Stagnation-Point Flow Toward a Stretching/Shrinking Sheet in a Nanofluid Containing Both Nanoparticles and Gyrotactic Microorganisms

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Khairy Zaimi ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Stagnation Point ◽  
Sherwood Number ◽  
Local Nusselt Number ◽  
Local Density ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Gyrotactic Microorganisms ◽  
Local Sherwood Number

The stagnation-point flow and heat transfer toward a stretching/shrinking sheet in a nanofluid containing gyrotactic microorganisms with suction are investigated. Using a similarity transformation, the nonlinear system of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a shooting method. The skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms profiles are analyzed subject to several parameters of interest, namely suction parameter, thermophoresis parameter, Brownian motion parameter, Lewis number, Schmidt number, bioconvection Péclet number, and the stretching/shrinking parameter. It is found that dual solutions exist for a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms increase with suction effect. It is also observed that suction widens the range of the stretching/shrinking parameter for which the solution exists.

Viscous Dissipation and Joule Heating Effects on MHD Bioconvection Flow of a Nanofluid Containing Gyrotactic Microorganisms Over a Vertical Isothermal Cone

2020 ◽  
Vol 9 (3) ◽  
pp. 242-255
Author(s):  
Hossam A. Nabwey ◽  
S. M. M. El-Kabeir ◽  
A. M. Rashad ◽  
M. M. M. Abdou
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Sherwood Number ◽  
Local Density ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Gyrotactic Microorganisms ◽  
Local Skin Friction ◽  
Local Sherwood Number

The main objective of the present study is to explore the flow of a nanofluid containing gyrotactic microorganisms over a vertical isothermal cone surface in the presence of viscous dissipation and Joule heating. The combined effects of a transverse magnetic field and Navier slip in the flow are considered. Using appropriate transforms the set of partial differential equations governing the flow are converted to a set of ordinary differential equations. Influence of the parameters governing the flow is shown for velocity, temperature, concentration and motilemicroorganisms as well as local skin Friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number. An increasing in the value of Eckert number rises the velocity of the fluid and reduce the temperature, concentration and density of motile microorganisms profiles, while buoyancy ratio Nr and magnetic field parameters increase local skin friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number decrease as a result of the presence of Lorentz force which resist the motion of the flow. On the other hand, the motile microorganisms boundary layer thickness decreases with an increasing on the bioconvection Lewis number.

Non-similar characteristics of mixed convective slip flow over a wedge with temperature-dependent thermo-physical properties

2019 ◽  
Vol 33 (36) ◽  
pp. 1950455
Author(s):  
Nepal Chandra Roy ◽  
Sudharonjon Roy ◽  
Naved Azum ◽  
Anish Khan ◽  
Abdullah M. Asiri ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Sherwood Number ◽  
Local Nusselt Number ◽  
Slip Flow ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Local Skin Friction ◽  
Local Sherwood Number

We examined heat and mass transfer characteristics of mixed convective slip flow over a wedge taking into account the effect of variable transport properties. Unlike other studies, we have utilized non-similar transformation to get the non-similar features of the mixed convective slip flow. For comparison, stream function formulation is used to reduce the governing equation into a convenient form for short- and long-time regimes. We have determined the series solutions by adopting the perturbation techniques. The agreement between the numerical and series solutions is found to be excellent. Numerical solutions reveal that the slip parameters augment the momentum, thermal and concentration boundary layers. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are found to decrease for higher value of slip parameters. For the increasing value of the variable viscosity parameter, the velocity is stronger, but the temperature and concentration lessen. Contrary to this, this parameter diminishes the local skin friction coefficient, local Nusselt number and local Sherwood number. Due to the increase of mass diffusivity parameter, the velocity and concentration significantly increase whereas the temperature remains almost unaffected. Moreover, the mass diffusivity variation parameter leads to an increase in the local skin friction coefficient and local Nusselt number, but it reduces the local Sherwood number.

scholarly journals Magnetohydrodynamic Time-Dependent Bio-Nanofluid Flow in a Porous Medium with Variable Thermophysical Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
M. Irfan ◽  
M. Asif Farooq ◽  
A. Aslam ◽  
A. Mushtaq ◽  
Z. H. Shamsi
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Local Nusselt Number ◽  
Shooting Method ◽  
Local Density ◽  
Skin Friction Coefficient ◽  
Published Data ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Local Sherwood Number

In this work, a theoretical model with a numerical solution is brought forward for a bio-nanofluid with varying fluid features over a slippery sheet. The partial differential equations (PDEs) involving temperature-dependent quantities have been translated into ordinary differential equations (ODEs) by using similarity variables. Numerical verifications have been done in three different methods: finite difference method, shooting method, and bvp4c. To figure out the influence of parameters on the flows, the graphs are plotted for the velocity, temperature, concentration, and microorganism curves. The boundary layer thickness of the microorganism profile reduces with the Schmidt number and Peclet number. In addition to adding radiative heat flux, we added heat generation, rate of chemical reaction, and first-order slip. Adding these parameters brought new aspects to the underlying profiles. Moreover, the obtained data of the skin friction coefficient, the local Nusselt number, the local Sherwood number, and the local density of motile microorganisms are tabulated against various parameters for the physical parameters. From the results, it is apparent that the local Nusselt number decreases with the Brownian and thermophoretic parameters. The data obtained for physical parameters have a close agreement with the published data. Finally, the graphs for slip conditions are significantly different when the comparison is drawn with no-slip condition.

