scholarly journals MHD Flow and Heat Transfer in a Channel Bounded by a Shrinking Sheet and a Porous Medium Bed: Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Dileep Singh Chauhan ◽  
Rashmi Agrawal
Keyword(s):  
Porous Medium ◽  
Mhd Flow ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Analysis Method ◽  
Governing Equations ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Surface Similarity

MHD flow of viscous conducting fluid is considered between a shrinking sheet and a porous medium bed. Suction is applied at the upper shrinking sheet and its surface temperature is always maintained higher than the temperature of the lower porous bed surface. Similarity transformations and HAM are used to solve the governing equations for velocity and temperature fields. The effects of various pertinent parameters on the results are discussed graphically.

Stagnation Flow of a Jeffrey Fluid over a Shrinking Sheet

2010 ◽  
Vol 65 (6-7) ◽  
pp. 540-548 ◽  
Author(s):  
Sohail Nadeem ◽  
Anwar Hussain ◽  
Majid K
Keyword(s):  
Jeffrey Fluid ◽  
Shrinking Sheet ◽  
Series Solutions ◽  
Analysis Method ◽  
Governing Equations ◽  
Stagnation Flow ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Equations Of Motions

January 22, 2009 The present paper describes the analytical solutions for the steady boundary layer flow of a Jeffrey fluid over a shrinking sheet. The governing equations of motions are reduced into a set of nonlinear ordinary differential equations by using similarity transformations. Two types of problems, namely, (1) two-dimensional stagnation flow towards a shrinking sheet and (2) axisymmetric stagnation flow towards an axisymmetric shrinking sheet, have been discussed. The series solutions of the problems are obtained by using the homotopy analysis method (HAM). The convergence of the obtained series solutions are analyzed and discussed in detail through graphs for various parameters of interest.

Flow and Heat Transfer of Nanofluids Over a Rotating Porous Disk with Velocity Slip and Temperature Jump

2015 ◽  
Vol 70 (5) ◽  
pp. 351-358 ◽  
Author(s):  
Chenguang Yin ◽  
Liancun Zheng ◽  
Chaoli Zhang ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Temperature Fields ◽  
Analysis Method ◽  
Governing Equations ◽  
Porous Disk ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Good Agreement

AbstractIn this article, we discuss the flow and heat transfer of nanofluids over a rotating porous disk with velocity slip and temperature jump. Three types of nanoparticles – Cu, Al2O3, and CuO – are considered with water as the base fluid. The nonlinear governing equations are reduced into ordinary differential equations by Von Karman transformations and solved using homotopy analysis method (HAM), which is verified in good agreement with numerical ones. The effects of involved parameters such as porous parameter, velocity slip, temperature jump, as well as the types of nanofluids on velocity and temperature fields are presented graphically and analysed.

Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid

2014 ◽  
Vol 23 (4) ◽  
pp. 048203 ◽  
Author(s):  
Sadegh Khalili ◽  
Saeed Dinarvand ◽  
Reza Hosseini ◽  
Hossein Tamim ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Stagnation Point ◽  
Mhd Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

scholarly journals Flow and Heat Transfer in a Liquid Film over a Permeable Stretching Sheet

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
R. C. Aziz ◽  
I. Hashim ◽  
A. K. Alomari
Keyword(s):  
Heat Transfer ◽  
Liquid Film ◽  
Stretching Sheet ◽  
Temperature Fields ◽  
Temperature Profiles ◽  
Suction Parameter ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

An analysis has been carried out to study the flow and heat transfer in a liquid film over a permeable stretching sheet. Using similarity transformations, the time-dependent boundary layer equations are reduced to a set of nonlinear ordinary differential equations. The resulting parameter problem and velocity as well as temperature fields are solved using the homotopy analysis method (HAM). Analytic series solutions are given, and numerical results for velocity and the temperature profiles are presented through graphs of different values for pertinent parameter. The effects of unsteadiness parameter and permeability parameter on the velocity and temperature profiles are explored for different values of blowing or suction parameter.

Unsteady Flow of Third Grade Fluid With Soret and Dufour Effects

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
T. Hayat ◽  
M. Awais ◽  
S. Asghar ◽  
S. Obaidat
Keyword(s):  
Unsteady Flow ◽  
Temperature Fields ◽  
Third Grade ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Soret And Dufour Effects ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Homotopy Analysis ◽  
Grade Fluid

Unsteady flow of a third grade fluid in the presence of Soret and Dufour effects is considered. Employing similarity transformations, the governing equation for the velocity, concentration, and temperature fields is presented. The computations for the corresponding problems are performed by using a homotopy analysis method (HAM). The associated behavior of the flow parameters is discussed and important conclusions have been pointed out.

