Access the full text.
Sign up today, get DeepDyve free for 14 days.
S. Kazem, J. Rad, K. Parand, S. Abbasbandy (2011)
A New Method for Solving Steady Flow of a Third-Grade Fluid in a Porous Half Space Based on Radial Basis FunctionsZeitschrift für Naturforschung A, 66
S. Liao (2010)
An optimal homotopy-analysis approach for strongly nonlinear differential equationsCommunications in Nonlinear Science and Numerical Simulation, 15
Muhammad Sajid, Muhammad Sajid, T. Hayat, S. Asghar (2007)
Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving beltNonlinear Dynamics, 50
Masood Khan, Zaheer Abbas, T. Hayat (2008)
Analytic solution for flow of Sisko fluid through a porous mediumTransport in Porous Media, 71
M. Shaban, S. Kazem, J. Rad (2013)
A modification of the homotopy analysis method based on Chebyshev operational matricesMath. Comput. Model., 57
Z. Ziabakhsh, G. Domairry, M. Mozaffari, M. Mahbobifar (2010)
Analytical solution of heat transfer over an unsteady stretching permeable surface with prescribed wall temperatureJournal of The Taiwan Institute of Chemical Engineers, 41
(1987)
Free convection heat transfer over a non-isothermal body of arbitrary shape embedded in a fluid saturated porous media
K. Parand, S. Abbasbandy, S. Kazem, J. Rad (2011)
A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equationCommunications in Nonlinear Science and Numerical Simulation, 16
A. Nakayama, H. Koyama (1987)
Free Convective Heat Transfer Over a Nonisothermal Body of Arbitrary Shape Embedded in a Fluid-Saturated Porous MediumJournal of Heat Transfer-transactions of The Asme, 109
Z. Ziabakhsh, G. Domairry, H. Bararnia, H. Babazadeh (2010)
Analytical solution of flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous mediumJournal of The Taiwan Institute of Chemical Engineers, 41
T. Hayat, N. Ahmed, M. Sajid, S. Asghar (2007)
On the MHD flow of a second grade fluid in a porous channelComput. Math. Appl., 54
S. Kazem, M. Shaban, J. Rad (2012)
Solution of the Coupled Burgers Equation Based on Operational Matrices of d-Dimensional Orthogonal FunctionsZeitschrift für Naturforschung A, 67
H. Attia (2009)
HIEMENZ FLOW THROUGH A POROUS MEDIUM OF A NON-NEWTONIAN RIVLIN-ERICKSEN FLUID WITH HEAT TRANSFER, 12
L. Soltani, E. Shivanian, R. Ezzati (2016)
Convection–radiation heat transfer in solar heat exchangers filled with a porous medium: Exact and shooting homotopy analysis solutionApplied Thermal Engineering, 103
S. Abbasbandy, D. Modarrespoor, K. Parand, J. Rad (2013)
Analytical solution of the transpiration on the boundary layer flow and heat transfer over a vertical slender cylinderQuaestiones Mathematicae, 36
(2013)
A modi cation of the homotopy analysis method based on Chebyshev operational matri
S. Liao, Y. Tan (2007)
A General Approach to Obtain Series Solutions of Nonlinear Differential EquationsStudies in Applied Mathematics, 119
K. Parand, Y. Lotfi, Jamal Rad (2017)
An accurate numerical analysis of the laminar two-dimensional flow of an incompressible Eyring-Powell fluid over a linear stretching sheetThe European Physical Journal Plus, 132
K. Parand, Sayyed-Ali Hossayni, J. Rad (2016)
Operation matrix method based on Bernstein polynomials for the Riccati differential equation and Volterra population modelApplied Mathematical Modelling, 40
F. Awawdeh, A. Adawi, Z. Mustafa (2009)
Solutions of the SIR models of epidemics using HAMChaos Solitons & Fractals, 42
E. Shivanian, S. Abbasbandy (2014)
Predictor homotopy analysis method: Two points second order boundary value problemsNonlinear Analysis-real World Applications, 15
S. Abbasbandy, E. Shivanian (2010)
A new analytical technique to solve Fredholm’s integral equationsNumerical Algorithms, 56
J. Rad, S. Ghaderi, K. Parand (2011)
Numerical and Analytical Solution of Gas Flow Through a Micro-Nano Porous Media: A ComparisonJournal of Computational and Theoretical Nanoscience, 8
S. Abbasbandy, E. Shivanian (2011)
Predictor homotopy analysis method and its application to some nonlinear problemsCommunications in Nonlinear Science and Numerical Simulation, 16
Mohammad Rashidi, G. Domairry, S. Dinarvand (2009)
Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis methodCommunications in Nonlinear Science and Numerical Simulation, 14
F. Allan (2007)
Derivation of the Adomian decomposition method using the homotopy analysis methodAppl. Math. Comput., 190
I. Liu (2005)
Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic fieldInternational Journal of Non-linear Mechanics, 40
S. Abbasbandy (2008)
Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis methodChemical Engineering Journal, 136
S. Abbasbandy, E. Babolian, M. Ashtiani (2009)
Numerical solution of the generalized Zakharov equation by homotopy analysis methodCommunications in Nonlinear Science and Numerical Simulation, 14
M. Seddeek (2005)
Effects of non-Darcian on forced convection heat transfer over a flat plate in a porous medium-with temperature dependent viscosityInternational Communications in Heat and Mass Transfer, 32
T. Hayat, T. Javed (2007)
On analytic solution for generalized three-dimensional MHD flow over a porous stretching sheetPhysics Letters A, 370
A. Alizadeh-Pahlavan, K. Sadeghy (2009)
On the use of homotopy analysis method for solving unsteady MHD flow of Maxwellian fluids above impulsively stretching sheetsCommunications in Nonlinear Science and Numerical Simulation, 14
S. Abbasbandy, E. Magyari, E. Shivanian (2009)
The homotopy analysis method for multiple solutions of nonlinear boundary value problemsCommunications in Nonlinear Science and Numerical Simulation, 14
T. Hayat, Arshia Yousaf, M. Mustafa, S. Obaidat (2012)
MHD squeezing flow of second‐grade fluid between two parallel disksInternational Journal for Numerical Methods in Fluids, 69
F. Allan (2009)
Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis methodChaos Solitons & Fractals, 39
(1992)
The proposed homotopy analysis technique for the solution of nonlinear problems
(2017)
Shooting homotopy analysis method: A fast method to nd multiple solutions of nonlinear boundary value problems arising in fluid mechanics
R. Ellahi, E. Shivanian, S. Abbasbandy, T. Hayat (2016)
Numerical study of magnetohydrodynamics generalized Couette flow of Eyring-Powell fluid with heat transfer and slip conditionInternational Journal of Numerical Methods for Heat & Fluid Flow, 26
S. Liao (2003)
On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheetJournal of Fluid Mechanics, 488
S. Abbasbandy, A. Shirzadi (2011)
A new application of the homotopy analysis method: Solving the Sturm–Liouville problemsCommunications in Nonlinear Science and Numerical Simulation, 16
S. Abbasbandy (2006)
THE APPLICATION OF HOMOTOPY ANALYSIS METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFERPhysics Letters A, 360
Mohammad Rashidi, S. Dinarvand (2009)
Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis methodNonlinear Analysis-real World Applications, 10
O. Abdulaziz, N. Noor, I. Hashim (2009)
Homotopy analysis method for fully developed MHD micropolar fluid flow between vertical porous platesInternational Journal for Numerical Methods in Engineering, 78
M. Massoudi, M. Ramezan (1992)
Heat transfer analysis of a viscoelastic fluid at a stagnation pointMechanics Research Communications, 19
Annie Nyander, P. Addison, I. McEwan, G. Pender (2003)
Analysis of river bed surface roughnesses using 2D wavelet transform-based methodsArabian Journal for Science and Engineering, 28
I. Hassanien, A. Bakier, R. Gorla (1998)
Effects of thermal dispersion and stratification on non-darcy mixed convection from a vertical plate in a porous mediumHeat and Mass Transfer, 34
V. Garg (1994)
Heat transfer due to stagnation point flow of a non-Newtonian fluidActa Mechanica, 104
S. Liao (1999)
An explicit, totally analytic approximate solution for Blasius’ viscous flow problemsInternational Journal of Non-linear Mechanics, 34
F. Homann (1936)
Der Einfluß großer Zähigkeit bei der Strömung um den Zylinder und um die KugelZamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 16
T. Hayat, M. Sajid (2007)
Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheetInternational Journal of Heat and Mass Transfer, 50
S. Abbasbandy, E. Shivanian, K. Vajravelu (2011)
Mathematical properties of ℏ-curve in the frame work of the homotopy analysis methodCommunications in Nonlinear Science and Numerical Simulation, 16
T. Hayat, R. Naz, S. Abbasbandy (2011)
Poiseuille Flow of a Third Grade Fluid in a Porous MediumTransport in Porous Media, 87
(1996)
E ects of thermal dispersion and strati cation on combined convection on a vertical surface embedded in a porous medium
A. Alomari, M. Noorani, R. Nazar, Changpin Li (2010)
Homotopy analysis method for solving fractional Lorenz systemCommunications in Nonlinear Science and Numerical Simulation, 15
