Analysis of Forced Convection in a Circular Tube Filled With a Darcy–Brinkman–Forchheimer Porous Medium Using Spectral Homotopy Analysis Method

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
Seyed Moein Rassoulinejad-Mousavi ◽  
Saeid Abbasbandy
Keyword(s):  
Porous Medium ◽  
Forced Convection ◽  
Homotopy Analysis Method ◽  
Circular Tube ◽  
Darcy Number ◽  
Uniform Heat Flux ◽  
Analysis Method ◽  
Wide Range ◽  
Homotopy Analysis ◽  
Spectral Homotopy Analysis Method

This paper provides a fresh analytical solution for fully developed forced convection through a Darcy–Brinkman–Forchheimer porous medium imbedded inside a circular tube, with imposed uniform heat flux at walls. A spectral homotopy analysis method is applied to present a solution which spans a wide range of the main parameters (the Darcy number (Da), viscosity ratio (M), and Forchheimer number (F)). The analytical results are compared with data available in the literature, and excellent agreement is found. The paper is capable of addressing the problem in a general porous medium for which both inertial and boundary-friction effects affect the flow and heat transfer physics. In order to serve this aim, the influence of Da, M, and F on the dimensionless velocity and temperature profiles, as well as Nusselt number, are investigated.

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.

Analytical Solution of Forced Convection in a Duct of Rectangular Cross Section Saturated by a Porous Medium

2005 ◽  
Vol 128 (6) ◽  
pp. 596-600 ◽  
Author(s):  
Kamel Hooman ◽  
Ali A. Merrikh
Keyword(s):  
Porous Medium ◽  
Forced Convection ◽  
Cross Section ◽  
Viscosity Ratio ◽  
Rectangular Cross Section ◽  
Darcy Number ◽  
Uniform Heat Flux ◽  
Brinkman Model ◽  
Type Solution ◽  
Series Type

A theoretical analysis is presented to investigate thermally and hydrodynamically fully developed forced convection in a duct of rectangular cross section filled with a hyper-porous medium. The Darcy-Brinkman model was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e., the H boundary condition in the terminology of Kays and Crawford (1993, Convective Heat and Mass Transfer, 3rd ed., McGraw-Hill, NY), is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

scholarly journals On Spectral Homotopy Analysis Method for Solving Linear Volterra and Fredholm Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Z. Pashazadeh Atabakan ◽  
A. Kılıçman ◽  
A. Kazemi Nasab
Keyword(s):  
Exact Solutions ◽  
Homotopy Analysis Method ◽  
Integrodifferential Equations ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Spectral Homotopy Analysis Method

A modification of homotopy analysis method (HAM) known as spectral homotopy analysis method (SHAM) is proposed to solve linear Volterra integrodifferential equations. Some examples are given in order to test the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to SHAM results and exact solutions.

scholarly journals Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Z. Pashazadeh Atabakan ◽  
A. Kazemi Nasab ◽  
A. Kılıçman ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Existence And Uniqueness ◽  
Lagrange Interpolation ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Uniqueness Of The Solution ◽  
Spectral Homotopy Analysis Method

Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

scholarly journals Numerical Solutions of Heat Transfer for Magnetohydrodynamic Jeffery-Hamel Flow Using Spectral Homotopy Analysis Method

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 626 ◽  
Author(s):  
Asad Mahmood ◽  
Md Md Basir ◽  
Umair Ali ◽  
Mohd Mohd Kasihmuddin ◽  
Mohd. Mansor
Keyword(s):  
Heat Transfer ◽  
Temperature Profile ◽  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Reynold Number ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear Differential ◽  
Spectral Homotopy Analysis Method

This paper studies heat transfer in a two-dimensional magnetohydrodynamic viscous incompressible flow in convergent/divergent channels. The temperature profile was obtained numerically for both cases of convergent/divergent channels. It was found that the temperature profile increases with an increase in Reynold number, Prandtl number, Nusselt number and angle of the wall but decreases with an increase in Hartmann number. A relatively new numerical method called the spectral homotopy analysis method (SHAM) was used to solve the governing non-linear differential equations. The SHAM 3rd order results matched with the DTM and shooting, showing that SHAM is feasible as a technique to be used.

scholarly journals On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. S. Motsa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Analysis Method ◽  
Partial Differential ◽  
New Approach ◽  
Homotopy Analysis ◽  
Spectral Homotopy Analysis Method

This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.

A new spectral-homotopy analysis method for the MHD Jeffery–Hamel problem

2010 ◽  
Vol 39 (7) ◽  
pp. 1219-1225 ◽  
Author(s):  
S.S. Motsa ◽  
P. Sibanda ◽  
F.G. Awad ◽  
S. Shateyi
Keyword(s):  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Spectral Homotopy Analysis Method
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