Mathematical Problems in Engineering
Volume 2005 (2005), Issue 3, Pages 275-291

On modelling the drying of porous materials: analytical solutions to coupled partial differential equations governing heat and moisture transfer

Don Kulasiri1 and Ian Woodhead2

1Centre for Advanced Computational Solutions (C-fACS), Lincoln University, P.O. Box 84, Canterbury, New Zealand
2Lincoln Technology, Lincoln Ventures Ltd, Lincoln University, Canterbury, New Zealand

Received 10 August 2004; Revised 2 December 2004

Copyright © 2005 Don Kulasiri and Ian Woodhead. 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.


Luikov's theory of heat and mass transfer provides a framework to model drying porous materials. Coupled partial differential equations governing the moisture and heat transfer can be solved using numerical techniques, and in this paper we solve them analytically in a setting suitable for industrial drying situations. We discuss the nature of the solutions using the physical properties of Pinus radiata. It is shown that the temperature gradients play a significant role in deciding the moisture profiles within the material when thickness is large and that models based only on moisture potential gradients may not be sufficient to explain the drying phenomena in moist porous materials.