Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Lie Group Symmetry Analysis Of Transport In Porous Media With Variable Transmissivity, James Hill, Maureen Edwards, A P S Selvadurai
Lie Group Symmetry Analysis Of Transport In Porous Media With Variable Transmissivity, James Hill, Maureen Edwards, A P S Selvadurai
Dr Maureen Edwards
We determine the Lie group symmetries of the coupled partial differential equations governing a novel problem for the transient flow of a fluid containing a solidifiable gel, through a hydraulically isotropic porous medium. Assuming that the permeability ($K^*$) of the porous medium is a function of the gel concentration ($c^*$), we determine a number of exact solutions corresponding to the cases where the concentration-dependent permeability is either arbitrary or has a power law variation or is a constant. Each case admits a number of distinct Lie symmetries and the solutions corresponding to the optimal systems are determined. Some typical concentration …