Thermo-bioconvection in a suspension of gravitactic micro-organisms in vertical cylinders

We investigate the effect of heating or cooling from below at constant temperature and constant heat flux on the development of gravitactic bioconvection in vertical cylinders with stress free sidewalls. The governing equations are the continuity equation, the Navier–Stokes equations with the Boussinesq approximation, the diffusion equation for the motile micro-organisms and the energy equation. The control volume method is used to solve numerically the complete set of governing equations. The governing parameters are the thermal and bioconvection Rayleigh numbers, the bioconvection Peclet number, the Lewis number, the Schmidt number and the aspect ratio. We found that subcritical bifurcations of bioconvection became supercritical bifurcations when the thermal Rayleigh number Ra_T is different than zero. For Ra_T < 0, i.e. for cooling from below, we have opposing buoyancy forces, the convection is decreased and the critical thermo-bioconvection Rayleigh number is increased with respect to that of bioconvection. For Ra_T > 0, i.e. for heating from below, we have cooperating buoyancy forces, the convection is increased and the critical thermo-bioconvection Rayleigh number is decreased with respect to that of bioconvection. Heating and cooling from below at constant temperature and heat flux modify considerably the pattern formation of the gravitactic bioconvection.     

Bioconvection in a squeezing flow of a micropolar fluid in a horizontal channel

The bioconvection flow of an incompressible micropolar fluid containing microorganisms between two infinite stretchable parallel plates is considered. A mathematical model, with a fully coupled nonlinear system of equations describing the total mass, momentum, thermal energy, mass diffusion, and microorganisms is presented. The governing equations are reduced to a set of nonlinear ordinary differential equations with the help of suitable transformations. The resulting nonlinear ordinary differential equations are linearized using successive linearization method, and the resulting system of linear equations is solved using the Chebyshev collocation method. The detailed analysis illustrating the influences of various physical parameters, such as the micropolar coupling number, squeezing parameter, the bioconvection Schmidt number, Prandtl numbers, Lewis number, and bioconvection Peclet number on the velocity, microrotation, temperature, concentration and motile microorganism distributions, skin friction coefficient, Nusselt number, Sherwood number, and density number of motile microorganism, is examined. The influence of the squeezing parameter is to increase the dimensionless velocities and temperature and to decrease the local Nusselt number and local Sherwood number. The density number of motile microorganism is decreasing with squeezing parameter, bioconvection Lewis number, bioconvection Peclet number, and bioconvection Schmidt number.     

Mixed convection of a nanofluid past an inclined wavy surface in the presence of gyrotactic microorganisms

The mixed convection of a nanofluid flow past an inclined wavy surface in the existence of gyrotactic microbes is considered. To convert the wavy surface to a plane surface, a transformation of coordinates is applied. The governing equations that are nonlinear and the accompanying boundary conditions are converted into a dimensionless form using pseudo-similarity variables. Using a local linearization process, the system of nonlinear partial differential equations is linearized. The resulting system is solved using the Bivariate Chebyshev pseudo-spectral collocation method. The influence of different physical and geometrical factors on the parameters of engineering importance of the flow is analyzed and illustrated graphically. It is observed that the skin friction, the density of motile microorganisms, and nanoparticle mass transfer rate are increasing with an increase in the bioconvection Peclet and Schmidt numbers whereas these quantities are decreasing with an increase in Rayleigh number. The local Nusselt number, nanoparticle Sherwood number, and density number of microbes increases with an increase in the Brownian motion and thermophoresis parameter. These physical quantities are increasing when the surface changes from horizontal to vertical.     

Gyrotactic microorganisms bioconvection in combined convective magnetohydrodynamic Casson nanofluid flow over a vertically surfaced saturated porous media with variable viscosity

The current article focuses on mass and thermal transfer analysis of a two-dimensional immovable combined convective nanofluid flow including motile microorganisms with temperature-dependent viscosity on top of a vertical plate through a porous medium, and a model has been developed to visualize the velocity slip impacts on a nonlinear partial symbiotic flow. The governed equations include all of the above physical conditions, and suitable nondimensional transfigurations are utilized to transfer the governed conservative equations to a nonlinear system of differential equations and obtain numerical solutions by using the Shooting method. Numerical studies have been focusing on the effects of intricate dimensionless parameters, namely, the Casson fluid parameter, Brownian motion parameter, thermophoresis parameter, Peclet number, bioconvection parameter, and Rayleigh number, which have all been studied on various profiles such as momentum, thermal, concentration, and density of microorganisms. The concentration boundary layer thickness and density of microorganisms increased as the Casson fluid parameter, Brownian and thermophoresis parameters increased, whereas the bioconvection parameter, Peclet number, and Rayleigh number increased. The thermal boundary layer thickness, concentration boundary layer thickness, and density of microorganisms all decreased. The velocity distribution decreases as the Peclet number, bioconvection, and thermophoresis parameters rise but rises as the Rayleigh number, Brownian motion parameter, and Casson fluid parameter rise. These are graphed via plots along with divergent fluid parameters.     

