Journal ArticleDOI
Analytic solutions of the temperature distribution in Blasius viscous flow problems
Shijun Liao,Antonio Campo +1 more
TLDR
In this article, the homotopy analysis method is applied to give an analytic approximation of temperature distributions for a laminar viscous flow over a semi-infinite plate.Abstract:
We apply a new analytic technique, namely the homotopy analysis method, to give an analytic approximation of temperature distributions for a laminar viscous flow over a semi-infinite plate. An explicit analytic solution of the temperature distributions is obtained in general cases and recurrence formulae of the corresponding constant coefficients are given. In the cases of constant plate temperature distribution and constant plate heat flux, the first-order derivative of the temperature on the plate at the 30th order of approximation is given. The convergence regions of these two formulae are greatly enlarged by the Pade technique. They agree well with numerical results in a very large region of Prandtl number 1[les ]Pr[les ]50 and therefore can be applied without interpolations.read more
Citations
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Journal ArticleDOI
On the homotopy analysis method for nonlinear problems
TL;DR: A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e. the algebraically decaying viscous boundary layer flow due to a moving sheet.
Book
Homotopy Analysis Method in Nonlinear Differential Equations
TL;DR: In this paper, a convergence series for Divergent Taylor Series is proposed to solve nonlinear initial value problems and nonlinear Eigenvalue problems with free or moving boundary in heat transfer.
Journal ArticleDOI
On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet
TL;DR: In this paper, the homotopy analysis method is employed to give analytic solutions of magnetohydrodynamic viscous flows of non-Newtonian fluids over a stretching sheet.
Journal ArticleDOI
Solving nonlinear fractional partial differential equations using the homotopy analysis method
TL;DR: In this paper, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations (FPDE) with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives, and the results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.
Journal ArticleDOI
The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions
Rahmat Ellahi,Rahmat Ellahi +1 more
TL;DR: In this article, the authors examined the magnetohydrodynamic flow of non-Newtonian nanofluid in a pipe and derived explicit analytical expressions for the velocity field, the temperature distribution and nano concentration.
References
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Book
Perturbation Methods
Ali H. Nayfeh,Vimal Singh +1 more
TL;DR: This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.
Book
Introduction to perturbation techniques
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Book
Multiple Scale and Singular Perturbation Methods
J. Kevorkian,Julian D. Cole +1 more
TL;DR: In this article, the authors present a model for singular boundary problems with variable coefficients and a method of multiple scale expansions for Ordinary Differential Equations (ODE) in the standard form.
Journal ArticleDOI
A kind of approximate solution technique which does not depend upon small parameters — II. An application in fluid mechanics
TL;DR: In this paper, the homotopy analysis method was further improved by introducing a non-zero parameter into the traditional way of constructing a homhotopy, which can converge even in the whole region η ϵ [0, + ∞].