Uniform energy generation per unit volume at $=2\mathrm{.}4106$ W$/$m$3$ is occurring within a spherical nuclear fuel element of $20$ cm diameter. Under steady conditions the temperature distribution is given by T $=90010,000$ r $2$ where r is in meters and T is in degrees Celsius. a$)$ Determine the thermal conductivity of the nuclear fuel element. b$)$ What is the average heat transfer coefficient at the surface of the sphere if the ambient temperature is $35$C$?$ Answer: a$)40$ W$/$m$.$K b$)104\mathrm{.}6$ W$/$m$2.$K