Unsteady bioconvection Darcy-Forchheimer nanofluid flow through a horizontal channel with impact of magnetic field and thermal radiation

Unsteady bioconvection Darcy-Forchhiemer nanofluid flow is considered in the current investigation in the presence of micro-organisms. The flow is exposed to thermal radiation and a uniform magnetic field in a horizontal channel. The impacts of Brownian motion and thermophoresis are also considered for the flow problem. The unsteady governing equations are modeled and transformed into a nondimensional form by employing a suitable group of similar variables. The solution of the modeled equations is determined by the semianalytical method homotopy analysis method. The features of flow characteristics such as temperature, concentration, velocity, and the motile micro-organism distributions in response to the variations of the emerging parameters are simulated and examined in detail. Among the many results of the study, it is found that velocity upsurges with rising values of the unsteadiness parameter while declining with growth in the magnetic, inertial, and porosity parameters. Temperature augments with growing estimations of Brownian, unsteadiness, and radiation parameters and declines with enhancing values of Prandtl number. Amassed estimations of the Brownian factor reduce the concentration of nanoparticles while growing values of thermophoresis, unsteadiness parameters, and Schmidt number increase it. Moreover, the motile micro-organism profile is a reducing function of the bioconvection Lewis numbers, Peclet, and bioconvection concentration difference parameter.     

A revised viscoelastic micropolar nanofluid model with motile micro‐organisms and variable thermal conductivity

In the present study, a magnetized micropolar nanofluid and motile micro‐organism with variable thermal conductivity over a moving surface have been discussed. The mathematical modeling has been formulated using a second‐grade fluid model and a revised form of the micropolar fluid model. The governing fluid contains micro‐organisms and nanoparticles. The resulting nonlinear mathematical differential equations have been solved with the help of the homotopy analysis method. The graphical and physical features of buoyancy force, micro‐organisms, magnetic field, microrotation, and variable thermal conductivity have been discussed in detail. The numerical results for Nusselt number, motile density number, and Sherwood number are presented with the help of tables. According to the graphical effects, it is noted that the buoyancy ratio and the bioconvection parameter resist the fluid motion. An enhancement in the temperature profile is observed due to the increment in thermal conductivity. Peclet number tends to diminish the motile density profile; however, the viscoelastic parameter magnifies the motile density profile.     

Numerical investigation of thermo-bioconvection in a suspension of gravitactic microorganisms

This paper investigates the effect of heating or cooling from below on the development of gravitactic bioconvection in a square enclosure with stress free sidewalls. The governing equations are the Navier–Stokes equations with the Boussinesq approximation, the diffusion equation for the motile microorganism and the energy equation for the temperature. The control volume method is used to solve numerically the complete set of governing equations. It was found that the suspension is destabilized by heating from below and stabilized by cooling from below. A transition from a subcritical bifurcation to a supercritical bifurcation was observed in the case of heating from below when the thermal Rayleigh number was increased.     

The effect of computational processing of temperature- and concentration-dependent parameters on non-Newtonian fluid MHD: Applications of numerical methods

This investigation aims to introduce a new solution with aid of numerical methods to the blood flow of Carreau–Yasuda fluid through a microvessel. Swimming of gyrotactic microorganisms with nanoparticles is considered. A resulting system of partial differential equations is simplified by the meaning of low Reynolds number and long wavelength. This system of partial differential equations was formulated and transformed mathematically using new theories of differential transform method. Variable nonndimensional physical parameters effects, such as numbers of bioconvection Peclet and bioconvection Rayleigh, and so forth on velocity, temperature, and concentration distribution as well as oxytactic microorganism and oxygen concentration profiles are studied. All results are constructed in two cases of viscosity on the same figure, one of them in the case of variable parameters and the other in constant parameters. The existing study assured that the microorganism density in the direction near to the hypoxic tumor tissues regions grows with a rise in oxygen concentrations and the blood viscosity diminutions.     

