In this study, based on the continuous transformations of Lie groups, the exact analytic solutions of the
laser heating carbon nanotubes formulated by using the classical heat conduction equation with various
physical properties were constructed. These solutions are the type of group invariant solutions. The
constructed solutions have expanded and enriched the solution forms of this new model existing in the
literature. With the help of the Maple package program, 3D, density, and contour graphs were drawn
for the special values of the parameters in the solutions, and the physical structures of the solutions
obtained in this way were also observed. The solutions obtained can be used in the explanation of
physical phenomena occurring in cancer investigations.