This work explores the interaction of mixed bio convection and non-Newtonian fluid flow around a vertical cylinder. It considers different slip effects and the impact of suction/injection boundary conditions. The inquiry is driven by the substantial implications of comprehending the interconnected dynamics of living organisms and non-Newtonian fluids, with wide-ranging applications in biotechnology, medicine, and environmental science. The study incorporates the intricacies of shear-thinning or shear-thickening fluids by utilizing the generalized power-law model to capture non-Newtonian rheological phenomena. The vertical cylinder, selected as the archetype geometry, functions as a fundamental structure encountered in several engineering applications. The slip effects, which can vary from no-slip to full slip, are included in the model to represent the interactions between the fluid and solid. Additionally, the suction/injection boundary conditions are used to simulate external forces that are provided to govern the motion of the fluid. The study utilizes similarity transformations to convert the governing equations and employs the MATLAB BVP4c scheme to solve the resulting ordinary differential equations. It investigates a parameter space that encompasses non-Newtonian parameters, slip coefficients, bio convection parameters, and suction/injection parameters. The results demonstrate intricate relationships between bio convection, non-Newtonian rheology, slip effects, and suction/injection. These findings state the suction parameter (s>1) and dilatant fluid (n>1) have great influence on heat, mass and motile microorganism rate and also slip parameters are responsible for reducing flow profiles. The study's findings enhance our comprehension of intricate fluid dynamics when biological activity and non-Newtonian behaviour are present. This provides valuable insights for the efficient design and optimization of processes involving vertical cylinders in fields such as biotechnology, medicine, and environmental engineering.

The goal of this research is to look at two dimensional steady free forced convective flows through a horizontal surface surrounded by a permeable medium with exponential decaying heat generation and chemical reaction. For describing non-isothermal phenomena power law exponent has been considered in boundary conditions. By imposing appropriate transformations, the nonlinear partial differential equations driving the flow, temperature, concentration, and microbe fields are reduced to a system of ordinary differential equations and numerically solved by MATLAB 14.0. Excellent compatibility has been discovered between our optimized results and the already-published literature when compared for validation. The velocity, temperature, concentration, and microbe profiles are reduced by the power law exponent, which shows fluctuation in wall temperature and concentrations. Lewis parameter Le has a significant impact on concentration. The bioconvection peclet number Pe and the Lewis parameter Lb both significantly affect the profile of microorganisms. The influence of internal heat generation and chemical reaction can cause heat and mass transfer rates to increase, but slow down the transfer rate of motile microorganisms. For regions of forced convection, all flow profiles and flow transfer rates increase whereas they drop for regions of pure mixed convection.

The goal of this study is to show how velocity, temperature, solutal and microorganism slip effects coupled with suction/injection affect mixed convective fluid flow through a vertical cone containing gyrotactic microorganism. To execute numerical computations, the controlling partial differential equations which comprise steady momentum, energy, conservation of mass and motile microorganism balances are initially reduced to a collection of linked non linear ordinary differential equations by similarity transformations, utilizing the MATLAB bvp4c scheme to solve numerically. The current study’s findings have been graphically compared to those of earlier research, revealing a high level of compatibility. The flow fields are numerically exhibited for diversified parameters. For some precise parameter values, dual solutions can be discovered throughout the domain of free, mixed and forced convection and only in the free convection zone do dual solutions exist beyond a critical point. This research has applications for microbial fuel cells, a green sustainable technology for the production of bioelectricity and the treatment of wastewater.

This paper investigates the influence of dispersion impact on mixed convection flow over a horizontal cone within a non-Darcy porous medium. Multiple convective boundary conditions are applied to address the heat, mass and motile microorganism transfer phenomena. This paper incorporates the dispersion effect for gyrotactic microorganisms due to biological and environmental applications. By imposing appropriate similarity transformations, the nonlinear partial differential equations governing flow, temperature, concentration, and microbe fields are reduced to a system of ordinary differential equations then solved using the MATLAB BVP4C function. The computation of grid independence test is analyzed for different flow profiles to show the precision of the points. In a few instances, our present numerical data is compared with previously published works, leading to excellent agreement. The non-Darcy effect, as well as mixed convection values from 0.1 to 0.9 and buoyancy parameters from 0.2 to 0.8, all significantly affects the velocity profile. The reduction in the microorganism profile is brought on by the increase in the bioconvection Lewis parameter and bio convection peclet number between 0.3 and 1. In the absence of dispersion, the variation of Biot numbers between 0.5 and 2, favor heat, mass, and motile microorganism transfer the most in the range of mixed convection parameter 0.5 to pure forced convection 1. Thermal, solutal and microorganism dispersion coefficients a, b, c that lie between 1/7 and 1/3 and higher values of modified peclet number ranges from 2 to 10 cause increased dispersion effects which lower flow transfer rates mostly in forced convection regime.

