Magnetohydrodynamics and Soret Effects on Bioconvection in a Porous Medium Saturated With a Nanofluid Containing Gyrotactic Microorganisms

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
S. Shaw ◽  
P. Sibanda ◽  
A. Sutradhar ◽  
P. V. S. N. Murthy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Sherwood Number ◽  
Peclet Number ◽  
Volume Fraction ◽  
Soret Effect ◽  
Magnetic Field Effect ◽  
Lewis Number ◽  
Solute Concentration ◽  
Péclet Number

We investigate the bioconvection of gyrotactic microorganism near the boundary layer region of an inclined semi infinite permeable plate embedded in a porous medium filled with a water-based nanofluid containing motile microorganisms. The model for the nanofluid incorporates Brownian motion, thermophoresis, also Soret effect and magnetic field effect are considered in the study. The governing partial differential equations for momentum, heat, solute concentration, nanoparticle volume fraction, and microorganism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations and solved numerically. The effects of the bioconvection parameters on the thermal, solutal, nanoparticle concentration, and the density of the micro-organisms are analyzed. A comparative analysis of our results with previously reported results in the literature is given. Some interesting phenomena are observed for the local Nusselt and Sherwood number. It is shown that the Péclet number and the bioconvection Rayleigh number highly influence the local Nusselt and Sherwood numbers. For Péclet numbers less than 1, the local Nusselt and Sherwood number increase with the bioconvection Lewis number. However, both the heat and mass transfer rates decrease with bioconvection Lewis number for higher values of the Péclet number.

NUMERICAL STUDY OF MIXED BIOCONVECTION IN POROUS MEDIA SATURATED WITH NANOFLUID CONTAINING OXYTACTIC MICROORGANISMS

2013 ◽  
Vol 13 (04) ◽  
pp. 1350067 ◽  
Author(s):  
O. ANWAR BÉG ◽  
V. R. PRASAD ◽  
B. VASU
Keyword(s):  
Boundary Layer ◽  
Peclet Number ◽  
Mechanical Design ◽  
Numerical Study ◽  
Lewis Number ◽  
Nanoparticle Concentration ◽  
Péclet Number ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Oxytactic Microorganisms

A mathematical model has been developed for steady-state boundary layer flow of a nanofluid past an impermeable vertical flat wall in a porous medium saturated with a water-based dilute nanofluid containing oxytactic microorganisms. The nanoparticles were distributed sufficiently to permit bioconvection. The product of chemotaxis constant and maximum cell swimming speed was assumed invariant. Using appropriate transformations, the partial differential conservation equations were non-dimensionalised to yield a quartet of coupled, non-linear ordinary differential equations for momentum, energy, nanoparticle concentration and dimensionless motile microorganism density, with appropriate boundary conditions. The dominant parameters emerging in the normalised model included the bioconvection Lewis number, bioconvection Peclet number, Lewis number, buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter, local Darcy-Rayleigh number and the local Peclet number. An implicit numerical solution to the well-posed two-point non-linear boundary value problem is developed using the well-tested and highly efficient Keller box method. Computations are validated with the Nakamura tridiagonal implicit finite difference method, demonstrating excellent agreement. Nanoparticle concentration and temperature were found to be generally enhanced through the boundary layer with increasing bioconvection Lewis number, whereas dimensionless motile microorganism density was only increased closer to the wall. Temperature, nanoparticle concentration and dimensionless motile microorganism density were all greatly increased with a rise in Peclet number. Temperature and dimensionless motile microorganism density were reduced with increasing buoyancy parameter, whereas nanoparticle concentration was increased. The present study found applications in the fluid mechanical design of microbial fuel cell and bioconvection nanotechnological devices.

