Abstract: In our report, the heat conduction model defined in the three-dimensional cylindrical region was analyzed, which is widely used in binary mixtures. Firstly, by constructing auxiliary functions, three different types of cylindrical unbounded regions were analyzed. Secondly, the method of energy estimation was used to obtain the alternative results of Phragmén-Lindelöf type. Lastly, it was proved that "energy" grows exponentially（polynomial or logarithmic） or decays exponentially（polynomial or logarithmic） with spatial variable. Under the case of decay, the explicit upper bound of total energy was established.