Consider a steel sphere with a radius of \(r=0.01 \mathrm{~m}\) submerged in a hot water bath, with a heat transfer coefficient of h = 350 W/(m² ·°C). For steel, the density is ρ = 7850 kg/m³ , the specific heat capacity is \(c=440 \mathrm{~J} /\left(\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\), and the thermal conductivity is \(\mathrm{k}=43 \mathrm{~W} /\left(\mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)\). The temperature of the water \(T_{\mathrm{f}}\) is \(100^{\circ} \mathrm{C}\), and the initial temperature of the sphere \(T_{0}\) is \(25^{\circ} \mathrm{C}\).

a. Determine whether the sphere's temperature can be considered uniform.

b. Derive the differential equation relating the sphere's temperature \(T(t)\) and the water's temperature \(T_{\mathrm{f}}\).

c. Using the differential equation obtained in Part (b), construct a Simulink block diagram to find the sphere's temperature \(T(t)\).