Small Péclet-number mass transport to a finite strip: An advection–diffusion–reaction model of surface-based biosensors

2019 ◽  
Vol 31 (5) ◽  
pp. 763-781
Author(s):  
EHUD YARIV
Keyword(s):  
Shear Flow ◽  
Mass Transport ◽  
Sherwood Number ◽  
Peclet Number ◽  
Outer Region ◽  
Diffusion Reaction ◽  
Background Concentration ◽  
Leading Order ◽  
Péclet Number ◽  
Inner Region

AbstractWe consider two-dimensional mass transport to a finite absorbing strip in a uniform shear flow as a model of surface-based biosensors. The quantity of interest is the Sherwood number Sh, namely the dimensionless net flux onto the strip. Considering early-time absorption, it is a function of the Péclet number Pe and the Damköhler number Da, which, respectively, represent the characteristic magnitude of advection and reaction relative to diffusion. With a view towards modelling nanoscale biosensors, we consider the limit Pe«1. This singular limit is handled using matched asymptotic expansions, with an inner region on the scale of the strip, where mass transport is diffusively dominated, and an outer region at distances that scale as Pe-1/2, where advection enters the dominant balance. At the inner region, the mass concentration possesses a point-sink behaviour at large distances, proportional to Sh. A rescaled concentration, normalised using that number, thus possesses a universal logarithmic divergence; its leading-order correction represents a uniform background concentration. At the outer region, where advection by the shear flow enters the leading-order balance, the strip appears as a point singularity. Asymptotic matching with the concentration field in that region provides the Sherwood number as $${\rm{Sh}} = {\pi \over {\ln (2/{\rm{P}}{{\rm{e}}^{1/2}}) + 1.0559 + \beta }},$$ wherein β is the background concentration. The latter is determined by the solution of the canonical problem governing the rescaled inner concentration, and is accordingly a function of Da alone. Using elliptic-cylinder coordinates, we have obtained an exact solution of the canonical problem, valid for arbitrary values of Da. It is supplemented by approximate solutions for both small and large Da values, representing the respective limits of reaction- and transport-limited conditions.

scholarly journals New exact and numerical solutions for the effect of suction or injection on flow of nanofluids past a stretching sheet

2019 ◽  
Vol 8 (1) ◽  
pp. 172-178
Author(s):  
Nader Y. Abd Elazem
Keyword(s):  
Nusselt Number ◽  
Exact Solutions ◽  
Sherwood Number ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Lewis Number ◽  
Suction Or Injection ◽  
Wall Mass ◽  
Good Agreement

Abstract The flow of nanofluids past a stretching sheet has attracted much attention due to its wide applications in industry and engineering. Theoretical and numerical solutions have been discussed in this paper for studying the effect of suction or injection on flow of nanofluids past a stretching sheet. In the absence of thermophoresis the analytical exact solution of the stream function was obtained in terms of exponential function, while the exact solutions for temperature and nanoparticle volume fraction were obtained in terms of the generalized incomplete gamma function. In addition, in the presence of thermophoresis, the exact solutions are not available. Therefore, the numerical results, carried out by using Chebyshev collocation method (ChCM). It is found that a good agreement exists between the present results and with those published works. Useful results for temperature profile, concentration profile, reduced Nusselt number and reduced Sherwood number are discussed in details graphically. It was also demonstrated that both temperature and concentration profiles decrease by an increase from injection to suction. Finally, the present results showed that increase of the wall mass transfer from injection to suction decreased both reduced Nusselt number and the reduced Sherwood number when Brownian motion parameter and Lewis number increased.

scholarly journals Magneto Convection in a Layer of Nanofluid With Soret Effect

2015 ◽  
Vol 9 (2) ◽  
pp. 63-69 ◽  
Author(s):  
Ramesh Chand ◽  
Gian Chand Rana
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Fluid Layer ◽  
Soret Effect ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Diffusive Convection ◽  
Mode Method ◽  
Double Diffusive

AbstractDouble diffusive convection in a horizontal layer of nanofluid in the presence of uniform vertical magnetic field with Soret effect is investigated for more realistic boundary conditions. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries. The normal mode method is used to find linear stability analysis for the fluid layer. Oscillatory convection is ruled out because of the absence of the two opposing buoyancy forces. Graphs have been plotted to find the effects of various parameters on the stationary convection and it is found that magnetic field, solutal Rayleigh number and nanofluid Lewis number stabilizes fluid layer, while Soret effect, Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number destabilize the fluid layer.

