The one dimensional time-dependant heat transfer equation in a vertical
direction is introduced in terms of general formula of density and
thermal conductivity. One-parameter Lie symmetry group transformation is
used to determine the suitable forms of density and thermal conductivity
of the water based on experimental measurements. The general equation is
investigated again using Lie group analysis after substitution by the
two possible cases of water density and thermal conductivity from the
first part. The obtained partial differential equation is solved
numerically using explicit 4th and 5th Runge-Kutta formula or
analytically if it is possible by assuming the physical parameters of
Lake Tahoe in the Sierra Nevada of the United States. The temperature
distribution across the lake depth from each case is illustrated
graphically to indicate the thermal stratification phenomenon of lakes.