Mathematical Problems in Engineering
Volume 2004 (2004), Issue 3, Pages 185-195

An analytical solution of the generalized equation of energy transport in one-dimensional semi-infinite domains

Vladimir V. Kulish

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.


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.