scholarly journals On Combined Effects of Heat Transfer and Chemical Reaction for the Flow through an Asymmetric Channel with Orthogonally Deformable Porous Walls

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Naveed Ahmed ◽  
Umar Khan ◽  
Asif Waheed ◽  
Saqib Hussain ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Chemical Reaction ◽  
Residual Error ◽  
Combined Effects ◽  
Asymmetric Channel ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Flow Through ◽  
Optimal Values ◽  
Porous Walls

The combined effects of heat transfer and chemical reaction are studied for the flow through a semi-infinite asymmetric channel with orthogonally deformable porous walls. The similarity transforms have been used to reduce the conservation laws to a corresponding system of nonlinear ordinary differential equations. The resulting equations are solved, both analytically and numerically, by using Homotopy Analysis Method (HAM) and the fourth-order Runge-Kutta (RK-4) method, respectively. The convergence of the analytical solution is assured through the so-called total squared residual error analysis. The optimal values of auxiliary parameters are obtained by minimizing the total squared residual error.

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

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.

scholarly journals Homotopy Analysis Solution for Magnetohydrodynamic Squeezing Flow in Porous Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan ◽  
Mubashir Qayyum
Keyword(s):  
Porous Medium ◽  
Control Parameter ◽  
Analytical Techniques ◽  
Squeezing Flow ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Flow Through ◽  
Convergence Control Parameter ◽  
Good Agreement

The aim of the present work is to analyze the magnetohydrodynamic (MHD) squeezing flow through porous medium using homotopy analysis method (HAM). Fourth-order boundary value problem is modeled through stream functionψ(r,z)and transformationψ(r,z)=r2f(z). Absolute residuals are used to check the efficiency and consistency of HAM. Other analytical techniques are compared with the present work. It is shown that results of good agreement can be obtained by choosing a suitable value of convergence control parameterhin the valid regionRh. The influence of different parameters on the flow is argued theoretically as well as graphically.

scholarly journals Constructing analytic solutions on the Tricomi equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 143-148 ◽  
Author(s):  
Emran Khoshrouye Ghiasi ◽  
Reza Saleh
Keyword(s):  
Homotopy Analysis Method ◽  
Series Solution ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Tricomi Equation ◽  
Homotopy Analysis ◽  
Optimal Values

AbstractIn this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

Predictor homotopy analysis method for nanofluid flow through expanding or contracting gaps with permeable walls

2015 ◽  
Vol 08 (04) ◽  
pp. 1550050 ◽  
Author(s):  
Navid Freidoonimehr ◽  
Behnam Rostami ◽  
Mohammad Mehdi Rashidi
Keyword(s):  
Homotopy Analysis Method ◽  
Volume Fraction ◽  
Expansion Ratio ◽  
Analysis Method ◽  
Nanofluid Flow ◽  
Analytical Technique ◽  
Study Results ◽  
Permeable Walls ◽  
Homotopy Analysis ◽  
Flow Through

In this paper a definitely new analytical technique, predictor homotopy analysis method (PHAM), is employed to solve the problem of two-dimensional nanofluid flow through expanding or contracting gaps with permeable walls. Moreover, comparison of the PHAM results with numerical results obtained by the shooting method coupled with a Runge–Kutta integration method as well as previously published study results demonstrates high accuracy for this technique. The fluid in the channel is water containing different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The effects of the nanoparticle volume fraction, Reynolds number, wall expansion ratio, and different types of nanoparticles on the flow are discussed.

scholarly journals Falkner-Skan Flow of a Maxwell Fluid with Heat Transfer and Magnetic Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Qasim ◽  
S. Noreen
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Prandtl Number ◽  
Comparative Study ◽  
Homotopy Analysis Method ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Analysis Method ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

This investigation deals with the Falkner-Skan flow of a Maxwell fluid in the presence of nonuniform applied magnetic fi…eld with heat transfer. Governing problems of flow and heat transfer are solved analytically by employing the homotopy analysis method (HAM). Effects of the involved parameters, namely, the Deborah number, Hartman number, and the Prandtl number, are examined carefully. A comparative study is made with the known numerical solution in a limiting sense and an excellent agreement is noted.

Nonlinear study of heat transfer in nanofluid saturated horizontal porous medium

2017 ◽  
Vol 3 (01) ◽  
Author(s):  
Alok Srivastava ◽  
Vineet Kumar ◽  
B. S. Bhadauria ◽  
I. Hashimt
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Landau Equation ◽  
High Accuracy ◽  
Analysis Method ◽  
Nonlinear Stability Analysis ◽  
Governing Equations ◽  
Ginzburg Landau ◽  
Homotopy Analysis ◽  
Saturated Porous Layer

The present paper deals with weak nonlinear stability analysis of heat transfer in a nanofluid saturated porous layer. We consider a set of new boundary conditions for the nanoparticle fraction, which is physically more realistic. The new boundary condition is based on the assumption that the nanoparticle fraction adjusts itself so that the nanoparticle flux is zero on the boundaries. We use Darcy model that incorporates the effects of Brownian motion and thermophoresis. The governing equations has been reduced to Ginzburg-Landau equation and solved by homotopy analysis method (HAM). The obtained results have been compared with the numerical results obtained by Mathematica NDSolve. The results are valid for the feasible domain with high accuracy. Thermal Nusselt number and Nanoparticle Nusselt number are calculated for different values of parameters. The results have been depicted graphically.

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