scholarly journals MHD Powell–Eyring dusty nanofluid flow due to stretching surface with heat flux boundary condition

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Omima A. Abo-zaid ◽  
R. A. Mohamed ◽  
F. M. Hady ◽  
A. Mahdy
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Fluid Phase ◽  
Spherical Shape ◽  
Dust Particles ◽  
Stretching Surface ◽  
Flux Boundary Condition ◽  
Fluid Phases

AbstractA steady MHD boundary layer flow of Powell–Eyring dusty nanofluid over a stretching surface with heat flux condition is studied numerically. It is assumed that the fluid is incompressible and the impacts of thermophoresis and Brownian motion are taken into regard. In addition, the Powell–Eyring terms are considered in the momentum boundary layer and thermal boundary layer. The dust particles are seen as to be having the same size and conform to the nanoparticles in a spherical shape. We obtain a system of ordinary differential equations that are suitable for analyzed numerically using the fourth-order Runge–Kutta method via software algebraic MATLAB by applying appropriate transformations to the system of the governing partial differential equations in our problem. There is perfect compatibility between the bygone and current results when comparing our numerical solutions with the available data for values of the selected parameters. This confirms the validity of the method used here and thus the validity of the results. The influence of some parameters on the boundary layer profiles (the velocity and temperature for the particle phase and fluid phase, and nanoparticle concentration) is discussed. The results of this study display that the profiles of the velocity for particle and fluid phases increase with increasing Powell–Eyring fluid parameter, but reduce with height in magnetic field values. Mass concentration of the dust particles decreases the temperature of both the particle and fluid phases. The results also indicate the concentration of nanoparticle contraction as Schmidt number increases.

scholarly journals An Exact Solution of MHD Boundary Layer Flow of Dusty Fluid over a Stretching Surface

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Mudassar Jalil ◽  
Saleem Asghar ◽  
Shagufta Yasmeen
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Particle Interaction ◽  
Dust Particles ◽  
Stretching Surface ◽  
Dusty Fluid ◽  
Layer Flow

This paper deals with the boundary layer flow of electrically conducting dusty fluid over a stretching surface in the presence of applied magnetic field. The governing partial differential equations of the problem are transformed to nonlinear nondimensional coupled ordinary differential equations using suitable similarity transformations. The problem is now fully specified in terms of characterizing parameters known as fluid particle interaction parameter, magnetic field parameter, and mass concentration of dust particles. An exact analytical solution of the resulting boundary value problem is presented that works for all values of the characterizing parameters. The effects of these parameters on the velocity field and the skin friction coefficient are presented graphically and in the tabular form, respectively. We emphasize that an approximate numerical solution of this problem was available in the literature but no analytical solution was presented before this study.

scholarly journals Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 684
Author(s):  
Saeed Islam ◽  
Haroon Ur Rasheed ◽  
Kottakkaran Sooppy Nisar ◽  
Nawal A. Alshehri ◽  
Mohammed Zakarya
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Variable Thickness ◽  
Heat Mass Transfer ◽  
Mathematical Formulation ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
The Impact

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

Effects of Viscoelastic Oil-Based Nanofluids on a Porous Nonlinear Stretching Surface with Variable Heat Source/Sink

2018 ◽  
Vol 387 ◽  
pp. 260-272
Author(s):  
Christian John Etwire ◽  
Ibrahim Yakubu Seini ◽  
Rabiu Musah ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Layer Thickness ◽  
Fourth Order ◽  
Boundary Layer Thickness ◽  
Stretching Surface ◽  
Variable Heat ◽  
Nonlinear Stretching

The effect of variable heat source on viscoelastic fluid of CuO-oil based nanofluid over a porous nonlinear stretching surface is analyzed. The problem was modelled in the form of partial differential equations and transformed into a coupled fourth order ordinary differential equations by similarity techniques. It was further reduced to a system of first order ordinary differential equations and solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. The results for various controlling parameters have been tabulated and the flow profiles graphically illustrated. The study revealed that the viscoelastic parameter has a decreasing effect on the magnitude of both the skin friction coefficient and the rate of heat transfer from the surface. It enhanced the momentum boundary layer thickness whilst adversely affecting the thermal boundary layer thickness.

Numerical Solutions on Boundary Layer of Casson Micropolar Fluid Over a Stretching Surface

2019 ◽  
pp. 127-133
Author(s):  
Abdul Rahman Mohd Kasim ◽  
Hussein Ali Mohammed Al-Sharifi ◽  
Nur Syamilah Arifin ◽  
Mohd Zuki Salleh ◽  
Sharidan Shafie
Keyword(s):  
Boundary Layer ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Stretching Surface

Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature

2021 ◽  
Vol 87 (1) ◽  
pp. 30-40
Author(s):  
Anisah Dasman ◽  
Abdul Rahman Mohd Kasim ◽  
Iskandar Waini ◽  
Najiyah Safwa Khashi’ie
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Wall Temperature ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Particle Interaction ◽  
Dust Particles ◽  
Constant Wall Temperature

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

Exponentially Decaying Heat Source on MHD Tangent Hyperbolic Two-Phase Flows over a Flat Surface with Convective Conditions

