Numerical solutions for nonlinear gyrotactic bioconvection in nanofluid-saturated porous media with stefan blowing and multiple slip effects

A mathematical model is developed to examine the effects of the Stefan blowing, second order velocity slip, thermal slip and microorganism species slip on nonlinear bioconvection boundary layer flow of a nanofluid over a horizontal plate embedded in a porous medium with the presence of passively controlled boundary condition. Scaling group transformations are used to find similarity equations of such nanobioconvection flows. The similarity equations are numerically solved with a Chebyshev collocation method. Validation of solutions is conducted with a Nakamura tri-diagonal finite difference algorithm. The effects of nanofluid characteristics and boundary properties such as the slips, Stefan blowing, Brownian motion and Grashof number on the dimensionless fluid velocity, temperature, nanoparticle volume fraction, motile microorganism, skin friction, the rate of heat transfer and the rate of motile microorganism transfer are investigated. The work is relevant to bio-inspired nanofluid-enhanced fuel cells and nano-materials fabrication processes

Lie symmetry analysis and numerical solutions for thermo-solutal chemicallyreacting radiative micropolar flow from an inclined porous surface

Steady, laminar, incompressible thermo-solutal natural convection flow of micropolar fluid from an inclined perforated surface with convective boundary conditions is studied. Thermal radiative flux and chemical reaction effects are included to represent phenomena encountered in high-temperature materials synthesis operations. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Lie scaling group transformation is implemented to derive a self-similar form of the partial differential conservation equations. The resulting coupled nonlinear boundary value problem is solved with Runge-Kutta fourth order numerical quadrature (shooting technique). Validation of solutions with an optimized Adomian decomposition method algorithm is included. Verification of the accuracy of shooting is also conducted as a particular case of non-reactive micropolar flow from a vertical permeable surface. The evolution of velocity, angular velocity (micro-rotation component), temperature and concentration are examined for a variety of parameters including coupling number, plate inclination angle, suction/injection parameter, radiation-conduction parameter, Biot number and reaction parameter. Numerical results for steady state skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are tabulated and discussed. Interesting features of the hydrodynamic, heat and mass transfer characteristics are examined

Unsteady reactive magnetic radiative micropolar flow, heat and mass transfer from an inclined plate with joule heating: a model for magnetic polymer processing

Magnetic polymer materials processing involves many multi-physical and chemical effects. Motivated by such applications, in the present work a theoretical analysis is conducted of combined heat and mass transfer in unsteady mixed convection flow of micropolar fluid over an oscillatory inclined porous plate in a homogenous porous medium with heat source, radiation absorption and Joule dissipation. A first order homogenous chemical reaction model is used. The transformed non-dimensional boundary value problem is solved using a perturbation method and Runge-Kutta fourth order numerical quadrature (shooting technique). The emerging parameters dictating the transport phenomena are shown to be the gyro-viscosity micropolar material parameter, magnetic field parameter, permeability of the porous medium, Prandtl number, Schmidt number, thermal Grashof number, species Grashof number, thermal radiation-conduction parameter, heat absorption parameter, radiation absorption parameter, Eckert number, chemical reaction parameter and Eringen coupling number (vortex viscosity ratio parameter). The impact of these parameters on linear velocity, microrotation (angular velocity), temperature and concentration are evaluated in detail. Results for skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are also included. Couple stress is observed to be reduced with stronger magnetic field. Verification of solutions is achieved with earlier published analytical results

On time dependent MHD nanofluid dynamics due to enlarging sheet with bioconvection and two thermal boundary conditions

The current study pertains to heat and mass transportation of magnetic fluid flow having dilute diffusion of nanoparticles and motile microorganisms over a permeable stretched sheet to examine the influence of thermal radiation and activation energy. Similarity functions are utilized to convert the highly mixed non-linear partial differential equations into higherorder non-linear ordinary differential equations. Five coupled equations are derived to be resolved numerically by employing a computing function Bvp4c, built-in Matlab. Two sets of thermal boundaries prescribed surface temperature (PSF) and prescribed heat flux (PHF) are considered. Basic physical quantities, temperature distribution, concentration, velocity field, and motile micro-organism profiles are observed as influenced by emerging parameters. The microorganisms distribution undergoes decreasing behavior against growing values of bio-convection Lewis number and Peclet number. These results are highly useful in the application of heat-transmitting devices and microbial fuel cells. It is seen that decreasing trend is observed in velocity profile when parameters Nr and Nc are uplifted. Also, the motility of the nanofluid decreases when the Lb parameter is raised. On the other hand, an increase in Peclet number Pe showed a rising trend in motility profile. Additionally, the implications of Brownian motion, Rayleigh number, Bioconvection Lewis number thermophoresis parameter, Peclet number, and buoyancy ratio parameter are discussed. Moreover, the obtained outcomes are validated as compared to the existing ones as limiting cases. Representative findings for microorganism concentration, skin friction coefficient, temperature gradient, local Sherwood number and density number of motile microorganisms, velocity field, temperature, the volumetric concentration of nanoparticles, are discussed in tabulated and graphical form

MHD thermogravitational convection and thermal radiation of a micropolar nanoliquid in a porous chamber

This work studies the thermogravitational transmission and thermal radiation of micropolar nanoliquid within

Numerical study of slip effects on unsteady aysmmetric bioconvective nanofluid flow in a porous microchannel with an expanding/ contracting upper wall using Buongiorno’s model