MHD Flow of an Oldroyd-B Fluid Through a Porous Channel

2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Meraj Mustafa ◽  
Awatif Hendi
Keyword(s):  
Analytic Solution ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Porous Channel ◽  
Analysis Method ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Number Comparison ◽  
Homotopy Analysis ◽  
Layer Flow

This paper discusses the hydromagnetic boundary layer flow of an Oldroyd-B fluid in a porous channel. Both suction and injection (blowing) cases are considered. Appropriate similarity transformations are invoked to convert the partial differential equations into ordinary ones. Homotopy analysis method (HAM) is used for the presentation of analytic solution of the nonlinear differential system. Graphical results provide the salient features of the embedded flow parameters which include the Reynolds number, the Deborah numbers, and the Hartman number. Comparison between the existing numerical solution in a Maxwell fluid and present deduced series solution in a limiting sense is excellent.

scholarly journals A Framework for the Magnetic Dipole Effect on the Thixotropic Nanofluid Flow Past a Continuous Curved Stretched Surface

Crystals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 645
Author(s):  
Noor Saeed Khan ◽  
Auwalu Hamisu Usman ◽  
Arif Sohail ◽  
Abid Hussanan ◽  
Qayyum Shah ◽  
...  
Keyword(s):  
Magnetic Dipole ◽  
Radiation Effects ◽  
Analysis Method ◽  
Governing Equations ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Nanoparticles Concentration

The magnetic dipole effect for thixotropic nanofluid with heat and mass transfer, as well as microorganism concentration past through a curved stretching surface, is discussed. The flow is in a porous medium, which describes the Darcy–Forchheimer model. Through similarity transformations, the governing equations of the problem are transformed into non-linear ordinary differential equations, which are then processed using an efficient and powerful method known as the homotopy analysis method. All the embedded parameters are considered when analyzing the problem through solution. The dipole and porosity effects reduce the velocity, while the thixotropic nanofluid parameter increases the velocity. Through the dipole and radiation effects, the temperature is enhanced. The nanoparticles concentration increases as the Biot number and curvature, solutal, chemical reaction parameters increase, while it decreases with increasing Schmdt number. The microorganism motile density decreases as the Peclet and Lewis numbers increase. Streamlines demonstrate that the trapping on the curved stretched surface is uniform.

scholarly journals A New Approach for the Solution of Three-Dimensional Magnetohydrodynamic Rotating Flow over a Shrinking Sheet

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Three Dimensional ◽  
Rotating Flow ◽  
Shrinking Sheet ◽  
Analysis Method ◽  
Governing Equations ◽  
New Approach ◽  
Homotopy Analysis ◽  
Stress Variations ◽  
Spectral Homotopy Analysis Method ◽  
Good Agreement

The numerical solution of magnetohydrodynamic (MHD) and rotating flow over a porous shrinking sheet is obtained by the new approach known as spectral homotopy analysis method (SHAM). Using a similarity transformation, the governing equations for the momentum are reduced to a set of ordinary differential equations and are solved by the SHAM approach to determine velocity distributions and shear stress variations for different governing parameters. The SHAM results are analysed and validated against numerical results obtained using MATLAB's built-inbvp4croutine, and good agreement is observed.

Homotopy Analysis Method for Radiation and Hydrodynamic-Thermal Slips Effects on MHD Flow and Heat Transfer Impinging on Stretching Sheet

2018 ◽  
Vol 388 ◽  
pp. 317-327 ◽  
Author(s):  
Fazle Mabood ◽  
Giulio Lorenzini ◽  
Nopparat Pochai ◽  
Stanford Shateyi
Keyword(s):  
Heat Transfer ◽  
Thermal Radiation ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Published Data ◽  
Analysis Method ◽  
Flow And Heat Transfer ◽  
Special Cases ◽  
Homotopy Analysis

This article deals with the analytical study of MHD flow and heat transfer over a permeable stretching sheet via homotopy analysis method (HAM). The effect of thermal radiation is included in the energy equation, while velocity and thermal slips are included in the boundary conditions. The governing boundary layer equations are transformed into a set of ordinary differential equations by means of similarity transformations. The effects of different parameters on the flow field and heat transfer characteristics are examined. The results obtained were shown to compare well with the numerical results and for some special cases with the published data available in the literature, which are in favorable agreement. Keywords: MHD; Slip flow; Stretching sheet; Thermal radiation; Homotopy analysis method

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