MHD Stagnation-Point Flow of a Nanofluid Past a Stretching Sheet with a Convective Boundary Condition and Radiation Effects

2019 ◽  
Vol 892 ◽  
pp. 168-176 ◽  
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Mohd Ishak ◽  
Ioan Pop
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Stagnation Point ◽  
Local Nusselt Number ◽  
Radiation Effects ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Convective Boundary

In this paper, the investigation of magnetohydrodynamic (MHD) stagnation point flow of a nanofluid past a stretching sheet with a convective boundary condition and radiation effects is carried out numerically. Similarity transformation is used to reduce the governing partial differential equations into third and second order non-linear ordinary differential equations. These equations are then being solved numerically using a problem solver built in the MATLAB software. The numerical solutions for the skin friction coefficient, local Nusselt number, velocity and temperature profiles for different values of the physical parameters are presented graphically and discussed further. The results indicate that the velocity and the temperature are influenced by the magnetic parameter M, Brownian motion parameter Nb and radiation parameter Nr. The local Nusselt number and the skin friction coefficient are affected significantly in the presence of suction at the boundary.

scholarly journals Three-Dimensional Flow and Heat Transfer Past a Permeable Exponentially Stretching/Shrinking Sheet in a Nanofluid

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Syahira Mansur ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Three Dimensional ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Three Dimensional Flow ◽  
Flow And Heat Transfer

The three-dimensional flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated. Numerical results are obtained using bvp4c in MATLAB. The results show nonunique solutions for the shrinking case. The effects of the stretching/shrinking parameter, suction parameter, Brownian motion parameter, thermophoresis parameter, and Lewis number on the local skin friction coefficient and the local Nusselt number are studied. Suction increases the solution domain. Furthermore, as the sheet is shrunk in thex-direction, suction increases the skin friction coefficient in the same direction while decreasing the skin friction coefficient in they-direction. The local Nusselt number is consistently lower for higher values of thermophoresis parameter and Lewis number. On the other hand, the local Nusselt number increases as the Brownian motion parameter increases.

scholarly journals The Magnetohydrodynamic Boundary Layer Flow of a Nanofluid past a Stretching/Shrinking Sheet with Slip Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Syahira Mansur ◽  
Anuar Ishak
Keyword(s):  
Nusselt Number ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Slip Parameter ◽  
Slip Boundary ◽  
Layer Flow ◽  
Local Sherwood Number

The magnetohydrodynamic (MHD) boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Golam Mortuja Sarkar ◽  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Friction Coefficient ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Hiemenz Flow ◽  
Self Similar ◽  
The Stability

Purpose This paper aims to theoretically and numerically investigate the steady two-dimensional (2D) Hiemenz flow with heat transfer of Reiner-Rivlin fluid over a linearly stretching/shrinking sheet. Design/methodology/approach The Navier–Stokes equations are transformed into self-similar equations using appropriate similarity transformations and then solved numerically by using shooting technique. A simple but effective mathematical analysis has been used to prove the existence of a solution for stretching case (λ> 0). Moreover, an attempt has been laid to carry the asymptotic solution behavior for large stretching. The obtained asymptotic solutions are compared with direct numerical solutions, and the comparison is quite remarkable. Findings It is observed that the self-similar equations exhibit dual solutions within the range [λc, −1] of shrinking parameter λ, where λc is the turning point from where the dual solutions bifurcate. Unique solution is found for all stretching case (λ > 0). It is noticed that the effects of cross-viscous parameter L and shrinking parameter λ on velocity and thermal fields show opposite character in the dual solution branches. Thus, a linear temporal stability analysis is performed to determine the basic feasible solution. The stability analysis is based on the sign of the smallest eigenvalue, where positive or negative sign leading to a stable or unstable solution. The stability analysis reveals that the first solution is stable that describes the main flow. Increase in cross-viscous parameter L resulting in a significant increment in skin friction coefficient, local Nusselt number and dual solutions domain. Originality/value This work’s originality is to examine the combined effects of cross-viscous parameter and stretching/shrinking parameter on skin friction coefficient, local Nusselt number, velocity and temperature profiles of Hiemenz flow over a stretching/shrinking sheet. Although many studies on viscous fluid and nanofluid have been investigated in this field, there are still limited discoveries on non-Newtonian fluids. The obtained results can be used as a benchmark for future studies of higher-grade non-Newtonian flows with several physical aspects. All the generated results are claimed to be novel and have not been published elsewhere.

Hall Effects on Unsteady Magnetohydrodynamic Flow of a Nanofluid Past an Oscillatory Vertical Rotating Flat Plate Embedded in Porous Media

2021 ◽  
Vol 10 (2) ◽  
pp. 259-269
Author(s):  
M. Veera Krishna ◽  
N. Ameer Ahamad ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Local Nusselt Number ◽  
Hall Current ◽  
Skin Friction Coefficient ◽  
Engineering Industry ◽  
Hall Effects ◽  
The Impact

In the current investigative paper, the impact of Hall current on an unsteady magnetohydrodynamic liberated convection revolving flow of a nanofluid restricted with a uniform absorbent medium over an oscillatory moving vertical smooth plate with convective as well as diffusive frontier conditions has been reviewed. The non-dimensionalized governing differential equations by the appropriate frontier conditions are resolved by the perturbations technique. The impacts of the physical constants on the flow as well as the heat transfer features are displayed graphically and analyzed for Cu as well as Al2O3 nanoparticles. For the engineering industry, the skin friction coefficient, local Nusselt number, along with the Sherwood’s number are examined numerically in detail.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1175
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

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