On a hot day, when the temperature $T_d = 27$$\displaystyle{^{\circ }C}$, a rectangular sheet of aluminum $L = 183$ $mm$ long and $W = 167$ $mm$ wide and $t = 8$ $mm$ thick is fixed in a rigid frame. Find the change in thickness of the plate that occurs during the night when the temperature reaches $T_n = 24$$\displaystyle{^{\circ }C}$. For simplicity, you may assume that the rigid frame is not temperature-sensitive, and stays exactly the same size. For the aluminum sheet, $E = 70$ $GPa$, $\nu = 0.33$ and $\alpha =$$23 \cdot 10^{-6}$ / $\displaystyle{^{\circ }C}$. $\Delta t=$ $mm$