P. G. Department of Chemistry, Bhagalpur University, Bhagalpur-812 007 Manuscript received 12 April 1979, revised 31 March 7980, accepted 25 August 1980 An attempt has been made to obtain a non-linear phenomenological relation between fluxes and forces for the mass transport of matter and the transport of heat energy in thermo-osmosis as viewed from the physical parameters of the classical theory. Poiseuilleasn flow for fluids (liquids and gases) through membrane capillaries has been taken into consideration for such an attempt. Occurrences of higher order symmetries have also been examined and observed in the present study.