As per the given figure, two plates $$A$$ and $$B$$ of thermal conductivity $$K$$ and $$2K$$ are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm$$^2$$ for each plate. The equivalent thermal conductivity of the compound plate is $$\left(1 + \frac{5}{\alpha}\right)K$$, then the value of $$\alpha$$ will be ______.