Unsteady hydromagnetic flow of Oldroyd-B fluid over an oscillatory stretching surface: a mathematical model

2017 ◽  
Vol 1 (20) ◽  
pp. 87-100 ◽  
Author(s):  
Sami Ullah Khan ◽  
Nasir Ali
Keyword(s):  
Hartmann Number ◽  
Transverse Velocity ◽  
Angular Frequency ◽  
Physical Parameters ◽  
Rate Parameter ◽  
Stretching Surface ◽  
Homotopy Analysis ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Oscillatory Stretching Surface

In the present work, we have studied an unsteady, two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) Oldroyd-B fluid over an oscillatory stretching surface. The problem is modeled by using constitutive equations. The number of independent variables in the governing equations are reduced by using appropriate dimensionless variables. The analytical solution is computed by using homotopy analysis method. The influences of various physical parameters such as Deborah numbers, ratio of angular frequency to stretching rate parameter and Hartmann number on time-series of velocity and transverse velocity profiles at different time instants are investigated and discussed quantitatively with the help of various graphs. It is observed that amplitude of velocity increases by increasing ratio of oscillating frequency to stretching rate parameter while decreases by increasing Hartmann number. It is further observed that the magnitude of velocity decreases by increasing Hartmann number and Deborah numbers in the terms of relaxation time parameter.

scholarly journals On a Bivariate Spectral Homotopy Analysis Method for Unsteady Mixed Convection Boundary Layer Flow, Heat, and Mass Transfer due to a Stretching Surface in a Rotating Fluid

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Sandile S. Motsa ◽  
Zodwa G. Makukula
Keyword(s):  
Convection Boundary Layer ◽  
Analysis Method ◽  
Rotating Fluid ◽  
Stretching Surface ◽  
Unsteady Mixed Convection ◽  
Convection Boundary ◽  
Homotopy Analysis ◽  
Flow Heat ◽  
Layer Flow ◽  
Spectral Homotopy Analysis Method

A bivariate spectral homotopy analysis method (BSHAM) is extended to solutions of systems of nonlinear coupled partial differential equations (PDEs). The method has been used successfully to solve a nonlinear PDE and is now tested with systems. The method is based on a new idea of finding solutions that obey a rule of solution expression that is defined in terms of the bivariate Lagrange interpolation polynomials. The BSHAM is used to solve a system of coupled nonlinear partial differential equations modeling the unsteady mixed convection boundary layer flow, heat, and mass transfer due to a stretching surface in a rotating fluid, taking into consideration the effect of buoyancy forces. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The effects of the flow parameters on the local skin-friction coefficient, the Nusselt number, and the Sherwood number were presented in graphs.

Viscous Dissipation and Thermal Radiation effects in MHD flow of Jeffrey Nanofluid through Impermeable Surface with Heat Generation/Absorption

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Kalpna Sharma ◽  
Sumit Gupta
Keyword(s):  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Radiation Effects ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Homotopy Analysis ◽  
Two Dimensional Flow ◽  
Jeffrey Nanofluid ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

AbstractThis paper investigates steady two dimensional flow of an incompressible magnetohydrodynamic (MHD) boundary layer flow and heat transfer of nanofluid over an impermeable surface in presence of thermal radiation and viscous dissipation. By using similarity transformation, the arising governing equations of momentum, energy and nanoparticle concentration are transformed into coupled nonlinear ordinary differential equations, which are than solved by homotopy analysis method (HAM). The effect of different physical parameters, namely, Prandtl number Pr, Eckert number

Rotating Flow of a Micropolar Fluid Induced by a Stretching Surface

2010 ◽  
Vol 65 (10) ◽  
pp. 829-843 ◽  
Author(s):  
Tariq Javed ◽  
Iftikhar Ahmad ◽  
Zaheer Abbas ◽  
Tasawar Hayat
Keyword(s):  
Differential Equations ◽  
Micropolar Fluid ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Flow ◽  
Nonlinear Ordinary Differential Equations ◽  
Series Solutions ◽  
Analysis Method ◽  
Stretching Surface ◽  
Homotopy Analysis ◽  
Layer Flow

