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.

Bioconvection in nanofluid-saturated porous square cavity containing oxytactic microorganisms

2019 ◽  
Vol 29 (4) ◽  
pp. 1448-1465 ◽  
Author(s):  
Chandra Shekar Balla ◽  
C. Haritha ◽  
Kishan Naikoti ◽  
A.M. Rashad
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Peclet Number ◽  
Lewis Number ◽  
Square Cavity ◽  
Flow Strength ◽  
Content Type ◽  
Péclet Number ◽  
Thermophoretic Force ◽  
Oxytactic Microorganisms

PurposeThe purpose of this paper is to investigate the bioconvection flow in a porous square cavity saturated with both oxytactic microorganism and nanofluids.Design/methodology/approachThe impacts of the effective parameters such as Rayleigh number, bioconvection number, Peclet number and thermophoretic force, Brownan motion and Lewis number reduces the flow strength in the cavity on the flow strength, oxygen density distribution, motile isoconcentrations and heat transfer performance are investigated using a finite volume approach.FindingsThe results obtained showed that the average Nusselt number is increased with Peclet number, Lewis number, Brownian motion and thermophoretic force. Also, the average Sherwood number increased with Brownian motion and Peclet number and decreased with thermophoretic force. It is concluded that the flow strength is pronounced with Rayleigh number, bioconvection number, Peclet number and thermophoretic force. Brownan motion and Lewis number reduce the flow strength in the cavity.Originality/valueThere is no published study in the literature about sensitivity analysis of Brownian motion and thermophoresis force effects on the bioconvection heat transfer in a square cavity filled by both nanofluid and oxytactic microorganisms.

Convective diffusion to a slowly rotating spherical electrode; Basic model for Re → O, Pe → ∞

1983 ◽  
Vol 48 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Péclet Number ◽  
Spherical Electrode ◽  
Basic Model ◽  
Boundary Layer Solution ◽  
Layer Solution

Theory has been formulated of a convective rotating spherical electrode in the creeping flow regime (Re → 0). The currently available boundary layer solution for Pe → ∞ has been confronted with an improved similarity description applicable in the whole range of the Peclet number.

Convective transport of thermal and solutal energy in unsteady MHD Oldroyd-B nanofluid flow

2021 ◽  
Author(s):  
Muhammad Yasir ◽  
Masood Khan ◽  
Awais Ahmed ◽  
Malik Zaka Ullah
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Heat Generation ◽  
Axisymmetric Flow ◽  
Convective Transport ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

Abstract In this work, an analysis is presented for the unsteady axisymmetric flow of Oldroyd-B nanofluid generated by an impermeable stretching cylinder with heat and mass transport under the influence of heat generation/absorption, thermal radiation and first-order chemical reaction. Additionally, thermal and solutal performances of nanofluid are studied using an interpretation of the well-known Buongiorno's model, which helps us to determine the attractive characteristics of Brownian motion and thermophoretic diffusion. Firstly, the governing unsteady boundary layer equation's (PDEs) are established and then converted into highly non-linear ordinary differential equations (ODEs) by using the suitable similarity transformations. For the governing non-linear ordinary differential equations, numerical integration in domain [0, ∞) is carried out using the BVP Midrich scheme in Maple software. For the velocity, temperature and concentration distributions, reliable results are prepared for different physical flow constraints. According to the results, for increasing values of Deborah numbers, the temperature and concentration distribution are higher in terms of relaxation time while these are decline in terms of retardation time. Moreover, thermal radiation and heat generation/absorption are increased the temperature distribution and corresponding boundary layer thickness. With previously stated numerical values, the acquired solutions have an excellent accuracy.

A Numerical Study of Impulsively Started External Convection at Microscale

2014 ◽  
Vol 31 (1) ◽  
pp. 79-90
Author(s):  
K. Ramadan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Thermal Boundary Layer ◽  
Numerical Study ◽  
Velocity Slip ◽  
Transition Time ◽  
Surface Cooling ◽  
Linear Ordinary Differential Equations

ABSTRACTImpulsively started external convection at microscale level is studied numerically in both planar and axisymmetric geometries. Using similarity transformation, the resulting coupled partial and non-linear ordinary differential equations are simultaneously solved by finite differences together with a well established ordinary differential equation solver, over a range of problem parameters. Rarefaction effects within the slip flow regime on the thermal boundary layer response, heat transfer rate and transition time when system experiences sudden changes in surface temperature are analyzed, and a comparison between sudden surface cooling and heating is presented. The results show that the thermal boundary layer thickness, heat transfer rate and the transition time is considerably influenced by the degree of rarefaction. The transition time tends to be less sensitive with increasing rarefaction. The velocity slip and temperature jump factors are found to have opposite effects on the transition time and the heat transfer rate, with the velocity slip factor having the most profound influence on these parameters.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

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.

