scholarly journals Mathematical analysis of bio-convective micropolar nanofluid

2019 ◽  
Vol 6 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Sohail Nadeem ◽  
Muhammad Naveed Khan ◽  
Noor Muhammad ◽  
Shafiq Ahmad
Keyword(s):  
Differential Equations ◽  
Microbial Fuel Cells ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Convection Flow ◽  
Micropolar Nanofluid ◽  
Exponentially Stretching ◽  
Micro Organisms

Abstract The present investigation concentrates on three dimensional unsteady forced bio-convection flow of a viscous fluid. An incompressible flow of a micropolar nanofluid encloses micro-organisms past an exponentially stretching sheet with magnetic field is analyzed. By employing convenient transformation the partial differential equations are converted into the ordinary differential equations which are non-linear. By using shooting method to solved these equations numerically. The influence of the determining parameters on the velocity, temperature, micro-rotation, nanoparticle volume fraction, microorganism are incorporated. The skin friction, heat transfer rate, and the microorganism rate are analyzed. The results depicts that the value of the wall shear stress and Nusselt number are declined while an enhancement take place in the microorganism number. The slip parameters increases the velocity, thermal energy, and microorganism number consequentially. The present investigation are important in improving achievement of microbial fuel cells.

Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Soraya Torkaman ◽  
Ghasem Barid Loghmani ◽  
Mohammad Heydari ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Operational Matrices ◽  
Nanofluid Flow ◽  
Content Type ◽  
Nonlinearly Stretching Sheet

Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

MHD Three Dimensional Flow of Casson Fluid over an Unsteady Exponentially Stretching Sheet with Slip Conditions

2018 ◽  
Vol 388 ◽  
pp. 77-95 ◽  
Author(s):  
M. Krishna Murthy
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Slip Conditions ◽  
Exponentially Stretching Sheet ◽  
Similarity Transformations ◽  
Layer Flow ◽  
Exponentially Stretching

Magnetohydrodynamic (MHD) three dimensional boundary layer flow of Casson fluid over an unsteady exponentially stretching sheet with slip conditions is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and are solved numerically using shooting technique. The effects of pertinent parameters on velocity and temperature distributions are shown in graphically. The skin friction coefficient and the Nusselt number are computed numerically. We noticed that Casson parameter increases then the velocities and temperature decrease.

scholarly journals Hydromagnetic rotating flow of Casson fluid in Darcy-Forchheimer porous medium

2018 ◽  
Vol 192 ◽  
pp. 02059 ◽  
Author(s):  
Gauri Shanker Seth ◽  
Prashanta Kumar Mandal
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Shooting Method ◽  
Radiative Heat ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Casson Fluid ◽  
Rotating Flow ◽  
Flow Parameters

Present study investigates three dimensional rotating flow of Casson fluid in the presence of magnetic field over a convectively heated linear stretching sheet. Concept of nonlinear radiative heat transfer is considered. The governing nonlinear partial differential equations are converted into ordinary differential equations with the help of similarity transformation and then solved by using shooting method along with Runge-Kutta-Fehlberg integration technique. The primary and secondary velocities and temperature profiles are plotted and analysed corresponding to various pertinent flow parameters. Also, the skin friction for both directions and rate of heat transfer at the surface are computed and explained.

Three-dimensional flow of Eyring Powell nanofluid over an exponentially stretching sheet

2015 ◽  
Vol 25 (3) ◽  
pp. 593-616 ◽  
Author(s):  
Tasawar Hayat ◽  
Bilal Ashraf ◽  
Sabir Ali Shehzad ◽  
Elbaz Abouelmagd
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching ◽  
Made In

Purpose – The purpose of this paper is to analyze the Eyring Powell fluid over an exponentially stretching surface. Heat and mass transfer effects are taken into account with nanoparticles. Design/methodology/approach – Appropriate transformations are employed to reduce the boundary layer partial differential equations into ordinary differential equations. Series solutions of the problem are obtained and impacts of physical parameters on the velocities, temperature and concentration profiles are discussed. Findings – Numerical values of local Nusselt and Sherwood numbers for all the involved physical parameters are computed and analyzed. A comparative study between the present and previous results is made in a limiting sense. Local Nusselt number −′(0) increases by increasing ε, Pr, λ and N while it decreases for δ, N_{t{, N_{b} and Sc. Originality/value – This analysis has not been discussed in the literature yet.

Three-dimensional mixed convection flow of viscoelastic nanofluid over an exponentially stretching surface

2015 ◽  
Vol 25 (2) ◽  
pp. 333-357 ◽  
Author(s):  
Tasawar Hayat ◽  
Bilal Ashraf ◽  
Sabir Ali Shehzad ◽  
A. Alsaedi ◽  
N. Bayomi
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Content Type ◽  
Viscoelastic Nanofluid ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

