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The purpose of this study is to discuss the Darcy–Forchheimer nanoliquid bio-convection flow by stretching cylinder/plate with modified heat and mass fluxes, activation energy and gyrotactic motile microorganism features.

The proposed flow model is based on flow rate, temperature of nanomaterials, volume fraction of nanoparticles and gyrotactic motile microorganisms. Heat and mass transport of nanoliquid is captured by the usage of popular Buongiorno relation, which allows us to evaluate novel characteristics of thermophoresis diffusion and Brownian movement. Additionally, Wu’s slip (second-order slip) mechanisms with double stratification are incorporated. For numerical and graphical results, the built-in bvp4c technique in computational software MATLAB along with shooting technique is used.

The influence of key elements is illustrated pictorially. Velocity decays for higher magnitude of first- and second-order velocity slips and bioconvection Rayleigh number. The velocity of fluid has an inverse relation with mixed convection parameter and local inertia coefficient. Temperature field enhances with the increase in estimation of thermal stratification Biot number and radiation parameter. A similar situation for concentration field is observed for mixed convection parameter and concentration relaxation parameter. Microorganism concentration profile decreases for higher values of bioconvection Lewis number and Peclet number. A detail discussion is given to see how the graphical aspects justify the physical ones.

To the best of the authors’ knowledge, original research work is not yet available in existing literature.

The purpose of this paper is to investigate the stability of a suspension containing both gyrotactic and oxytactic microorganisms for the case when the suspension occupies a horizontal layer of finite depth. The lower boundary of the layer is assumed rigid while at the upper boundary both situations of rigid and stress‐free boundary conditions are considered.

Linear instability analysis is utilized, and the obtained eigenvalue problem is solved analytically using a one‐term Galerkin method.

The obtained eigenvalue equation relates three Rayleigh numbers, the traditional thermal Rayleigh number and two bioconvection Rayleigh numbers, for gyrotactic and oxytactic microorganisms.

Only the case of non‐oscillatory instability (which always occurs when heating from the bottom is considered) is analyzed. Further experimental research is needed to elucidate possible interaction between gyrotactic and oxytactic microorganisms. The developed theory is applicable only for dilute suspensions.

This paper extends the traditional theory of bio‐thermal convection to the case when the suspension contains two types of motile microorganisms exhibiting different behaviors.

This paper aims to deal with the heat transmission of Sutterby fluid-containing gyrotactic microorganism by incorporating non-Darcy resistance law. The mathematical modeling is based on nanoparticle concentration, energy, momentum and motile microorganism equations.

The governing nonlinear coupled equations are first rendered into nonlinear ordinary equations using appropriate transformation and are then solved analytically by using the optimal homotopy.

Graphical illustration of results depict the behavior of flow involved physical parameters on temperature, gyrotactic microorganism, concentration and velocity. Additionally, local Nusselt number and skin friction coefficient are computed numerically and validated through comparison with existing literature as a special case of proposed model. It is found that the temperature profile decreases by increasing values of Brownian-motion parameter and Prandtl number. An increase in thermophoresis parameter and Schmidt number results in decrease in concentration of nanoparticles. Bioconvection Peclet number corresponds to decreasing behavior of nondimensional gyrotactic microorganism field is observed. Finally, a comparison with the existing literature is made, and an excellent agreement is seen.

To the best of the authors’ knowledge, this study is reported for the first time.

A parabolic trough solar collector is an advanced concentrated solar power technology that significantly captures radiant energy. Solar power will help different sectors reach their energy needs in areas where traditional fuels are in use. This study aims to examine the sensitivity analysis for optimizing the heat transfer and entropy generation in the Jeffrey magnetohydrodynamic hybrid nanofluid flow under the influence of motile gyrotactic microorganisms with solar radiation in the parabolic trough solar collectors. The influences of viscous dissipation and Ohmic heating are also considered in this investigation.

Governing partial differential equations are derived via boundary layer assumptions and nondimensionalized with the help of suitable similarity transformations. The resulting higher-order coupled ordinary differential equations are numerically investigated using the Runga-Kutta fourth-order numerical approach with the shooting technique in the computational MATLAB tool.

The numerical outcomes of influential parameters are presented graphically for velocity, temperature, entropy generation, Bejan number, drag coefficient and Nusselt number. It is observed that escalating the values of melting heat parameter and the Prandl number enhances the Nusselt number, while reverse effect is observed with an enhancement in the magnetic field parameter and bioconvection Lewis number. Increasing the magnetic field and bioconvection diffusion parameter improves the entropy and Bejan number.

