Flow by a Porous Shrinking Surface in a Rotating Frame

2010 ◽  
Vol 65 (1-2) ◽  
pp. 45-52 ◽  
Author(s):  
Tasawar Hayat ◽  
Sania Iram ◽  
Tariq Javed ◽  
Saleem Asghar
Keyword(s):  
Differential Equations ◽  
Series Solution ◽  
Porous Plate ◽  
Frame Of Reference ◽  
Rotating Frame ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Derived Series ◽  
Shrinking Surface

AbstractWe derive series solution of a nonlinear problem which models the magnetohydrodynamic (MHD) shrinking flow due to a porous plate in a rotating frame of reference. The governing partial differential equations are first converted into ordinary differential equations and then solved by homotopy analysis method. The convergence of the derived series solution is carefully analyzed. Graphical results are presented to examine the role of various interesting parameters.

scholarly journals Approximate Solutions of Nonlinear Partial Differential Equations by Modifiedq-Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Shaheed N. Huseen ◽  
Said R. Grace
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Approximate Solutions ◽  
Power Series Solution ◽  
Analysis Method ◽  
Exactly Solvable ◽  
Homotopy Analysis

A modifiedq-homotopy analysis method (mq-HAM) was proposed for solvingnth-order nonlinear differential equations. This method improves the convergence of the series solution in thenHAM which was proposed in (see Hassan and El-Tawil 2011, 2012). The proposed method provides an approximate solution by rewriting thenth-order nonlinear differential equation in the form ofnfirst-order differential equations. The solution of thesendifferential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

Series Solution of the System of Integro-Differential Equations

2009 ◽  
Vol 64 (12) ◽  
pp. 811-818 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Elyas Shivanian
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

This investigation presents a mathematical model describing the homotopy analysis method (HAM) for systems of linear and nonlinear integro-differential equations. Some examples are analyzed to illustrate the ability of the method for such systems. The results reveal that this method is very effective and highly promising

scholarly journals Series Solution of the System of Fuzzy Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
M. S. Hashemi ◽  
J. Malekinagad ◽  
H. R. Marasi
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Solution Series ◽  
Homotopy Analysis ◽  
Contour Plots ◽  
And Control

The homotopy analysis method (HAM) is proposed to obtain a semianalytical solution of the system of fuzzy differential equations (SFDE). The HAM contains the auxiliary parameterħ, which provides us with a simple way to adjust and control the convergence region of solution series. Concept ofħ-meshes and contour plots firstly are introduced in this paper which are the generations of traditionalh-curves. Convergency of this method for the SFDE has been considered and some examples are given to illustrate the efficiency and power of HAM.

Analytic Solution of Three-Dimensional Viscous Flow and Heat Transfer Over a Stretching Flat Surface by Homotopy Analysis Method

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Ahmer Mehmood ◽  
Asif Ali
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Porous Plate ◽  
Three Dimensional ◽  
Parallel Plates ◽  
Analysis Method ◽  
Electrically Conducting ◽  
Homotopy Analysis

In this paper heat transfer in an electrically conducting fluid bonded by two parallel plates is studied in the presence of viscous dissipation. The plates and the fluid rotate with constant angular velocity about a same axis of rotation where the lower plate is a stretching sheet and the upper plate is a porous plate subject to constant injection. The governing partial differential equations are transformed to a system of ordinary differential equations with the help of similarity transformation. Homotopy analysis method is used to get complete analytic solution for velocity and temperature profiles. The effects of different parameters are discussed through graphs.

scholarly journals Effects of Heat Transfer on the Stagnation Flow of a Third-Order Fluid over a Shrinking Sheet

2010 ◽  
Vol 65 (11) ◽  
pp. 969-994 ◽  
Author(s):  
Sohail Nadeem ◽  
Anwar Hussain ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Shrinking Sheet ◽  
Analysis Method ◽  
Stagnation Flow ◽  
Third Order ◽  
Flow Problems ◽  
Homotopy Analysis ◽  
Shrinking Surface

This paper is devoted to the study of a stagnation point flow of an incompressible third-order fluid towards a shrinking sheet (with heat transfer). The governing nonlinear partial differential equations are reduced into nonlinear ordinary differential equations by means of a similarity transformation and then solved by the homotopy analysis method. Two types of flow problems, namely, (i) two dimensional stagnation flow toward a shrinking sheet and (ii) axisymmetric stagnation flow towards an axisymmetric shrinking surface have been discussed. Also, two types of boundary conditions are taken into account: (i) prescribed surface temperature (PST) and (ii) prescribed heat flux (PHF) case. The effects of various emerging parameters of non-Newtonian fluid have been investigated in detail and shown pictorically. The convergence of the solutions have been discussed through ¯h-curves and residual error. For further validity, the homotopy Pad´e approximation is also applied.

The Series Solution of Fractional Partial Differential Equations via Homotopy Analysis Method

2014 ◽  
Vol 530-531 ◽  
pp. 613-616
Author(s):  
Jia Ju Yu
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Analysis Method ◽  
Fractional Partial Differential Equations ◽  
Homotopy Analysis ◽  
Fractional Equation

In this letter, we apply the homotopy analysis method (HAM) to obtain analytical solution of the fractional equation where the fractional derivatives are Caputo sense. The example is given to show the efficiency of the method.

The Series Solution of Problems in the Calculus of Variations via the Homotopy Analysis Method

2009 ◽  
Vol 64 (1-2) ◽  
pp. 30-36 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Ahmand Shirzadi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Calculus Of Variations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Numerical Results ◽  
Analysis Method ◽  
Homotopy Analysis

The homotopy analysis method (HAM) is used for solving the ordinary differential equations which arise from problems of the calculus of variations. Some numerical results are given to demonstrate the validity and applicability of the presented technique. The method is very effective and yields very accurate results.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

Sign in / Sign up

Export Citation Format

Share Document