scholarly journals Bioconvection of Micropolar Fluid in an Annulus

2020 ◽  
Vol 5 (2) ◽  
pp. 237-247
Author(s):  
D. Srinivasacharya ◽  
I. Sreenath
Keyword(s):  
Differential Equations ◽  
Outer Cylinder ◽  
Lewis Number ◽  
Coupled System ◽  
Linearization Method ◽  
Physical Parameters ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Successive Linearization Method ◽  
Fully Coupled

This paper deals with the bioconvection of microploar fluid in an annulus containing microorganisms in which the outer cylinder is rotating. A mathematical model, with a fully coupled system of partial differential equations presenting the velocity, total mass, momentum, thermal energy, mass diffusion, and motile microorganisms is presented. A suitable transformations is adopted to reduce the governing non-linear governing to a set of non-linear ordinary differential equations and then linearized by means of successive linearization method. The resulign linearized equaions are solved using Chebyshev collocation method. The illustrating analysis of influences of the various flow governing physical parameters such as the micropolar coupling number, the bioconvection Schmidt-number, Prandtl number, Lewis number and bioconvection Peclet-number and Reynolds number on motile microorganism distribution are studied and is presented. Also, the density number of motile microorganism is examined for various governing parameters along with slip parameter of motile microorganism.

scholarly journals Convection heat and mass transfer in a hydromagnetic flow of a micropolar fluid over a porous medium

2014 ◽  
Vol 41 (2) ◽  
pp. 93-117
Author(s):  
B.I. Olajuwon ◽  
J.I. Oahimire ◽  
M.A. Waheed
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Micropolar Fluid ◽  
Perturbation Technique ◽  
Skin Friction Coefficient ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

This study presents a mathematical analysis of a hydromagnetic boundary layer flow, heat and mass transfer characteristics on steady twodimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field in the presence of thermal radiation. The governing system of partial differential equations is first transformed into a system of non- linear ordinary differential equation using the usual similarity transformation. The resulting coupled non-linear ordinary differential equations are then solved using perturbation technique. With the help of graphs, the effects of the various important parameters entering into the problem on the velocity, temperature and concentration fields within the boundary layer are separately discussed. The effects of the pertinent parameters on the wall temperature, wall solutal concentration, skin friction coefficient and the rate of heat and mass transfer are presented numerically in tabular form. The results obtained showed that these parameters have significant influence on the flow.

scholarly journals Magneto-Burgers Nanofluid Stratified Flow with Swimming Motile Microorganisms and Dual Variables Conductivity Configured by a Stretching Cylinder/Plate

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Hassan Waqas ◽  
Umair Manzoor ◽  
Zahir Shah ◽  
Muhammad Arif ◽  
Meshal Shutaywi
Keyword(s):  
Thermal Conductivity ◽  
Activation Energy ◽  
Brownian Motion ◽  
Peclet Number ◽  
Current Model ◽  
Lewis Number ◽  
Motion Parameter ◽  
Stretching Cylinder ◽  
Péclet Number ◽  
Brownian Motion Parameter

Background. The study of nanofluid gains interest of researchers because of its uses in treatment of cancer, wound treatment, fuel reserves, and elevating the particles in the bloodstream to a tumour. This artefact investigates the magnetohydrodynamic flow of Burgers nanofluid with the interaction of nonlinear thermal radiation, activation energy, and motile microorganisms across a stretching cylinder. Method. The developed partial differential equations (PDEs) are transformed into a structure of ODEs with the help of similarity transformation. The extracted problem is rectified numerically by using the bvp4c program in computational software MATLAB. The novelty of analysis lies in the fact that the impacts of bioconvection with magnetic effects on Burgers nanofluid are taken into account. Moreover, the behaviours of thermal conductivity and diffusivity are discussed in detail. The impacts of activation energy and motile microorganism are also explored. No work has been published yet in the literature survey according to the authors’ knowledge. The current observation is the extension of Khan et al.’s work [51]. Results. The consequences of the relevant parameters, namely, thermophoresis parameter, Brownian motion parameter, the reaction parameter, temperature difference parameter, activation energy, bioconvection Lewis number and Peclet number against the velocity of Burgers nanofluid, temperature profile for nanoliquid, the concentration of nanoparticles, and microorganisms field, have been explored in depth. The reports had major impacts in the development of medications for the treatment of arterial diseases including atherosclerosis without any need for surgery, which may reduce spending on cardiovascular and postsurgical problems in patients. Conclusions. The current investigation depicts that fluid velocity increases for uplifting values of mixed convection parameter. Furthermore, it is analyzed that flow of fluid is risen by varying the amount of Burgers fluid parameter. The temperature distribution is escalated by escalating the values of temperature ratio parameter and thermal conductivity parameter. The concentration field turns down for elevated values of Lewis number and Brownian motion parameter, while conflicting circumstances are observed for the thermophoresis parameter and solutal Biot number. Larger values of Peclet number reduce the microorganism’s field. Physically the current model is more significant in the field of applied mathematics. Furthermore, the current model is more helpful to improve the thermal conductivity of base fluids and heat transfer rate.

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