Nanotechnology has captured the interest of researchers due to its engrossing performance and wide range of applications in heat transfer and solar energy storage. There are numerous advantages of hybrid nanofluids over traditional heat transfer fluids. In addition, the upswing suspension of the motile gyrotactic microorganisms improves the hybrid nanofluid stability, enhancing the performance of the solar collector. The use of solar energy reduces the industry’s dependency on fossil fuels.

The purpose of this paper is to provide an insight into the influence of gyrotactic microorganisms and Hall effect on the boundary layer flow of 29 nm CuO-water mixture on the upper pointed surface of a rocket, over the bonnet of a car and upper pointed surface of an aircraft. This is true since all these objects are examples of an object with variable thickness.

The simplification of Rosseland approximation (Taylor series expansion of T⁴ about T_∞) is avoided; thus, two different parameters relating to the study of nonlinear thermal radiation are obtained. The governing equation is non-dimensionalized, parameterized and solved numerically.

Maximum vertical and horizontal velocities of the 29 nm CuO-water nanofluid flow is guaranteed at a small value of Peclet number and large value of buoyancy parameter depending on the temperature difference. When the magnitude of thickness parameter χ is small, cross-flow velocity decreases with the velocity index and the opposite effect is observed when the magnitude of χ is large.

Directly or indirectly, the importance of the fluid flow which contains 29 nm CuO nanoparticle, water, and gyrotactic microorganisms in the presence of Hall current has been pointed out as an open question in the literature due to its relevance in imaging, ophthalmological and translational medicine informatics.

This paper aims to explore the study of magnetohydrodynamic viscous fluid flow past on a stretching cylinder with nonlinear thermal radiation having gyrotactic microorganisms.

Appropriate transformations reduce the nonlinear partial differential equation to ordinary ones. Subsequent nonlinear equations are calculated to get convergent series solutions.

Fluid velocity declines for elevating values of magnetic field parameter. For larger values of curvature parameter near the cylinder temperature reduces.

To the best of the authors’ knowledge, magnetohydrodynamic boundary layer flow of viscous fluid by nonlinear stretching cylinder with nonlinear thermal radiation having gyrotatic microorganisms is not studied yet. The purpose is to study this.

The modern day has seen an increase in the prevalence of the improvement of high-performance thermal systems for the enhancement of heat transmission. Numerous studies and research projects have been carried out to acquire an understanding of heat transport performance for their functional application to heat conveyance augmentation. The idea of this study is to inspect the entropy production in Darcy-Forchheimer Ree-Eyring nanofluid containing bioconvection flow toward a stretching surface is the topic of discussion in this paper. It is also important to take into account the influence of gravitational forces, double stratification, heat source–sink and thermal radiation. In light of the second rule of thermodynamics, a model of the generation of total entropy is presented.

Incorporating boundary layer assumptions allows one to derive the governing system of partial differential equations. The dimensional flow model is transformed into a non-dimensional representation by applying the appropriate transformations. To deal with dimensionless flow expressions, the built-in shooting method and the BVP4c code in the Matlab software are used. Graphical analysis is performed on the data to investigate the variation in velocity, temperature, concentration, motile microorganisms, Bejan number and entropy production concerning the involved parameters.

The authors have analytically assessed the impact of Darcy Forchheimer's flow of nanofluid due to a spinning disc with slip conditions and microorganisms. The modeled equations are reset into the non-dimensional form of ordinary differential equations. Which are further solved through the BVP4c approach. The results are presented in the form of tables and figures for velocity, mass, energy and motile microbe profiles. The key conclusions are: The rate of skin friction incessantly reduces with the variation of the Weissenberg number, porosity parameter and Forchheimer number. The rising values of the Prandtl number reduce the energy transmission rate while accelerating the mass transfer rate. Similarly, the effect of Nb (Brownian motion) enhances the energy and mass transfer rates. The rate of augments with the flourishing values of bioconvection Lewis and Peclet number. The factor of concentration of microorganisms is reported to have a diminishing effect on the profile. The velocity, energy and entropy generation enhance with the rising values of the Weissenberg number.

According to the findings of the study, a slip flow of Ree-Eyring nanofluid was observed in the presence of entropy production and heat sources/sinks. There are features when the implementations of Darcy–Forchheimer come into play. In addition to that, double stratification with chemical reaction characteristics is presented as a new feature. The flow was caused by the stretching sheet. It has been brought to people's attention that although there are some investigations accessible on the flow of Ree-Eyring nanofluid with double stratification, they are not presented. This research draws attention to a previously unexplored topic and demonstrates a successful attempt to construct a model with distinctive characteristics.