Purpose – The purpose of this paper is to investigate the three-dimensional mixed convection flow of viscoelastic nanofluid induced by an exponentially stretching surface. Design/methodology/approach – Similarity transformations are utilized to reduce the partial differential equations into the ordinary differential equations. The corresponding non-linear problems are solved by homotopy analysis method. Findings – The authors found that an increase in thermophoresis and Brownian motion parameter enhance the temperature. Here thermal conductivity of fluid is enhanced due to which higher temperature and thicker thermal boundary layer thickness is obtained. Practical implications – Heat and mass transfer effects in mixed convection flow over a stretching surface have numerous applications in the polymer technology and metallurgy. Such flows are encountered in metallurgical processes which involve the cooling of continuous strips or filaments by drawing them through a quiescent fluid and that in the process of drawing, these strips are sometimes stretched. Originality/value – Three-dimensional flows over an exponentially stretching surface are very rare in the literature. Three-dimensional flow of viscoelastic nanofluid due to an exponentially stretching surface is first time investigated.

scholarly journals Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
I. Swain ◽  
S. R. Mishra ◽  
H. B. Pattanayak
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Mass Transfer Effect ◽  
Exponentially Stretching Sheet ◽  
Exponentially Stretching ◽  
Source Sink

An attempt has been made to study the heat and mass transfer effect in a boundary layer MHD flow of an electrically conducting viscous fluid subject to transverse magnetic field on an exponentially stretching sheet through porous medium. The effect of thermal radiation and heat source/sink has also been discussed in this paper. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. Graphical results are displayed for nondimensional velocity, temperature, and concentration profiles while numerical values of the skin friction local Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system.

g-Jitter Induced Mixed Convection Flow of Heat and Mass Transfer Past an Inclined Stretching Sheet

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Noraihan Afiqah Rawi ◽  
Abdul Rahman Mohd Kasim ◽  
Mukheta Isa ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Keller Box Method ◽  
Unsteady Mixed Convection ◽  
Layer Flow

This paper studies unsteady mixed convection boundary layer flow of heat and mass transfer past an inclined stretching sheet associated with the effect of periodical gravity modulation or g-jitter. The temperature and concentration are assumed to vary linearly with x, where x is the distance along the plate. The governing partial differential equations are transformed to a set of coupled ordinary differential equations using non-similarity transformation and solved numerically by Keller-box method. Numerical results for velocity, temperature and concentration profiles as well as skin friction, Nusselt number and Sherwood number are presented and analyzed for different values of inclination angle parameter.

Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
K. Ganesh Kumar ◽  
N.G. Rudraswamy ◽  
B.J. Gireesha ◽  
M.R. Krishnamurthy
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Nonlinear Thermal Radiation ◽  
Nonlinear Ordinary Differential Equations ◽  
Three Dimensional Flow

AbstractPresent exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge–Kutta–Fehlberg fourth–fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

scholarly journals Unsteady flow over an expanding cylinder in a nanofluid containing gyrotactic microorganisms

2016 ◽  
Vol 94 (5) ◽  
pp. 466-473 ◽  
Author(s):  
Hui Chen ◽  
Hongxing Liang ◽  
Tianli Xiao ◽  
Heng Du ◽  
Ming Shen
Keyword(s):  
Differential Equations ◽  
Unsteady Flow ◽  
Shooting Method ◽  
Schmidt Number ◽  
Volume Fraction ◽  
Dual Solutions ◽  
Physical Parameters ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Fifth Order

In this paper, an analysis is made for the unsteady flow due to an expanding cylinder in a nanofluid that contains both nanoparticles and gyrotactic microoganisms with suction. The nonlinear system of partial differential equations is transformed into high-order nonlinear ordinary differential equations using similarity transformations, and then solved numerically using a shooting method with fourth-fifth-order Runge–Kutta integration technique. The influences of significant physical parameters on the distributions of the velocity, temperature, nanoparticle volume fraction, as well as the density of motile microorganisms are graphically presented and discussed in detail. It is found that dual solutions exist for both stretching and shrinking cases and the range of dual solutions increases with the strength of the expansion. The results also indicate that larger bioconvection Peclet number and smaller Schmidt number lead to an increased concentration of microorganisms and thicker boundary layer thickness.

On both MHD and slip effect in micropolar hybrid nanofluid past a circular cylinder under stagnation point region

2019 ◽  
Vol 97 (4) ◽  
pp. 392-399 ◽  
Author(s):  
S. Nadeem ◽  
Nadeem Abbas
Keyword(s):  
Circular Cylinder ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Hybrid Nanofluid ◽  
Shooting Technique ◽  
Slip Effects ◽  
Highly Nonlinear ◽  
Micropolar Nanofluid ◽  
Heat Transfer Improvement

The physical model of the micropolar hybrid nanofluid flow with magnetohydrodynamic and thermal slip effects is considered. The flow of three-dimensional stagnation point of micropolar hybrid nanofluid past a circular cylinder is also taken into account. The flow model is controlled through partial differential equations. These equations are highly nonlinear in character and reduce to ordinary differential equations through applying the suitable similarity transformation. The reduced system is solved numerically using the shooting technique. The mutual effects are presented using graphs while comparative numerical results are presented in the tables. The diverse physical parts of the issue have been talked about. This study aims to investigate the solid nano-sized particle on the surface of a circular cylinder having sinusoidal variation. These nanosized particles are used to analyze the heat transfer improvement of micropolar hybrid nanofluid as compared to micropolar nanofluid.

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