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.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

scholarly journals A mathematical model on MHD slip flow and heat transfer over a nonlinear stretching sheet

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 475-488 ◽  
Author(s):  
Kalidas Das
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Slip Flow ◽  
Inverse Function ◽  
Partial Slip ◽  
Physical Parameters ◽  
Fluid Viscosity ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Non Linear

Some analyses have been carried out to study the influence of suction/blowing, thermal radiation and temperature dependent fluid properties on the hydro-magnetic incompressible electrically conducting fluid flow and heat transfer over a permeable stretching surface with partial slip boundary conditions. It is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature respectively. Using the similarity transformation, the governing system of non-linear partial differential equations are transformed into non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0. The effects of various physical parameters on the flow and heat transfer characteristics as well as the skin friction coefficient and Nusselt number are illustrated graphically. The physical aspects of the problem are highlighted and discussed.

Numerical exploration of the combined effects of non-linear thermal radiation and variable thermo-physical properties on the flow of Casson nanofluid over a wedge

2017 ◽  
Vol 13 (4) ◽  
pp. 628-647 ◽  
Author(s):  
Archana M. ◽  
Gireesha B.J. ◽  
Prasannakumara B.C. ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Physical Properties ◽  
Physical Parameters ◽  
Content Type ◽  
Casson Nanofluid ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Non Linear ◽  
Thermo Physical Properties

Purpose The effect of non-linear thermal radiation and variable thermo-physical properties are investigated in the Falkner-Skan flow of a Casson nanofluid in the presence of magnetic field. The paper aims to discuss this issue. Design/methodology/approach Selected bunch of similarity transformations are used to reduce the governing partial differential equations into a set of non-linear ordinary differential equations. The resultant equations are numerically solved using Runge-Kutta-Fehlberg fourth-fifth-order method along with shooting technique. Findings The velocity, temperature and concentration profiles are evaluated for several emerging physical parameters and are analyzed through graphs and tables in detail. Research limitations/implications This study only begins to reveal the research potential and pitfalls of research and publishing on boundary-layer flow, heat and mass transfer of Casson nanofluid past and the moving and static wedge-shaped bodies. Originality/value It is found that the presence of non-linear thermal radiation and variable properties has more influence in heat transfer. Furthermore, temperature profile increases as the radiation parameter increases.

scholarly journals An Unsteady Flow and Melting Heat Transfer of a Nanofluid Over a Stretching Sheet Embedded in a Porous Medium

2019 ◽  
Vol 24 (2) ◽  
pp. 245-258 ◽  
Author(s):  
K. Ganesh Kumar ◽  
B.J. Gireesha ◽  
N.G. Rudraswamy ◽  
M.R. Krishnamurthy
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Unsteady Flow ◽  
Stretching Sheet ◽  
Physical Parameters ◽  
Local Skin ◽  
Melting Heat ◽  
Linear Ordinary Differential Equations ◽  
Melting Heat Transfer ◽  
Non Linear

Abstract An unsteady flow and melting heat transfer of a nanofluid over a stretching sheet was numerically studied by considering the effect of chemical reaction and thermal radiation. The governing non-linear partial differential equations describing the flow problem are reduced to a system of non-linear ordinary differential equations using the similarity transformations and solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method. Numerical results for concentration, temperature and velocity profiles are shown graphically and discussed for different physical parameters. Effect of pertinent parameters on momentum, temperature and concentration profiles along with local Sherwood number, local skin-friction coefficient and local Nusselt number are well tabulated and discussed.