The purpose of this paper is to scrutinize the heat and mass transfer attributes of three-dimensional bio convective flow of nanofluid across a slendering surface with slip effects. The analysis is carried out subject to irregular heat sink/source, thermophoresis and Brownian motion of nanoparticles.

At first, proper transmutations are pondered to metamorphose the basic flow equations as ODEs. The solution of these ODEs is procured by the consecutive application of Shooting and Runge-Kutta fourth order numerical procedures.

The usual flow fields along with density of motile microorganisms for sundry physical parameters are divulged via plots and scrutinized. Further, the authors analyzed the impact of same parameters on skin friction, heat and mass transfer coefficients and presented in tables. It is discovered that the variable heat sink/source parameters play a decisive role in nature of the heat and mass transfer rates. The density of motile microorganisms will improve if we add Al-Cu alloy particles in regular fluids instead of Al particles solely. A change in thermophoresis and Brownian motion parameters dominates heat and mass transfer performance.

To the best of the knowledge, no author made an attempt to investigate the flow of nanofluids over a variable thickness surface with bio-convection, Brownian motion and slip effects.

Mechanisms of deposition and declogging are considered while formulating a new continuum model for bioconvection in a dilute suspension of motile, negatively geotactic microorganisms in a porous medium. According to research in 1988, bioconvection is the name given to pattern‐forming convective motions set up in suspensions of swimming microorganisms. “Negative geotaxis” means that the microorganisms tend to swim against the gravitational force. This paper is motivated by experimental research by Kessler who investigated the effect of porous media on the development of convection instability in algal suspensions. In the model suggested in this paper, the decrease of permeability due to cell adsorption by the porous medium is considered and the influence of this permeability decrease on the development of bioconvection is studied. The existence and stability of a two‐dimensional plume in a rectangular enclosure with stress‐free sidewalls is investigated. Governing equations include the Darcy law as well as the microorganism conservation equations. A conservative finite‐difference scheme is utilized to solve these equations numerically. The analysis of the proposed model reveals that the major factors affecting the development of bioconvection are the initial permeability of the porous medium and the rate of cell deposition. For small permeability, the resistance to the fluid flow is too large, and bioconvection does not develop. If the rate of cell deposition is too large, the number of suspended cells quickly becomes too small because of cell capturing by the porous medium. For this reason, the critical density difference in the top fluid layer cannot be reached, and bioconvection does not develop.

The purpose of this paper is to study haemodynamic flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, magnetohydrodynamic (MHD) flow and aneurysm conditions. The findings of this study offer significant insights into the intricate interplay encompassing electro-osmosis, MHD flow, microorganisms, Joule heating and the ternary hybrid nanofluid.

The governing equations are first non-dimensionalised, and subsequently, a coordinate transformation is used to regularise the irregular boundaries. The discretisation of the governing equations is accomplished by using the Crank–Nicolson scheme. Furthermore, the tri-diagonal matrix algorithm is applied to solve the resulting matrix arising from the discretisation.

The investigation reveals that the velocity profile experiences enhancement with an increase in the Debye–Hückel parameter, whereas the magnetic field parameter exhibits the opposite effect, reducing the velocity profile. A comparative study demonstrates the velocity distribution in Au-CuO hybrid nanofluid and Au-CuO-GO ternary hybrid nanofluid. The results indicate a notable enhancement in velocity for the ternary hybrid nanofluid compared to the hybrid nanofluids. Moreover, an increase in the Brinkmann number results in an augmentation in entropy generation.

This study investigates the flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, MHD flow and aneurysm conditions. The governing equations are non-dimensionalised, and a coordinate transformation is applied to regularise the irregular boundaries. The Crank–Nicolson scheme is used to model blood flow in the presence of a ternary hybrid nanofluid (Au-CuO-GO/blood) within the arterial domain. The findings shed light on the complex interactions involving stenosis, MHD flow, aneurysms, Joule heating and the ternary hybrid nanofluid. The results indicate a decrease in the wall shear stress (WSS) profile with increasing stenosis size. The MHD effects are observed to influence the velocity distribution, as the velocity profile exhibits a declining nature with an increase in the Hartmann number. In addition, entropy generation increases with an enhancement in the Brinkmann number. This research contributes to understanding fluid dynamics and heat transfer mechanisms in bifurcated arteries, providing valuable insights for diagnosing and treating cardiovascular diseases.