Impact of Soret and Dufour on bioconvective flow of nanofluid in porous square cavity

This article addresses the bioconvection in a porous cavity associated with Soret and Dufour effects. The bioconvective flow in a porous medium is based on Hillesdon and Pedley's model and is governed by nonlinear partial differential equations. These equations are transformed into a dimensionless form with suitable nondimensional parameters. The finite element method is employed to solve the dimensionless equations. The outcomes of the study are presented by streamlines, temperature distributions, isoconcentrations of solute, nanoparticles, and microorganisms. Furthermore, the tendency of average Nusselt number and average Sherwood number and the influence of Soret parameter, Dufour parameter, Peclet number, and bioconvective Rayleigh number is interpreted. Thermophoresis and Soret number show a strong effect on the concentration of nanoparticles. Brownian motion and thermophoresis exhibit a significant effect on the density distributions of microorganisms. The novelty of the paper is to combine the effects of Soret–Dufour and oxytactic bioconvection. The present study can be useful in the following applications: microbial-enhanced oil recovery, toxin removal, antibiotics, and modeling of microfluidic devices.     

Bioconvection of gravitactic microorganisms in a vertical cylinder

Patterns formation of gravitactic microorganism in a vertical cylinder is described by the Navier–Stokes equation coupled with the microorganism conservation equation. The control volume method is used to solve numerically these equations. It is found that when the Peclet number is decreased, the critical Rayleigh number also decreases to approach the value corresponding to Bénard convection under fixed-flux heating condition. However, at high Peclet numbers, the development convection is very different from that of Bénard convection. The most fundamental difference is that, while Bénard convection is a supercritical instability, the gravitactic bioconvection is shown to be a subcritical bifurcation from the diffusion state.     

Simultaneous effects of radiation,magnetic field on peristaltic flow of Carreau nanofluid submerged in gyrotactic microorganisms with heat and mass transfer

Our study intends to examine the combined effects of radiation, magnetic field, and chemical reaction on the peristaltic flow of a non-Newtonian fluid containing gyrotactic microorganisms and nanoparticles. The system of our equations is understood numerically by using the Rung-Kutta-Merson method with Newton iteration in a shooting and matching procedure. The effect of physical implanted parameters is represented and discussed through a lot of charts for velocity, temperature, nanoparticle concentration, the density of motile microorganisms. From this discussion, we notice that the motile microorganisms profile is affected by the arising with the Brownian motion parameter and radiation parameter but the thermophoresis parameter, traditional Lewis number, and bioconvection of Peclet number are decremented the motile microorganisms profile.     

Effect of inclined and low magnetic field in gaseous slip flow in two‐dimensional rectangular microchannel using first‐order boundary conditions

In the present work, the effect of an oriented low magnetic field on near‐continuum gaseous slip flow inside a two‐dimensional rectangular microchannel has been studied using first‐order boundary conditions. The flow was assumed to be compressible, laminar, and steady. The governing equations were solved analytically to obtain the solutions of velocity, temperature, and the pressure of the flow. The influence of different parameters such as Knudsen number, aspect ratio, Hartmann number, and pressure ratio were studied and analyzed. It was found that the electric and magnetic field with an inclined angle had significant effects on the flow properties. The results showed that the velocity increases and the temperature decreases as the inclination angle of the magnetic field decreases. The velocity increases as the Knudsen number, pressure ratio, and aspect ratio increase, while it decreases with increasing of the Hartmann number. The temperature decreases with increasing of the Knudsen number, pressure ratio, and aspect ratio, while the temperature increases as the Hartmann number increases. The results of the present study were validated with published results in the literature.     

Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition

The aim of the present numerical study is to understand the natural convection flow and heat transfer in an inclined rectangular enclosure with sinusoidal temperature profile on the left wall. The top and bottom walls of the enclosure are kept to be adiabatic. The finite difference method is used to solve the governing equations with a range of inclination angles, aspect ratios and Rayleigh numbers. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first then decreases with increasing the inclination of the enclosure for all aspect ratio and Rayleigh number. Increasing the aspect ratio shows a decreasing trend of the heat transfer for all Rayleigh numbers considered. A correlation equation is also introduced for the heat transfer analysis in this study.     

Study of mixed convection in an annular vertical cylinder filled with saturated porous medium,using thermal non-equilibrium model

The present study deals with numerical investigation of effects of different parameters on enhancement or retardation of the heat transfer rate in an annular vertical cylinder filled with saturated porous medium. The heat transfer is assumed to take place by mixed convection mode. The thermal non-equilibrium approach is considered. The inner surface of the annular cylinder is maintained at constant wall temperature whereas the outer surface remains at ambient temperature. The governing partial differential equations are solved using finite element method. The results are discussed for the effects of Peclet number, interphase heat transfer co-efficient and thermal conductivity ratio.     

