  The concept of the theory of continuous groups of transformations has
attracted the attention of applied mathematicians and engineers to solve many
physical problems in the engineering sciences. Three applications are presented
in this paper. The first one is the problem of time-dependent vertical
temperature distribution in a stagnant lake. Two cases have been considered for
the forms of the water parameters, namely water density and thermal
conductivity. The second application is the unsteady free-convective
boundary-layer flow on a non-isothermal vertical flat plate. The third
application is the study of the dispersion of gaseous pollutants in the
presence of a temperature inversion. The results are found in closed form and
the effect of parameters are discussed.
