The beam of an overall depth $250$ mm (shown below) is used in a building subjected to two different thermal environments. The temperatures at the top and bottom surfaces of the beam are $36^{\circ}$ and $72^{\circ}$ respectively. Considering coefficient of thermal expansion $(\alpha)$ as $1.50 \times 10^{-5}$ per $^{\circ}C$, the vertical deflection of the beam (in mm) at its mid-span due to temperature gradient is ________