Convective transport in rectangular cavities partially heated at the bottom and cooled at one side

Laminar natural convection heat transfer inside air-filled, rectangular enclosures partially heated from below and cooled at one side is studied numerically. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of the mass, momentum, and energy transfer governing equations. Simulations are performed for a complete range of heater size, for Rayleigh numbers based on the height of the cavity ranging from 10~3to 10~6, and for height-to-width aspect ratios of the cavity spanning from 0.25 to 4. It is found that the heat transfer rate increases with increasing the heater size and the Rayleigh number, while it decreases with increasing the aspect ratio of the cavity. Dimensionless heat transfer correlations are also proposed.     

Double dispersed bioconvective Casson nanofluid fluid flow over a nonlinear convective stretching sheet in suspension of gyrotactic microorganism

Microorganisms play a vital role in understanding the ecological system. The motions of micororganisms are self‐propelled while the impact of thermophoresis and Brownian motion property of nanoparticle shows more challenges in biotechnological and medical applications. The present problem is based on the understanding of double‐dispensed bioconvection for a Casson nanofluid flow over a stretching sheet. Suction phenomenon is introduced at the surface of the stretching sheet along with the convective boundary condition. The convection and movement of the microorganisms are assisted by an applied magnetic field, nonlinear thermal radiation, and first‐order chemical reaction. The governing equations are highly coupled and thus we used the spectral quasilinearization method to solve the governing equations. The study of the residual errors on the systemic parameters had given a confidence with the present results. The final outcomes are displayed through graphs and tables. The thermal dispersion coefficient shows a positive response in the temperature while a similar response is observed for the concentration with solutal dispersion coefficient. The response is reversible for the heat transfer rate at the surface with thermal dispersion coefficient. The density of the motile microorganism at the surface decreases with increase in the Casson number, thermal dispersion coefficient, and solute dispersion coefficient, while an opposite phenomenon was observed with increase in the density ratio of the motile microorganism.     

Radiative flow of Maxwell nanofluid containing gyrotactic microorganism and energy activation with convective Nield conditions

On the account of industrial and technological applications, the enhancement of energy by inserting nanoparticles is a hot topic in the present century. Therefore, the current analysis presents a theoretical analysis regarding the flow of electrically conducted Maxwell nanofluid over a stretching surface in the presence of the gyrotactic microorganism. In addition, the influence of thermal conductivity and Arrhenius activation energy are considered. By using the apposite transformation, the system of contemporary partial differential expressions is first converted into nonlinear ordinary differential system. The set of these transmuted equations is solved with the help of the shooting method. Reliable results are obtained for the velocity profile, temperature, motile microorganism density and concentration. It is evaluated that by increasing the value of bioconvection Peclet and Lewis numbers, the microorganism distribution exhibited diminishing behavior. These results may be useful in improving the efficiency of heat transfer devices and microbial fuel cells.     

Heat transfer in inclined rectangular receivers for concentrated solar radiation

We study heat transfer in inclined rectangular cavities, which may be used as receivers of concentrated solar radiation. One of the active walls is subject to concentrated solar radiation and the other is kept at constant temperature. Continuity, momentum and energy equations are solved by finite difference — control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to10¹², the cavity aspect ratio, A = L/H from 0.5 to 2, the inclination angle, from 30 to 90°.We found that the Nusselt number is an increasing function of the Rayleigh number, the aspect ratio and the inclination angle. Based on the computed data a correlation is derived in the form of Nu = f(Ra, A, ).     

FLOW AND HEAT TRANSFER IN RECTANGULAR ENCLOSURES USING A NEW BLOCK-IMPLICIT NUMERICAL METHOD

This work reports a numerical investigation on buoyancy-induced flows occurring in enclosures of small aspect ratio and inclined with respect to the horizontal direction. The numerical method used consists of the control-volume approach and a new block-implicit error-smoothing operator. Governing equations are written in terms of primitive variables and are recast into a general form. In the proposed method, all governing equation are relaxed locally, in contrast with commonly used segregated schemes. The effects of Rayleigh number, aspect ratio, and cavity inclination on temperature and velocity patterns are discussed. It is expected that more advanced parallel computer architectures can benefit from the error-smoothing operator described here.     

Free convection in porous media filled right-angle triangular enclosures

Steady-state free convection heat transfer in a right-angle triangular enclosure, whose vertical wall insulated and inclined and bottom walls are differentially heated, is performed in this study. The governing equations are obtained using Darcy model. In this study, the governing equations were solved by finite difference method and solution of algebraic equations was made via Successive Under Relaxation method. The effect of aspect ratios ranging from 0.25 to 1.0 and Rayleigh numbers 50 ≤ Ra ≤ 1000 is investigated as governing parameters on heat transfer and flow field. It is observed that heat transfer is increased with the decreasing of aspect ratio and multiple cells are formed at high Rayleigh numbers.