An explicit analytic solution for free convection about a vertical flat plate embedded in a porous medium by means of homotopy analysis method

We apply a new kind of analytic technique, namely the homotopy analysis method (HAM), to give an explicit, totally analytic, uniformly valid solution of the two-dimensional laminar viscous flow over a semi-infinite flat plate governed by f‴(η)+αf(η)f″(η)+β[1−f′2(η)]=0 under the boundary conditions f(0)=f′(0)=0, f′(+∞)=1. This analytic solution is uniformly valid in the whole region 0[les ]η<+∞. For Blasius' (1908) flow (α=1/2, β=0), this solution converges to Howarth's (1938) numerical result and gives a purely analytic value f″(0)=0.332057. For the Falkner–Skan (1931) flow (α=1), it gives the same family of solutions as Hartree's (1937) numerical results and a related analytic formula for f″(0) when 2[ges ]β[ges ]0. Also, this analytic solution proves that when −0.1988[les ]β0 Hartree's (1937) family of solutions indeed possess the property that f′→1 exponentially as η→+∞. This verifies the validity of the homotopy analysis method and shows the potential possibility of applying it to some unsolved viscous flow problems in fluid mechanics.

Download Full-text

ON ACCELERATED FLOWS OF MAGNETOHYDRODYNAMIC THIRD GRADE FLUID IN A POROUS MEDIUM AND ROTATING FRAME VIA A HOMOTOPY ANALYSIS METHOD

Journal of Porous Media ◽

10.1615/jpormedia.v17.i11.30 ◽

2014 ◽

Vol 17 (11) ◽

pp. 969-981

Author(s):

Mojtaba Nazari ◽

Zainal Abdul Aziz ◽

Faisal Salah

Keyword(s):

Porous Medium ◽

Homotopy Analysis Method ◽

Third Grade ◽

Rotating Frame ◽

Analysis Method ◽

Third Grade Fluid ◽

Homotopy Analysis ◽

Grade Fluid

Download Full-text

An efficient analytic approach for solving Hiemenz flow through a porous medium of a non-Newtonian Rivlin-Ericksen fluid with heat transfer

Nonlinear Engineering ◽

10.1515/nleng-2017-0160 ◽

2018 ◽

Vol 7 (4) ◽

pp. 287-301

Author(s):

Kourosh Parand ◽

Yasaman Lotfi ◽

Jamal Amani Rad

Keyword(s):

Heat Transfer ◽

Porous Medium ◽

Homotopy Analysis Method ◽

Nonlinear Differential Equations ◽

Analytic Method ◽

Analysis Method ◽

Wide Range ◽

Hiemenz Flow ◽

Homotopy Analysis ◽

Flow Through

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.

Download Full-text