In this paper, the unsteady fully developed forced convective flow of viscous incompressible biofluid that contains both nanoparticles and gyrotactic microorganisms in a horizontal micro-channel is studied. Buongiorno’s model is employed. The upper channel wall is either expanding or contracting and permeable and the lower wall is static and impermeable. The plate separation is therefore a function of time. Velocity, temperature, nano-particle species (mass) and motile micro-organism slip effects are taken into account at the upper wall. By using the appropriate similarity transformation for the velocity, temperature, nanoparticle volume fraction and motile microorganism density, the governing partial differential conservation equations are reduced to a set of similarity ordinary differential equations. These equations under prescribed boundary conditions are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical quadrature in the MAPLE symbolic software. Excellent agreement between the present computations and solutions available in the literature (for special cases) is achieved. The key thermofluid parameters emerging are identified as Reynolds number, wall expansion ratio, Prandtl number, Brownian motion parameter, thermophoresis parameter, Lewis number, bioconvection Lewis number and bioconvection Péclet number. The influence of all these parameters on flow velocity, temperature, nano-particle volume fraction (concentration) and motile micro-organism density function is elaborated. Furthermore graphical solutions are included for skin friction, wall heat transfer rate, nano-particle mass transfer rate and micro-organism transfer rate. Increasing expansion ratio is observed to enhance temperatures and motile micro-organism density. Both nanoparticle volume fraction and microorganism increases with an increase in momentum slip. The dimensionless temperature and microorganism increases as wall expansion increases. Applications of the study arise in advanced nanomechanical bioconvection energy conversion devices, bio-nano-coolant deployment systems etc

Finite element analysis of rotating oscillatory magneto-convective radiative micropolar thermo-solutal flow

Micropolar fluids provide an alternative mechanism for simulating micro-scale and molecular fluid mechanics which require less computational effort. In the present paper, a numerical analysis is conducted for the primary and secondary flow characterizing dissipative micropolar convective heat and mass transfer from a rotating vertical plate with oscillatory plate velocity, adjacent to a permeable medium. Owing to high temperature, thermal radiation effects are also studied. The micropolar fluid is also chemically-reacting, both thermal and species (concentration) buoyancy effects and heat source/sink are included. The entire system rotates with uniform angular velocity about an axis normal to the plate. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. The partial differential equations governing the flow problem are rendered dimensionless with appropriate transformation variables. A Galerkin finite element method is employed to solve the emerging multi-physical components of fluid dynamics problem are examined for a variety of parameters including rotation parameter, radiation-conduction parameter, micropolar coupling parameter, Eckert number (dissipation), reaction parameter, magnetic body force parameter and Schmidt number. A comparison with previously published article is made to check the validity and accuracy of the present finite element solutions under some limiting case and excellent agreement is attained. The current simulations may be applicable to various chemical engineering systems, oscillating rheometry, and rotating MHD energy generator near-wall flows

Finite element computation of transient dissipative double diffusive magneto-convective nanofluid flow from a rotating vertical porous surface in porous media

This paper aimed to investigate the transient dissipative MHD double diffusive free convective boundary layer flow of electrically-conducting nanofluids from a stationary or moving vertical porous surface in a rotating high permeability porous medium, considering buoyancy, thermal radiation and first order chemical reaction. Thermo-diffusion (Soret) and diffuso-thermal (Dufour) effects are also considered. Darcy’s law is employed. The mathematical model is formulated by considering water-based nanofluids containing metallic nano-particles for both stationary and moving plate cases. Three nanofluids are examined, namely copper, aluminium oxide or titanium oxide in water. The transformed non-linear, coupled, dimensionless partial differential equations describing the flow are solved with physically appropriate boundary conditions by using Galerkin weighted residual scheme. For prescribed permeability, numerical results are presented graphically for the influence of a number of emerging parameters. Validation of finite element solutions for skin friction and Nusselt number is achieved via comparison with the previously published work as special cases of the present investigation and very good correlation obtained. Increasing rotational parameter is observed to reduce both primary and secondary velocity components. Primary and secondary velocities are consistently elevated with increasing Soret, Dufour, thermal Grashof and solutal Grashof numbers. Increasing Schmidt number, chemical reaction and suction parameter both suppress nano - particle concentration whereas the converse behavior is computed with increasing Soret number. The study is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids and also electromagnetic nanomaterial manufacturing processes

Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects

In recent years, significant progress has been made in modern micro- and nanotechnologies related to applications in micro/nano-electronic devices. These technologies are increasingly utilizing sophisticated fluent media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro-organisms. Motivated by bio-nanofluid rotating disk oxygenators in medical engineering, in the current work, a mathematical model is developed for steady convective Von Karman swirling flow from an impermeable power-law radially stretched disk rotating in a Darcy porous medium saturated with nanofluid doped with gyrotactic micro-organisms. Anisotropic slip at the wall and blowing effects due to concentration are incorporated. The nano-bio transport model is formulated using non-linear partial differential equations (NPDEs), which are transformed to a set of similarity ordinary differential equations (SODEs) by appropriate transformations. The transformed boundary value problem is solved by a Chebyshev collocation method. The impact of key parameters on dimensionless velocity components, concentration, temperature and motile microorganism density distributions are computed and visualized graphically. Validation with previous studies is included. It is found that that the effects of suction provide a better enhancement of the heat, mass and microorganisms transfer in comparison to blowing. Moreover, physical quantities decrease with higher slip parameters irrespective of the existence of blowing. Temperature is suppressed with increasing thermal slip whereas nanoparticle concentration is suppressed with increasing wall mass slip. Micro-organism density number increases with the greater microorganism slip. Radial skin friction is boosted with positive values of the power law stretching parameter whereas it is decreased with negative values. The converse response is computed for circumferential skin friction, nanoparticle mass transfer rate and motile micro-organism density number gradient. Results from this study are relevant to novel bioreactors, membrane oxygenators, food processing and bio-chromatography