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.

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.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Nurfazila Rasli ◽  
Norshafira Ramli
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Magnetohydrodynamic Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

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.

scholarly journals Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Mostafa Mahmoud ◽  
Shimaa Waheed
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

MHD hybrid nanofluid flow over a permeable stretching/shrinking sheet with thermal radiation effect

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ubaidullah Yashkun ◽  
Khairy Zaimi ◽  
Nor Ashikin Abu Bakar ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Thermal Radiation ◽  
Radiation Effects ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose This study aims to investigate the heat transfer characteristic of the magnetohydrodynamic (MHD) hybrid nanofluid over the linear stretching and shrinking surface in the presence of suction and thermal radiation effects. Design/methodology/approach Mathematical equations are transformed into pairs of self-similarity equations using similarity transformation. Boundary value problem solver (bvp4c) in MATLAB was adopted to solve the system of reduced similarity equations. In this study, the authors particularly examine the flow and heat transfer properties for different values of suction and thermal radiation parameters using single-phase nanofluid model. A comparison of the present results shows a good agreement with the published results. Findings It is noticed that the efficiency of heat transfer of hybrid nanofluid (Cu-Al2O3/H2O) is greater than the nanofluid (Cu/H2O). Furthermore, it is also found that dual solutions exist for a specific range of the stretching/shrinking parameter with different values of suction and radiation parameters. The results indicate that the skin friction coefficient and the local Nusselt number increase with suction effect. The values of the skin friction coefficient increases, but the local Nusselt number decreases for the first solution with the increasing of thermal radiation parameter. It is also observed that suction and thermal radiation widen the range of the stretching/shrinking parameter for which the solution exists. Practical implications In practice, the investigation on the flow and heat transfer of MHD hybrid nanofluid through a stretching/shrinking sheet with suction and thermal radiation effects is very important and useful. The problems related to hybrid nanofluid has numerous real-life and industrial applications, for example microfluidics, manufacturing, transportation, military and biomedical, etc. Originality/value In specific, this study focused on increasing thermal conductivity using a hybrid nanofluid mathematical model. This paper is able to obtain the dual solutions. To the best of author’s knowledge, this study is new and there is no previous published work similar to present study.

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.

Passive control of nanoparticle of micropolar fluid past a stretching sheet with nanoparticles, convective boundary condition and second-order slip

2016 ◽  
Vol 231 (4) ◽  
pp. 704-719 ◽  
Author(s):  
Wubshet Ibrahim
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Micropolar Fluid ◽  
Passive Control ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Non Linear

This article deals with a second-order slip flow and magnetic field on boundary layer flow of micropolar fluid past a stretching sheet. Situation of nil normal flux of nanoparticles at the wall for the stretching flow is taken into account. By employing appropriate similarity transformation and non-dimensional variables, the governing non-linear boundary-value problems were reduced into coupled higher order non-linear ordinary differential equation. Then, numerical solution for velocity, angular velocity (microrotation), temperature, and concentration has been established. The equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters. Numerical results have been obtained and discussed for non-dimensional velocity, temperature, microrotation, the skin friction coefficient, and local Nusselt number using some fixed values of the governing parameters. The results indicate that the skin friction coefficient Cf increases as the values of slip parameter γ increase. However, the local Nusselt number − [Formula: see text] increases as thermophoresis parameter Nt, microrotation parameter β, and convective parameter Bi increase. The wall couple stress coefficient decreases as the values of governing parameters such as magnetic parameter M, material parameter β, and for both slip parameters γ and δ increase. A comparison with earlier investigations available in the literature has been done and an excellent agreement is achieved.

Homotopy analysis method for unsteady mixed convective stagnation-point flow of a nanofluid using Tiwari-Das nanofluid model

2016 ◽  
Vol 26 (1) ◽  
pp. 40-62 ◽  
Author(s):  
Saeed Dinarvand ◽  
Reza Hosseini ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Nanoparticle Volume Fraction ◽  
Content Type

Purpose – The current study is mainly motivated by the need to the development of the transient MHD mixed convection stagnation-point flow and heat transfer of an electrically conducting nanofluid over a vertical permeable stretching/shrinking sheet by means of Tiwari-Das nanofluid model. The purpose of this paper is to investigate the effects of the parameters governing the flow i.e. the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter on dimensionless velocity and temperature distributions, skin friction coefficient and local Nusselt number. Design/methodology/approach – The mathematical model has been formulated based on Tiwari-Das nanofluid model. Three different types of water-based nanofluid with copper, aluminum oxide (alumina) and titanium dioxide (titania) as nanoparticles are considered in this investigation. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved analytically by the well-know homotopy analysis method. The present simulations agree closely with the previous studies in the especial cases. Findings – The results show that by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter or reducing the velocity ratio parameter, the skin friction coefficient enhances. Furthermore, the local Nusselt number enhances with different rates by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter. Besides, the skin friction coefficient and the local Nusselt number are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids. Originality/value – Tiwari-Das nanofluid model has not been applied for the flow with these characteristics as mentioned in the paper. A comprehensive survey on boundary layer behavior has been presented. There are few studies regarding as analysis on thermal and hydrodynamics boundary layer. All plots presented in the paper are new and did not report in any other study. The effects of the parameters governing the flow on skin friction coefficient and local Nusselt number have been illustrated in the paper while there are some conflicts with previous published article that have been interpreted in details in the paper.

scholarly journals Turbulent flow and heat transfer characteristics in U-tubes: A numerical study

2009 ◽  
Vol 13 (4) ◽  
pp. 175-181 ◽  
Author(s):  
Khalid Alammar
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Turbulent Flow ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Heat Transfer Characteristics ◽  
Local Skin ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer

Using the standard k-e model, 3-dimensional turbulent flow and heat transfer characteristics in U-tubes are investigated. Uncertainty is approximated using experimental correlations and grid independence study. Increasing the Dean number is shown to intensify a secondary flow within the curved section. The overall Nusselt number for the tube is found to decrease substantially relative to straight tubes, while the overall skin friction coefficient remains practically unaffected. Local skin friction coefficient, Nusselt number, and wall temperature along the tube wall are presented.

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.

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