P. Hilton (1953)
An Introduction to Homotopy Theory
Z. Ziabakhsh, G. Domairry (2009)
Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the homotopy analysis methodCommunications in Nonlinear Science and Numerical Simulation, 14
J. Rad, K. Parand (2014)
Numerical pricing of American options under two stochastic factor models with jumps using a meshless local Petrov-Galerkin methodArXiv, abs/1412.6064
S. Abbasbandy, E. Shivanian (2010)
Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis methodCommunications in Nonlinear Science and Numerical Simulation, 15
K. Yih (1998)
The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous mediaActa Mechanica, 130
H. Attia (2003)
HYDROMAGNETIC STAGNATION POINT FLOW WITH HEAT TRANSFER OVER A PERMEABLE SURFACE
X. Ran, Q. Zhu, Yi Li (2009)
An explicit series solution of the squeezing flow between two infinite plates by means of the homotopy analysis methodCommunications in Nonlinear Science and Numerical Simulation, 14
T. Hayat, M. Sajid, M. Ayub (2007)
A note on series solution for generalized Couette flowCommunications in Nonlinear Science and Numerical Simulation, 12
S. Liao, S. Sherif (2003)
Beyond Perturbation: Introduction to the Homotopy Analysis Method
F. Allan, M. Syam (2005)
On the analytic solutions of the nonhomogeneous Blasius problemJournal of Computational and Applied Mathematics, 182
S. Liao (2005)
Comparison between the homotopy analysis method and homotopy perturbation methodAppl. Math. Comput., 169
S. Liao (1999)
AN EXPLICIT TOTALLY ANALYTIC APPROXIMATION OF BLASIUS VISCOUS FLOW PROBLEMS, 34
(1998)
The e ect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media
S. Liao (2004)
On the homotopy analysis method for nonlinear problemsAppl. Math. Comput., 147
L. Soltani, E. Shivanian, R. Ezzati (2017)
Shooting homotopy analysis methodEngineering Computations, 34
V. Garg, K. Rajagopal (1990)
Stagnation point flow of a non-Newtonian fluidMechanics Research Communications, 17
Karl Hiemenz
Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder
R. Gorla, A. Bakier, L. Byrd (1996)
Effects of thermal dispersion and stratification on combined convection on a vertical surface embedded in a porous mediumTransport in Porous Media, 25
P. Ariel (1994)
Hiemenz flow in hydromagneticsActa Mechanica, 103
(2005)
Flow and heat transfer of an electrically conducting fluid of second grade in porous medium over a stretching sheet subject to a transverse magnetic eld
(2005)
E ects of non-Darcian on forced convection heat transfer over a flat plate in a porous medium with temper- ature dependent viscosity
T. Hayat, Z. Abbas (2008)
Heat transfer analysis on the MHD flow of a second grade fluid in a channel with porous mediumChaos Solitons & Fractals, 38
(1999)
An explicit
R. Ellahi, E. Shivanian, S. Abbasbandy, S. Rahman, T. Hayat (2012)
Analysis of steady flows in viscous fluid with heat/mass transfer and slip effectsInternational Journal of Heat and Mass Transfer, 55
T. Hayat, Z. Iqbal, M. Sajid, K. Vajravelu (2008)
Heat transfer in pipe flow of a Johnson-Segalman fluidInternational Communications in Heat and Mass Transfer, 35
T. Hayat, M. Qasim, Z. Abbas (2010)
Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous spaceCommunications in Nonlinear Science and Numerical Simulation, 15
(2011)
Mathematical properties of h-curve in the frame work of the homotopy analysis method
M. Sajid, Asim Siddiqui, T. Hayat (2007)
Wire coating analysis using MHD Oldroyd 8-constant fluidInternational Journal of Engineering Science, 45
AbstractIn the present work, the problem of Hiemenz flow through a porous medium of a incompressible non-Newtonian Rivlin-Ericksen fluid with heat transfer is presented and newly developed analytic method, namely the homotopy analysis method (HAM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This flow impinges normal to a plane wall with heat transfer. It has been attempted to show capabilities and wide-range applications of the homotopy analysis method in comparison with the numerical method in solving this problem. Also the convergence of the obtained HAM solution is discussed explicitly. Our reports consist of the effect of the porosity of the medium and the characteristics of the Non-Newtonian fluid on both the flow and heat.
Nonlinear Engineering – de Gruyter
Published: Dec 19, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.