三维空间内趋地性生物对流的数值模拟

采用数值解析方法分析了充满牛顿流体并悬浮有一定浓度微生物的圆柱体容器内趋地性生物对流现象,以控制容积法离散化方程,考察了细胞密度和运动能力对流动形态和细胞浓度分布的影响。结果表明:大约50秒左右即可形成初步的对流,在400秒时对流即达到稳定;ρ的减小和Vc的增大均可以增强细胞运动能力,ρ对于流动稳定性的影响要大于Vc;Vc的增大会使细胞较早从流股脱离,加入向上的流动,明显增强流股两侧对流中心处的流动,当Δρ为100 kg·m~(-3)时,流动在700 s时才达到稳定状态;而ρ对于对流中心处的影响很有限。     

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.     

Numerical and sensitivity analysis of MHD bioconvective slip flow of nanomaterial with binary chemical reaction and Newtonian heating

The impact of Stefan blowing on the MHD bioconvective slip flow of a nanofluid towards a sheet is explored using numerical and statistical tools. The governing partial differential equations are nondimensionalized and converted to similarity equations using apposite transformations. These transformed equations are solved using the Runge–Kutta–Fehlberg method with the shooting technique. Graphical visualizations are used to scrutinize the effect of the controlling parameters on the flow profiles, skin friction coefficient, local Nusselt, and Sherwood number. Moreover, the sensitivities of the reduced Sherwood and Nusselt number to the input variables of interest are explored by adopting the response surface methodology. The outcomes of the limiting cases are emphatically in corroboration with the outcomes from preceding research. It is found that the heat transfer rate has a positive sensitivity towards the haphazard motion of the nanoparticles and a negative sensitivity towards the thermomigration. The thermal field is enhanced by the Stefan blowing aspect. Moreover, the fluid velocity can be controlled by the applied magnetic field.     

Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

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.     

Investigation of flow parameters of Reiner–Philippoff nanofluid flow with higher-order slip properties,activation energy,and bioconvection by artificial neural networks

In this study, the flow parameters of Reiner–Philippoff nanofluid flow with high-order slip properties, activation energy, and bioconvection have been analyzed using artificial neural networks (ANNs). Local Nusselt number (LNN), local Sherwood number (LSN), and motile density number (MDN) are considered as flow parameters. Numerical values have been obtained by numerical methods using flow equations. To estimate the flow parameters, three different ANN models have been designed. The Levenberg–Marquardt training algorithm is used in multilayer perceptron network models with 10 neurons in the hidden layers. In all, 70% of the data set has been used for training the models, 15% for validation, and 15% for testing. The performance analysis of the network models has been made by calculating the determined performance parameters. The R values for the LNN, LSN, and MDN parameters have been calculated as 0.99261, 0.98769, and 0.99102, respectively, and the average deviation values are −0.65%, 0.06%, and −0.11%, respectively. The attained outcomes showed that the ANNs can predict the LNN, LSN, and MDN, which are the flow parameters of the Reiner–Philippoff nanofluid flow, with high accuracy.     

Bioconvective Casson nanofluid flow toward stagnation point in non-Darcy porous medium with buoyancy effects,chemical reaction,and thermal radiation

The emphasis on non-Newtonian fluid encountered in biomedical, pharmaceuticals, mining, food, chemical, and plastics industries and in noticeably enormous diverse industrial applications influenced this article. This study is accomplished in a non-Darcy porous stretching surface to investigate the stagnation point of bioconvective Casson nanofluid. Chemical reaction, applied consistent magnetic field, radiative heat transfer, and buoyancy force consequences are studied for numerical examination. Composed of nonlinear partial differential equations for the above presumptions and reforming them into ordinary differential equations by means of compatible transformations are enforced. Adopting the fifth order Runge–Kutta Felhberg method with the shooting technique obtained a numerical solution. Obtained solutions are authenticated by comparing previous solutions. The major finding includes the reduction of the Casson parameter on the skin friction coefficient.     

Magnetohydrodynamic bio‐nanoconvective Naiver slip flow of micropolar fluid in a stretchable horizontal channel

The purpose of this paper is to formulate and analyze a nano‐bio transport model for magnetohydrodynamic convective flow, heat, and mass diffusion of micropolar fluid containing gyrotactic microorganisms through a horizontal channel. Both the walls are considered to be stretched, and the Navier slip boundary condition is taken into account. The governing bio‐nano transport partial differential equations are rendered to ordinary differential equations using similarity variables. The resulting normalized self‐similar boundary value problem is solved computationally with the Matlab bvp4c function. The effect of the controlling parameters on the nondimensional velocity, temperature, nanoparticle concentration, and motile microorganism density functions, and their gradients at the wall are visualized graphically and in a tabular form and expounded at length. Validation with a previous simpler model is included. All physical quantities, except the local Nusselt number, increases with an increase in the velocity slip and magnetic parameters. The present problem finds applications in industries related to pharmaceutical, nanofluidic devices, microbial enhanced oil recovery, modeling oil, and gas‐bearing sedimentary basins.     

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.     

封闭腔体内生物对流二维流场的数值分析

采用数值解析方法分析了封闭腔体中充满牛顿流体并悬浮有一定浓度微生物的二维容器内趋地性生物对流现象,结果表明：大约50秒左右即可形成初步的对流,在300秒时对流即达到稳定;ρ的减小和Vc的增大均可以增强细胞运动能力,ρ对于流动稳定性的影响要大于Vc;Vc的增大会使细胞较早从流股脱离,加入向上的流动,明显增强流股两侧对流中心处的流动,而ρ对于对流中心处的影响很有限。