Actually, I got some temperature vs time graph for simple water samples. I need to get the thermal conductivity of those water samples only with that temperature-time profile.
The thermal conductivity for a given fluid is a function of temperature. For water, you may find tabulated values in the annex of heat transfer textbooks (for example Incropera). You need then to interpolate in order to find the conductivity corresponding to the desired temperature.
I would equally like to estimate thermal conductivity from temperate profiles measured during a given duration. I measured temperature profiles of soil material exposed to source of heat during 8 hour period