical coordinates using long wavelength and low Reynolds number approximation. The resulting nonlinear differential equations are solved for velocity, temperature and concentration profile and pressure gradient using regular perturbation technique. Also, the numerical solutions for velocity profile have been computed employing finite difference technique. A comparative study is also presented for both the solutions.

Numerical integration has been performed to get the expression of pressure rise and frictional forces. Graphical results have been presented for pressure rise, frictional forces, temperature and concentration profile for various physical parameters of interest for five considered wave forms.

Trapping phenomena have been discussed at the end of the article.

The purpose of this paper, is to study the MHD double-diffusive natural convection of a nanofluid over a linearly stretching sheet using the Buongiorno model.

The transport equations are transformed into coupled similarity equations. The numerical self-similar solutions are compared with the literature for the special case of pure fluid flow and found to be in good agreement. Graphical results are presented to illustrate the effects of various fluid flow, heat transfer and nano concentration parameters for both assisting and opposing flows.

It is found that the heat transfer rate increases as nanoparticles and salt are suspended in water. It is also found that dual solutions exist for the stretching parameter.

First paper on this model for stretching sheet.

The present critical analysis has been performed to explore the steady stagnation point flow of Jeffery fluid toward a stretching surface, in the presence of convective boundary conditions. It is assumed that the fluid strikes the wall obliquely. The governing non-linear partial differential equations for the flow field are converted to ordinary differential equations by using suitable similarity transformations. Optimal homotopy analysis method (OHAM) is operated to deal the resulting ordinary differential equations. OHAM is found to be extremely effective analytical technique to obtain convergent series solutions of highly non-linear differential equations. Graphically, non-dimensional velocities and temperature profile are expressed. Numerical values of skin friction coefficients and heat flux are computed. The comparison of results from this paper with the previous existing literature authorizes the precise accuracy of the OHAM for the limited case. The paper aims to discuss these issues.

The governing non-linear partial differential equations for the flow field are converted to ordinary differential equations by using suitable similarity transformations. OHAM is operated to deal the resulting ordinary differential equations.

OHAM is found to be extremely effective analytical technique to obtain convergent series solutions of highly non-linear differential equations. Graphically, non-dimensional velocities and temperature profile are expressed. Numerical values of skin friction coefficients and heat flux are computed.

The comparison of results from this paper with the previous existing literature authorizes the precise accuracy of the OHAM for the limited case.

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.