Non-Newtonian Magneto-Hydrodynamic Fluid with Radiation by Stretching Cylinder

2020 ◽  
Vol 9 (2) ◽  
pp. 106-113
Author(s):  
Gamal M. Abdel-Rahman ◽  
Amal M. Al-Hanaya
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Physical Parameters ◽  
Temperature Profiles ◽  
Stretching Cylinder ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Energy Equations

The aim of the present paper is to study the numerical solutions of the steady magnetohydrodynamic and heat generation effects on anon-Newtonian fluid with radiation through a porous medium by a stretching cylinder. The governing continuity, momentum, and energy equations are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. Numerical results were presented for velocity and temperature profiles for different parameters of the problem are studied graphically. Finally, the effects of related physical parameters on skin friction and the rate of heat transfer are also studied.

scholarly journals Combined Effects of Soret and Dufour on MHD Flow of a Power-Law Fluid Over Flat Plate in Slip Flow Rigime

2018 ◽  
Vol 23 (3) ◽  
pp. 689-705
Author(s):  
K. Saritha ◽  
M.N. Rajasekhar ◽  
B.S. Reddy
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Flat Plate ◽  
Ordinary Differential Equations ◽  
Power Law ◽  
Physical Parameters ◽  
Power Law Fluid ◽  
Soret And Dufour Effects ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

Abstract A numerical model is developed to study the Soret and Dufour effects on MHD boundary layer flow of a power-law fluid over a flat plate with velocity, thermal and solutal slip boundary conditions. The governing equations for momentum, energy and mass are transformed to a set of non-linear coupled ordinary differential equations by using similarity transformations. These non-linear ordinary differential equations are first linearized using a quasi-linearization technique and then solved numerically based on the implicit finite difference scheme over the entire range of physical parameters with appropriate boundary conditions. The influence of various governing parameters along with velocity, thermal and mass slip parameters on velocity, temperature and concentration fields are examined graphically. Also, the effects of slip parameters, the Soret and Dufour number on the skin friction, Nusselt number and Sherwood number are studied. Results show that the increase in the Soret number leads to a decrease in the temperature distribution and to an increase in concentration fields.

Dissipative effects on a chemically and thermally radiative heat fluid flow past a shrinking porous sheet

2020 ◽  
pp. 1-14
Author(s):  
A. Shahid ◽  
M. Ali Abbas ◽  
H.L. Huang ◽  
S.R. Mishra ◽  
M.M. Bhatti
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Linearization Method ◽  
Surface Drag ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Dissipative Effects ◽  
Successive Linearization Method

The present study analyses the dissipative influence into an unsteady electrically conducting fluid flow embedded in a pervious medium over a shrinkable sheet. The behavior of thermal radiation and chemical reactions are also contemplated. The governing partial differential equations are reformed to ordinary differential equations by operating similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the Successive linearization method (SLM) via Matlab software. The velocity, temperature, and concentration magnitudes for distant values of the governing parametric quantities are conferred, and their conduct is debated via graphical curves. The surface drag coefficient increases, whereas the local Nusselt number and Sherwood number decreases for enhancing unsteadiness parameter across suction parameter. Moreover, the magnetic and suction parameters accelerate velocity magnitudes while by raising porosity parameter, velocity decelerates. Larger numeric of thermal radiation parameter and Eckert number accelerates the temperature profile while by enhancing Prandtl number it decelerates. Schmidt number and chemical reaction parameters slowdowns the concentration distribution, and the chemical reaction parameter influences on the point of chemical reaction that benefits the interface mass transfer. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities.

MHD STAGNATION POINT FLOW OF HYPERBOLIC TANGENT FLUID WITH VISCOUS DISSIPATION AND CHEMICAL REACTION

2021 ◽  
Vol 21 (2) ◽  
pp. 569-588
Author(s):  
KINZA ARSHAD ◽  
MUHAMMAD ASHRAF
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Normal Velocity ◽  
Hyperbolic Tangent ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In the present work, two dimensional flow of a hyperbolic tangent fluid with chemical reaction and viscous dissipation near a stagnation point is discussed numerically. The analysis is performed in the presence of magnetic field. The governing partial differential equations are converted into non-linear ordinary differential equations by using appropriate transformation. The resulting higher order non-linear ordinary differential equations are discretized by finite difference method and then solved by SOR (Successive over Relaxation parameter) method. The impact of the relevant parameters is scrutinized by plotting graphs and discussed in details. The main conclusion is that the large value of magnetic field parameter and wiessenberg numbers decrease the streamwise and normal velocity while increase the temperature distribution. Also higher value of the Eckert number Ec results in increases in temperature profile.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document