An exothermic reaction taking place in a spherical material causes uniform volumetric thermal energy generation of 106 W/m3 . The sphere is initially at 127°C, and is suddenly placed in a large room with wall temperatures of 27°C. The air in the room at 27°C yields a convective heat transfer coefficient of 5 W/m2 ·K. a. What should be the diameter of the sphere so that the initial rate of change of temperature will be dT/dt = 0.5 K/s? Take the properties of the spherical material as p = 6 g/cm3 , k = 18 W/m·K, c = 200 J/kg·K, and ε = 0.4. b. Write the differential equation (heat diffusion equation) governing the temperature distribution in the sphere. State also the boundary conditions and the initial condition. Do not solve the equation.