2018 ◽  
Vol 387 ◽  
pp. 286-295 ◽  
Author(s):  
S.U. Mamatha ◽  
Chakravarthula S.K. Raju ◽  
Putta Durga Prasad ◽  
K.A. Ajmath ◽  
Mahesha ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Weissenberg Number ◽  
Dust Particles ◽  
Convective Conditions ◽  
Two Phase ◽  
Velocity Boundary Layer

The present framework addresses Darcy-Forchheimer steady incompressible magneto hydrodynamic hyperbolic tangent fluid with deferment of dust particles over a stretching surface along with exponentially decaying heat source. To control the thermal boundary layer Convective conditions are considered. Appropriate transformations were utilized to convert partial differential equations (PDEs) into nonlinear ordinary differential equations (NODEs). To present numerical approximations Runge-Kutta Fehlberg integration is implemented. Computational results of the flow and energy transport are interpreted for both fluid and dust phase with the support of graph and table illustrations. It is found that non-uniform inertia coefficient of porous medium decreases velocity boundary layer thickness and enhances thermal boundary layer. Improvement in Weissenberg number improves the velocity boundary layer and declines the thermal boundary layer.

scholarly journals Velocity Slip and Thermal Jump on Maxwell Fluid with Non-Fourier Cattaneo-Christov Heat Flux Using SRM Solutions

2018 ◽  
Vol 7 (4.10) ◽  
pp. 233
Author(s):  
K. Gangadhar ◽  
K. V. Ramana ◽  
B. Rushi Kumar
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Differential Equations ◽  
Slip Velocity ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Stretching Cylinder ◽  
Zero Curvature ◽  
Curvature Parameter

The influence of the heat transfer within a boundary layer flow and magneto hydro dynamic slip flow of a Maxwell fluid over a stretching cylinder is analyzed and discussed in the present article. The effects of viscous dissipation and thermal jump are assumed. The procedure of heat transfer through hypothesis of Cattaneo-Christov heat flux is considered. We converted non-linear partial differential equations for mass, momentum and energy into a system of coupled highly non linear ordinary differential equations with proper boundary conditions by the help of suitable similarity transformations. The succeeding ordinary differential equations are solved by using Spectral relaxation technique. The solution is obtained in zero curvature parameter as well as non-zero curvature parameter.  i.e. for flow above a flat plate and flow above a cylinder. The flow and heat transfer attributes are witnessed to be encouraged in an elaborate mode by Prandtl number, thermal jump parameter, thermal relaxation parameter, Deborah number, slip velocity parameter, Eckert number and the magnetic parameter. Our findings reveal that one of the possible ways to decrease the Deborah number by boosting fluid velocity. It is also perceived that in the case of flow over a stretching cylinder, the momentum boundary layer thickness and the velocity of the fluid increases. Furthermore, an increase in slip velocity factor reduces the magnitude of skin friction.  

Heat transfer over an unsteady stretching surface with prescribed heat flux

2008 ◽  
Vol 86 (6) ◽  
pp. 853-855 ◽  
Author(s):  
A Ishak ◽  
R Nazar ◽  
I Pop
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Method Comparison ◽  
Temperature Fields ◽  
Stretching Surface ◽  
Keller Box Method ◽  
Unsteady Stretching Surface ◽  
Layer Flow

The unsteady laminar boundary-layer flow over a continuously stretching surface in a viscous and incompressible quiescent fluid is studied. The unsteadiness in the flow and temperature fields is caused by the time dependence of the stretching velocity and the surface heat flux. The nonlinear partial differential equations of continuity, momentum, and energy, with three independent variables, are reduced to nonlinear ordinary differential equations, before they are solved numerically by the Keller-box method. Comparison with available data from the open literature as well as the exact solution for the steady-state case of the present problem is made, and found to be in good agreement. Effects of the unsteadiness parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined.PACS No.: 47.15.Cb

scholarly journals Slip Effects on Boundary Layer Flow and Heat Transfer Along a Stretching Cylinder

2013 ◽  
Vol 18 (2) ◽  
pp. 447-459 ◽  
Author(s):  
S. Mukhopadhyay ◽  
R.S.R Gorla
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Velocity Slip ◽  
Heat Equations ◽  
Stretching Cylinder ◽  
Linear Ordinary Differential Equations ◽  
Layer Flow

An axi-symmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder is presented. Velocity slip is considered instead of the no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and heat equations into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by the shooting method. It is found that the velocity decreases with increasing the slip parameter. The skin friction as well as the heat transfer rate at the surface is larger for a cylinder compared to those for a flat plate.

scholarly journals Dual Solutions in the Boundary Layer Flow and Heat Transfer in the Presence of Thermal Radiation with Suction Effect

2018 ◽  
Vol 7 (4.33) ◽  
pp. 17
Author(s):  
Siti Nur Aisyah Azeman ◽  
. .
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Shooting Technique ◽  
Flow And Heat Transfer ◽  
Layer Flow

The dual solutions in the boundary layer flow and heat transfer in the presence of thermal radiation is quantitatively studied. The governing partial differential equations are derived into a system of ordinary differential equations using a similarity transformation, and afterward numerical solution obtained by a shooting technique. Dual solutions execute within a certain range of opposing and assisting flow which related to these numerical solutions. The similarity equations have two branches, upper or lower branch solutions, within a certain range of the mixed convection parameters. Further numerical results exist in our observations which enable to discuss the features of the respective solutions.  

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