کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
151235 456465 2011 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An analytical method to solve a general class of nonlinear reactive transport models
موضوعات مرتبط
مهندسی و علوم پایه مهندسی شیمی مهندسی شیمی (عمومی)
پیش نمایش صفحه اول مقاله
An analytical method to solve a general class of nonlinear reactive transport models
چکیده انگلیسی

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term, R(C) = ϕ2Cn, only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Chemical Engineering Journal - Volume 169, Issues 1–3, 1 May 2011, Pages 313–318
نویسندگان
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