A generalized integral solution of the diffusion equation with the convection term
by
Vladimir V. Kulish
School of Mechanical & Production Engineering, Nanyang Technological University, Singapore 639798

The paper presents an analytical solution of the generalized diffusion equation. The energy equation (diffusion equation) with the convection term written for the case of different geometries (planar, spherical and cylindrical) has been used in the model. An analytical solution of the problem has been found by a novel technique that involves the use of derivatives of a non-integer order (fractional calculus). As a by-product of the solution procedure, a relationship between the local values of the diffusing property (temperature, concentration, momentum, etc.) and its flux has been derived. The integral equation that arises in the course of the solution procedure and relates the local values of the diffusing quantity and its flux in the Laplace space involves confluent hyper-geometric functions, known as Kummer’s functions. The solution thus obtained may be applied to a wide range of problems such as, for instance, boiling, alveolar gas diffusion, cosmological models, expansion of markets, viscous fluid flow, and information transfer in biological systems and society.

Date received: February 29, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakt-83.