This investigation deals with the boundary layer flow of a micropolar fluid over a stretching surface. The flow is considered in a rotating frame of reference. The governing nonlinear partial differential equations are reduced to coupled nonlinear ordinary differential equations. The set of similarity equations has been solved analytically employing the homotopy analysis method (HAM). The series solutions are given for velocity and microrotation, and the convergence of these solutions are explicitly discussed. Attention has been focused to the variations of the emerging parameters on the velocity and microrotation are discussed through graphs.

scholarly journals BOUNDARY LAYER FLOW AND HEAT TRANSFER WITH VARIABLE VISCOSITY IN THE PRESENCE OF MAGNETIC FIELD

2016 ◽  
Vol 12 (7) ◽  
pp. 6412-6421
Author(s):  
Ajala O.A ◽  
Aseelebe L. O ◽  
Ogunwobi Z. O
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Layer Flow ◽  
Variable Viscosity ◽  
Physical Parameters ◽  
Flow And Heat Transfer ◽  
Dimensional Boundary ◽  
Layer Flow

A steady two dimensional boundary layer flow and heat transfer with variable viscosity electrically conducting fluid at T in the presence of magnetic fields and thermal radiation was considered. The governing equations which are partial differential equations were transformed into ordinary differential equations using similarity variables, and the resulting coupled ordinary differential equations were solved using collocation method in MAPLE 18. The velocity and temperature profiles were studied graphically for different physical parameters. The effects of the parameters on velocity and temperature profile were showed.

Nonlinear Heat Transfer in a Two-Layer Flow With Nanofluids by OHAM

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Umer Farooq ◽  
Lin Zhi-Liang
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Mixed Convection ◽  
Vertical Channel ◽  
Motion Parameter ◽  
Physical Parameters ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Brownian Motion Parameter

The problem of fully developed steady, laminar, incompressible flow in a vertical channel is studied analytically, one region is filled with water based copper nanofluid and the other region is filled with clear viscous fluid. The resulting coupled nonlinear ordinary differential equations (ODEs) are solved by optimal homotopy analysis method (OHAM). The convergence of our results is discussed by the so-called total average squared residual error. Analytical results are presented for different values of the physical parameters, such as the mixed convection parameters, the Brownian motion parameter, and thermophoresis parameter. Reversed flow is observed for sufficiently high buoyancy (mixed convection parameter). Further we investigate the effects of the Brownian motion parameter and thermophoresis parameter on the fluid flow and heat transfer at the interface of the two regions.

scholarly journals Flow of an Erying-Powell fluid over a stretching sheet in presence of chemical reaction

2016 ◽  
Vol 20 (6) ◽  
pp. 1903-1912 ◽  
Author(s):  
Ilyas Khan ◽  
Muhammad Qasim ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Similarity Transformation ◽  
Integration Scheme ◽  
Physical Parameters ◽  
Analysis Method ◽  
Stretching Surface ◽  
Shooting Technique ◽  
Homotopy Analysis

In this paper we study the flow of an incompressible Erying-Powell fluid bounded by a linear stretching surface. The mass transfer analysis in the presence of destructive /generative chemical reactions is also analyzed. A similarity transformation is used to transform the governing partial differential equations into ordinary differential equations. Computations for dimensionless velocity and concentration fields are performed by an efficient approach namely the homotopy analysis method (HAM) and numerical solution is obtained by shooting technique along with Runge-Kutta-Fehlberg integration scheme. Graphical results are prepared to illustrate the details of flow and mass transfer characteristics and their dependence upon the physical parameters. The values for gradient of mass transfer are also evaluated and analyzed. A comparison of the present solutions with published results in the literature is performed and the results are found to be in excellent agreement.

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