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 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.

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 Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates

2013 ◽  
Vol 18 (3) ◽  
pp. 779-791 ◽  
Author(s):  
K.V. Prasad ◽  
K. Vajravelu ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Arbitrary Power ◽  
Keller Box Method ◽  
Flow And Heat Transfer

Abstract The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

scholarly journals Magnetohydrodynamic Flow Past a Nonlinear Stretching or Shrinking Cylinder in Nanofluid with Viscous Dissipation and Heat Generation Effect

2021 ◽  
Vol 90 (1) ◽  
pp. 102-114
Author(s):  
Mahani Ahmad Kardri ◽  
Norfifah Bachok ◽  
Norihan Md. Arifin ◽  
Fadzilah Md. Ali ◽  
Yong Faezah Rahim
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Flow And Heat Transfer ◽  
Controlling Parameter ◽  
Numerical Computing ◽  
Nonlinear Stretching

The Tiwari-Das model is used to investigate magnetohydrodynamic stagnation point flow and heat transfer past a nonlinear stretching or shrinking cylinder in nanofluid with viscous dissipation and heat generation using. The partial differential equations, also known as governing equations, were reduced to nonlinear ordinary differential equations using similarity transformation. MATLAB with the bvp4c solver is used for numerical computing. The controlling parameter, such as nanoparticle volume fraction, magnetic, curvature, nonlinear, radiation, and heat generation parameters, as well as Eckert and Grashof numbers, influence the skin friction coefficient, heat transfer rate, velocity, and temperature profiles. The results are presented as graphs to show the influence of the variables studied. In some circumstances of stretching and shrinking cases, dual solutions can be obtained.

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.

Melting heat transfer in boundary layer stagnation-point flow of a nanofluid towards a stretching–shrinking sheet

2014 ◽  
Vol 92 (12) ◽  
pp. 1703-1708 ◽  
Author(s):  
Kishore Kumar Ch. ◽  
Shankar Bandari
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Fourth Order Method

The present analysis deals with the study of two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow of a nanofluid towards a melting stretching sheet. Using similarity transformations, the governing differential equations were transformed into coupled, nonlinear ordinary differential equations, which were then solved numerically by using the Runge–Kutta fourth-order method along with the shooting technique for two types of nanoparticles namely copper (Cu) and silver (Ag) in the water-based fluid with Prandtl number Pr = 6.2, the skin friction coefficient, the local Nusselt number, the velocity and the temperature profiles are presented graphically and discussed.

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.

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.

scholarly journals Unsteady Stagnation Point Flow and Heat Transfer over a Stretching/Shrinking Sheet with Suction or Injection

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
M. Suali ◽  
N. M. A. Nik Long ◽  
N. M. Ariffin
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Similarity Transformation ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Suction Or Injection

The unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction/injection is studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using a similarity transformation and solved numerically. Both stretching and shrinking cases are considered. Results for the skin friction coefficient, local Nusselt number, velocity, and temperature profiles are presented for different values of the governing parameters. It is found that the dual solutions exist for the shrinking case, whereas the solution is unique for the stretching case. Numerical results show that the range of dual solutions increases with mass suction and decreases with mass injection.

scholarly journals Nanofluid Flow over a Rotating Disk with Prescribed Heat Flux

2012 ◽  
Vol 11 (3) ◽  
pp. 77-92
Author(s):  
Julie Andrews ◽  
S P Anjali Devi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Prandtl Number ◽  
Skin Friction ◽  
Rotating Disk ◽  
Skin Friction Coefficient ◽  
Copper Water ◽  
Flow And Heat Transfer

An analysis is carried out to study the problem of the steady flow and heat transfer over a rotating disk with a prescribed heat flux in nanofluid. Nanofluid considered is Copper (Cu) with water as the base fluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, which are then solved using the Nachtsheim-Swigert Shooting iteration technique along with the fourth order Runga Kutta method. The features of the flow and heat transfer characteristics are analyzed and discussed. The radial velocity, tangential velocity and the axial velocity for copper-water nanofluid are calculated and are represented graphically. Numerical results for dimensionless temperature, the radial skin friction coefficient and the tangential skin friction coefficient of the nanofluid flows are obtained and computations are carried out for the various values of Prandtl number. It is found that for the prescribed heat flux case (PHF case), the effect of Prandtl number is to reduce the temperature as it increases for copper-water nanofluid.

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