Unsteady forced bioconvection slip flow of a micropolar nanofluid from a stretching/shrinking sheet

2016 ◽  
Vol 230 (4) ◽  
pp. 177-187 ◽  
Author(s):  
Nur Amalina Abdul Latiff ◽  
Md Jashim Uddin ◽  
O Anwar Bég ◽  
Ahmad Izani Ismail
Keyword(s):  
Skin Friction ◽  
Microbial Fuel Cells ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Shrinking Sheet ◽  
Local Skin ◽  
Linear Ordinary Differential Equations ◽  
Micropolar Nanofluid

The unsteady forced bioconvection boundary layer flow of a viscous incompressible micropolar nanofluid containing microorganisms over a stretching/shrinking sheet is studied numerically. A mathematical model, with the aid of appropriate transformations, is presented. The transformed non-linear ordinary differential equations are solved numerically by the Runge–Kutta–Fehlberg fourth- to fifth-order numerical method. The effect of the governing parameters on the dimensionless velocity, micro-rotation, temperature, nanoparticle volume fraction and microorganism as well as the local skin friction coefficient, the heat transfer rate and microorganisms transfer rate is thoroughly examined. The findings show that the value of skin friction and Nusselt number are decreased and microorganism number is increased as velocity slip, thermal slip and microorganism slip parameter are increased, respectively. Results from this investigation were compared with previous investigations demonstrating very good correlation. The present results are relevant to improving the performance of microbial fuel cells deploying nanofluids.

scholarly journals Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1649
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

scholarly journals Slip Flow of Kerosene Oil Based SWCNT Nanofluid over Stretching Sheet with Radiation and Suction/Injection Effects

2021 ◽  
Vol 6 (3) ◽  
pp. 860-877
Author(s):  
Susheela Chaudhary ◽  
Kiran Kunwar Chouhan ◽  
Santosh Chaudhary
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Skin Friction Coefficient ◽  
Single Wall Carbon Nanotubes ◽  
Local Skin ◽  
Slip Boundary ◽  
Similarity Transformations

Present study numerically investigates a two dimensional steady laminar boundary layer nanofluid flow of single-wall carbon nanotubes (SWCNTs) immersed into kerosene oil, due to a linearly stretched sheet. Flow is subjected to the slip boundary condition and suction/injection effects. Employing suitable similarity transformations, governing PDEs of the arising problem are converted into coupled nonlinear non-dimensional ordinary differential equations. A set of obtained ODEs with assisting boundary conditions is solved numerically by applying finite element method (FEM). Effect of pertinent factors, velocity slip parameter, suction/injection parameter and solid volume fraction parameter on non-dimensional velocity and temperature profiles are characterized graphically. In addition, physical emerging parameters, local Nusselt’s number and local skin friction coefficient are computed and presented via table. Furthermore, derived numerical values of shear stress and heat flux at the surface are compared with previously published results.

scholarly journals Double Solutions and Stability Analysis of Micropolar Hybrid Nanofluid with Thermal Radiation Impact on Unsteady Stagnation Point Flow

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 276
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Thermal Radiation ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Stable Solution ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Micropolar Nanofluid

The mathematical modeling of unsteady flow of micropolar Cu–Al2O3/water nanofluid driven by a deformable sheet in stagnation region with thermal radiation effect has been explored numerically. To achieve the system of nonlinear ordinary differential equations (ODEs), we have employed some appropriate transformations and solved it numerically using MATLAB software (built-in solver called bvp4c). Influences of relevant parameters on fluid flow and heat transfer characteristic are discussed and presented in graphs. The findings expose that double solutions appear in shrinking sheet case in which eventually contributes to the analysis of stability. The stability analysis therefore confirms that merely the first solution is a stable solution. Addition of nanometer-sized particle (Cu) has been found to significantly strengthen the heat transfer rate of micropolar nanofluid. When the copper nanoparticle volume fraction increased from 0 to 0.01 (1%) in micropolar nanofluid, the heat transfer rate increased roughly to an average of 17.725%. The result also revealed that an upsurge in the unsteady and radiation parameters have been noticed to enhance the local Nusselt number of micropolar hybrid nanofluid. Meanwhile, the occurrence of material parameter conclusively decreases it.

Heat Transfer Analysis of a Williamson Micropolar Nanofluid with Different Flow Controls

2018 ◽  
Vol 35 (3) ◽  
pp. 381-394 ◽  
Author(s):  
M. Muthtamilselvan ◽  
E. Ramya ◽  
D. H. Doh ◽  
G. R. Cho
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Radiation Effects ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Heat Transfer Analysis ◽  
Physical Parameters ◽  
Linear Ordinary Differential Equations ◽  
Micropolar Nanofluid

ABSTRACTThe present model is devoted for the steady stagnation point flow of a Williamson micropolar nanofluid with magneto-hydrodynamics and thermal radiation effects passed over a horizontal porous stretching sheet. The fluid is considered to be gray, absorbing-emitting but non-scattering medium. The Cogley-Vincent-Gilles formulation is adopted to simulate the radiation component of heat transfer. By applying similarity analysis, the governing partial differential equations are transformed into a set of non-linear ordinary differential equations and they are solved by using the bvp4c package in MATLAB. Numerical computations are carried out for various values of the physical parameters. The effects of momentum, microrotation, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, reduced Nusselt number and reduced Sherwood number of both active and passive controls on the wall mass flux are graphically presented. The present results are compared with previously obtained solutions and they are in good agreement. Results show that the skin friction is increasing functions of the Williamson parameter in both stretching and shrinking surfaces.

