Mathematical Problems in Engineering
Volume 2004 (2004), Issue 3, Pages 185-195
doi:10.1155/S1024123X0440307X
An analytical solution of the generalized equation of energy transport in one-dimensional semi-infinite domains
School of Mechanical and Production Engineering, Nanyang Technological University, 639798, Singapore
Received 23 March 2004; Revised 28 April 2004
Copyright © 2004 Vladimir V. Kulish. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper presents an integral solution of the
generalized one-dimensional equation of energy transport
with the convective term.The solution of the problem has been
achieved by the use of a novel technique that involves
generalized derivatives (in particular, derivatives of noninteger
orders). Confluent hypergeometric functions, known as Whittaker's
functions, appear in the course of the solution procedure upon
applying the Laplace transform to the original transport
equation.The analytical solution of the problem is written in
the integral form and provides a relationship between the
local values of the transported property (e.g.,
temperature, mass, momentum, etc.) and its flux.The solution is
valid everywhere within the domain, including the domain boundary.