A $50-$cm$-$diameter, $95-cm-$Iong cylindrical metal drum containing a chemical solution is stored outdoors in an open field. During the day, the solution inside the drum is heated to $80C$ due to exposure to intense sunlight. At night, the drum is subjected to cool, windy air at $18C$ with an average wind speed of $40k\frac{m}{h}.$ Assume the drum's surface temperature is uniform and equal to the solution's temperature and that the heat transfer coefficient for the top, bottom, and side surfaces is uniform. Evaluate the air properties at $50C.$

a$.$ Sketch the schematic of the system by labeling all the geometrical and technical data on it$.(4)$

b$.$ Estimate the temperature of the chemical solution inside the drum after $45$ minutes. $(12)$

$\backslash$table$[[$Properties of Chemical,$=971\mathrm{.}8k\frac{g}{m^3},$Properties of air:,$\backslash$table$[[k=0\mathrm{.}02735\frac{W}{m}C$