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.

Analytic Solution for the Magnetohydrodynamic Rotating Flow of Jeffrey Fluid in a Channel

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
T. Hayat ◽  
M. Awais ◽  
S. Asghar ◽  
Awatif A. Hendi
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Rotating System ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
Homotopy Analysis

In this work, the homotopy analysis method is applied to enable discussion of the three-dimensional shrinking flow of Jeffrey fluid in a rotating system. The fluid is electrically conducting in the presence of a uniform applied magnetic field, and the induced magnetic field is neglected. The similarity transformations reduce the nonlinear partial differential equations into ordinary differential equations. The convergence of the obtained solutions is checked. Graphs are plotted and discussed for various parameters of interest.

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.

Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

2010 ◽  
Vol 65 (11) ◽  
pp. 935-949 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian ◽  
Abbas Saadatmandi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Analysis Method ◽  
Partial Differential ◽  
Integer Order ◽  
Homotopy Analysis

In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

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