A slab of clay \(50 \mathrm{~mm}\) thick was dried from both flat surfaces-with the four thin edges sealed-by exposure to dry air. The initial uniform moisture content was \(15 \%\). The drying took place by internal diffusion of the liquid water to the surface, followed by evaporation at the surface. The surface moisture content remained constant at \(3 \%\). In \(5 \mathrm{~h}\), the average moisture content dropped to \(10.2 \%\). The resistance to diffusion is assumed to reside wholly within the solid. The diffusivity is assumed to be constant independent of the water concentration and position.

(a) Calculate the effective diffusivity.

(b) Under the same drying conditions, how long would it take to reduce the average water content to \(6 \%\) ?