Solidification With a Throughflow in a Porous Medium

1992 ◽  
Vol 114 (3) ◽  
pp. 675-680
Author(s):  
T. Banerjee ◽  
C. Chang ◽  
W. Wu ◽  
U. Narusawa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Analytical Solutions ◽  
Peclet Number ◽  
Flow In Porous Media ◽  
Circular Pipe ◽  
Parallel Plates ◽  
Péclet Number ◽  
Solid Interface

A steady throughflow in a porous medium is studied in the presence of a solidified layer due to cooling of the walls. Under the assumption of a moderately sloped melt-solid interface, analytical solutions are obtained for both a flow between parallel plates and a circular pipe. Differences and similarities are examined between the Darcian and the Brinkman porous media, as well as the effects of various parameters, such as the Peclet number, the ratio of diffusivities in the longitudinal and the lateral directions, and a parameter indicating the degree of wall cooling and flow heating, on thermofluid structure of a flow in porous media accompanied by solidification.

scholarly journals Mixed Convection of a Radiating Magnetic Nanofluid past a Heated Permeable Stretching/Shrinking Sheet in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Feleke Buta Tadesse ◽  
Oluwole Daniel Makinde ◽  
Lemi Guta Enyadene
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Volume Fraction ◽  
Flow Stability ◽  
Collective Effects ◽  
Shrinking Sheet ◽  
Convective Heating

This paper analyzes the collective effects of buoyancy force, thermal radiation, convective heating, and magnetic field on stagnation point flow of an electrically conducting nanofluid past a permeable stretching/shrinking sheet in a porous medium. Similarity transformations are used on the resulting nonlinear partial differential equations to transfer into a system of coupled nonlinear ordinary differential equations. The fourth-fifth-order Runge–Kutta–Fehlberg method with shooting technique is applied to solve numerically. Results are obtained for dimensionless velocity, temperature, and nanoparticle volume fraction as well as the skin friction and local Nusselt and Sherwood numbers. The results indicate the existence of two real solutions for the shrinking sheet in the range of λ c < λ < 0 . The fluid flow stability is maintained by increasing the magnetic field effect, whereas the porous medium parameter inflates the flow stability. It is also noted that both the skin friction coefficient and the local Sherwood number approximately decline with the intensification of thermal radiation within the range from 9.83% to 14% and the range from 48.86% to 78.66%, respectively. It is also evident in the present work that the local Nusselt number upsurges with the porous and suction/injection parameters.

scholarly journals Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell

2020 ◽  
Vol 13 (04) ◽  
pp. 2050026
Author(s):  
Nayema Islam Nima ◽  
M. Ferdows ◽  
O. Anwar Bég ◽  
S. Kuharat ◽  
Faris Alzahrani
Keyword(s):  
Porous Medium ◽  
Fuel Cell ◽  
Differential Equations ◽  
Buoyancy Force ◽  
Lewis Number ◽  
Oxygen Species ◽  
Modeling Framework ◽  
Gyrotactic Microorganisms ◽  
Biomathematical Modeling ◽  
Near Wall

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.

Steady Mixed Convection Flow on a Horizontal Circular Cylinder Embedded in a Porous Medium Filled by a Nanofluid Containing Gyrotactic Micro-Organisms

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
L. Tham ◽  
R. Nazar ◽  
I. Pop
Keyword(s):  
Porous Medium ◽  
Circular Cylinder ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Local Density ◽  
Lewis Number ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Micro Organisms ◽  
Horizontal Circular Cylinder

In this paper, the steady mixed convection boundary layer flow past a horizontal circular cylinder with a constant surface temperature embedded in a porous medium saturated by a nanofluid containing both nanoparticles and gyrotactic micro-organisms in a stream flowing vertically upwards for both cases of a heated and cooled cylinder is numerically studied. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme. By considering the governing parameters, namely, the mixed convection parameter λ, the bioconvection Lewis number Lb, the traditional Lewis number Le, the bioconvection Péclet number Pb, the buoyancy ratio Nr, the bioconvection Rayleigh number Rb, the Brownian motion Nb, and the thermophoresis Nt, the numerical results are obtained and discussed for the skin friction coefficient, the local Nusselt number, the local Sherwood number, the local density number of the motile micro-organisms as well as the velocity, temperature, nanoparticle volume fraction, and density motile micro-organisms profiles.

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