The problem of steady laminar mixed convection boundary layer flow along vertical thin needle with variable surface heat, mass and motile microorganism flux in the presence of gyrotactic microorganism is considered in this study. The dimensionless leading equations of continuity, momentum, concentraton and motile microorganism conservation are reduced to ordinary differential equations with the help of similarity transformations. The transformed governing equations are then numerically solved by using MATLAB BVP4C function. The research is reached to excellent argument by comparison in few cases between the results obtained from MATLAB and Maple algorithm with the help of dsolve command. Numerical calculations are carried out for various values of the dimensionless parameters of the problem which includes mixed convection parameter λ, power law index m, buoyancy parameters N 1 , N 2 Lewis parameter Le, bioconvection lewis parameter Lb, Bioconvection peclet number Pe and also the parameter a representing the needle size. It is also shown from the results that the surface (wall) temperature, surface fluid concentration, surface motile microorganism concentration and the corresponding velocity, temperature, concentration and motile microorganism profiles are significantly induced by these parameters. The results are pictured and discussed in detail.

The purpose of this research is to present dual solution for combined free and forced convection flow towards a non-isothermal permeable inclined cylinder containing gyrotactic microorganism. Though several researches were done on dual solutions for mixed convection and also along the vertical cylinder for the numerous engineering applications but very few works have done on dual solutions for mixed convection with gyrotactic microorganisms. Two steps are performed here to carry out numerical calculations. Firstly, the governing partial differential equations are simplified into set of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using bvp4c function from MATLAB. Dual solutions are observed for heat, mass and density of motile microorganism transfer rate and also for velocity, temperature, concentration, and microorganism profile beyond a critical point. The research is reached to excellent argument by comparison in few cases between the results obtained from MATLAB and Maple algorithm. The heat, mass and motile microorganism transfer rate decreases from free to mixed convection regime and then increases to forced convection regime with the influence of different flow control parameters. The results also indicate that dual solutions for different flow profiles exist only in free convection dominated regime.

Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ([Formula: see text] spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.

This paper investigates the effects of Soret and Dufour in a steady mixed convective boundary layer flow over a vertical surface in a magnetic field embedded in a porous medium with gyrotactic microorganisms. The governing momentum, energy, concentration, and microorganism equations are transformed into a set of coupled differential equations. These equations are solved by the Maple 14.0 algorithm. The numerical results for different nondimensional numbers (Soret number, Sr; Dufour number, Df; Lewis number, Le; bioconvection Lewis number, Lb; bioconvection Peclet number, Pe; Hartmann number, Ha(2); thermal radiation parameter, R-d; and buoyancy numbers, N-1, N-2) are presented graphically for both assisting and opposing flow. Comparisons with available literature show great agreement among results. The effects of physical parameters on Nusselt number, Sherwood number, and density of motile microorganisms are also presented. It is observed that diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects on temperature, concentration, and microorganism profile distributions are quite opposite.

The problem of free convective steady boundary layer flows over a solid horizontal flat plate nested in a porous medium filled with a nanofluid containing gyrotactic microorganisms is considered. The exponent of the temperature, the nanoparticle volume fraction and the density of motile microorganisms are introduced to make the quantities dimensionless. The impacts of the considered exponent and bioconvection parameters on the dimensionless temperature, velocity, nanoparticle concentration and density of motile microorganisms along with Nusselt, Sherwood and motile microorganism numbers are tabulated and shown graphically. For a regular fluid and also for the isothermal case, the results are compared with the existing data and excellent compatibility is found.