ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
An integral solution method based on the concept of the direct boundary element technique has been applied to develop a solution procedure for problems of diffusion with a non-linear reaction in one dimension. The non-linearity is handled by a process of quasi-linearization over subintervals or elements in the main domain of integration. The weighting functions are defined for each subinterval such that the discretization is exact for the corresponding linear problem. This leads to a new powerful and simple method for the solution of this class of problems. A banded global matrix is obtained with both the concentration and its gradient as the unknown variables, and the problem is solved in an iterative manner. Illustrative results are presented for a test problem of diffusion with a second order reaction in an infinite slab, an infinite cylinder and spherical geometries. The accuracy of the method for situations with a sharp concentration gradient is demonstrated. The technique can also be used to numerically compute the solution in the boundary layer for fast reactions.
Additional Material:
5 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620290508
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