Abstract
The similarity transformation is introduced for studying free boundary value problems for a class of generalized convection-diffusion equation. A class of singular nonlinear boundary value problems are obtained and solved by using Adomian decomposition method (ADM). The approximate solution can be expressed in terms of a rapid convergent power series with easily computable terms. The efficiency and reliability of the approximate solution are verified by numerical ones. The effects of the variable thermal conduction k(z), convection functional coefficient h(z), power law exponent n, and parameter α on the flux transport characteristics are presented graphically and analyzed in detail.
Highlights
Convection-diffusion equation is a class of very important equations; it often appears in many research fields such as hydrodynamics, transport, electronics, energy, and environmental science [1–4]
Others focus on the numerical solution of the convection-diffusion equation by all kinds of methods, for instance, the spectral element method [14], the finite element method [15–17], the finite difference method [18, 19], and the Runge-Kutta method [20]
In this paper we present similarity solutions for generalized convection-diffusion equation with free boundary conditions, which are solved using Adomian decomposition method (ADM)
Summary
Convection-diffusion equation is a class of very important equations; it often appears in many research fields such as hydrodynamics, transport, electronics, energy, and environmental science [1–4]. Some scholars consider the existence, uniqueness, or nonuniqueness of solutions for the convection-diffusion equations (for example, see [5–13]). The very important approximate solution [21, 22] of convection-diffusion equation has not been well solved. In this paper we present similarity solutions for generalized convection-diffusion equation with free boundary conditions, which are solved using ADM. ADM [23–25] has been shown as a useful way of obtaining accurate and computable solutions to operator equations involving nonlinear terms. The characteristic of ADM is to decompose the nonlinear terms in the equations into a peculiar series of polynomials which are the so-called Adomian polynomials. The solution of the equations is considered as the sum of a series rapidly converging to an accurate solution. The effects of the convection functional coefficient h(z), variable thermal conduction k(z), and power law index n on the flux transport characteristics are discussed by graph in detail
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