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.

The impacts of non-uniform magnetic field on free convection heat transfer of a magnetizable micropolar nanofluid

2019 ◽  
Vol 29 (10) ◽  
pp. 3685-3706
Author(s):  
Zafar Namazian ◽  
S.A.M. Mehryan
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Content Type ◽  
Viscosity Parameter ◽  
Micropolar Nanofluid ◽  
Free Convection Heat

Purpose The purpose of this study is to numerically study the heat transfer of free convection of a magnetizable micropolar nanofluid inside a semicircular enclosure. Design/methodology/approach The flow domain is under simultaneous influences of two non-uniform magnetic fields generated by current carrying wires. The directions of the currents are the same. Although the geometry is symmetric, it is physically asymmetric. The impacts of key parameters, including Rayleigh number Ra = 103-106, Hartman number Ha = 0-50, vortex viscosity parameter Δ = 0-4, nanoparticles volume fraction φ = 0-0.04 and magnetic number Mnf = 0-1000, on the macro- and micro-scales flows, temperature and heat transfer rate are studied. Finding The outcomes show that dispersing of the nanoparticles in the host fluid increases the strength of macro- and micro-scale flows. When Mnf = 0, the increment of the vortex viscosity parameter increases the strength of the particles micro-rotations, while this characteristic is decreased by growing Δ for Mnf ≠ 0. The increment of Δ and Ha decreases the rate of heat transfer. The increment of Ha decreases the enhancement percentage of heat transfer rate because of dispersing nanoparticles, known as En parameter. In addition, the value of Δ has no effect on En. Moreover, the average Nusselt number Nuavg and En remain constant by increasing the magnetic number Mnf for different volume fraction values. Originality/value The authors believe that all of the results, both numerical and asymptotic, are original and have not been published elsewhere yet.

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.

Nanofluid Viscoelastic Fluid Flow with Thermophoresis

2019 ◽  
Vol 11 (12) ◽  
pp. 1739-1749
Author(s):  
Gamal M. Abdel-Rahman ◽  
Faiza M. N. El-Fayez
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Skin Friction Coefficient ◽  
Jeffrey Fluid ◽  
Deposition Flux ◽  
Local Skin ◽  
Linear Ordinary Differential Equations

We in this study investigated Brownian motion and thermophoresis effects embedded in a porous medium flow with heat transfer generation and chemical reaction on a stretching sheet and Jeffrey fluid model for viscoelastic nanofluid under the effects of magnetic field and thermal radiation. The nanofluid was assumed incompressible and the flow was laminar, with base fluid containing the following types of nanoparticles: Copper (Cu), Aluminum (Al2O3) and Titanium Oxide (TiO2). The governing continuity, momentum, and energy equations for the nanofluid were reduced using similarity transformation and converted into a system of non-Linear ordinary differential equations which were solved numerically. Numerical solutions were also obtained for the velocity, temperature and nanoparticle concentration fields, as well as for skin friction coefficient and Nusselt number. Finally, numerical values for the physical quantities, such as local skin-friction coefficient, local Nusselt number, local Sherwood number and wall deposition flux are herein presented in tabular form.

scholarly journals Stagnation-point flow past a shrinking sheet in a nanofluid

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Roslinda Nazar ◽  
Mihaela Jaradat ◽  
Norihan Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Nonlinear System ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

AbstractIn this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It was found that nanoparticles of low thermal conductivity, TiO2, have better enhancement on heat transfer compared to nanoparticles Al2O3 and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.

Computational Study of Three-Dimensional Stagnation Point Nanofluid Bioconvection Flow on a Moving Surface With Anisotropic Slip and Thermal Jump Effect

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
M. J. Uddin ◽  
W. A. Khan ◽  
A. I. Md. Ismail ◽  
O. Anwar Bég
Keyword(s):  
Nusselt Number ◽  
Skin Friction ◽  
Stagnation Point ◽  
Local Nusselt Number ◽  
Local Density ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Slip Parameter ◽  
Moving Surface ◽  
Local Skin

The effects of anisotropic slip and thermal jump on the three-dimensional stagnation point flow of nanofluid containing microorganisms from a moving surface have been investigated numerically. Anisotropic slip takes place on geometrically striated surfaces and superhydrophobic strips. Zero mass flux of nanoparticles at the surface is applied to achieve practically applicable results. Using appropriate similarity transformations, the transport equations are reduced to a system of nonlinear ordinary differential equations with coupled boundary conditions. Numerical solutions are reported by means of very efficient numerical method provided by the symbolic code Maple. The influences of the emerging parameters on the dimensionless velocity, temperature, nanoparticle volumetric fraction, density of motile microorganism profiles, as well as the local skin friction coefficient, the local Nusselt number, and the local density of the motile microorganisms are displayed graphically and illustrated in detail. The computations demonstrate that the skin friction along the x-axis is enhanced with the velocity slip parameter along the y-axis. The converse response is observed for the dimensionless skin friction along the y-axis. The heat transfer rate is increased with greater velocity slip effects but depressed with the thermal slip parameter. The local Nusselt number is increased with Prandtl number and decreased with the thermophoresis parameter. The local density for motile microorganisms is enhanced with velocity slip parameters and depressed with the bioconvection Lewis number, thermophoresis, and Péclet number. Numerical results are validated where possible with published results and excellent correlation is achieved.

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