hollow aluminumphere $[$ka$=204$W$/($m K$))$ with a $100$ W electric heater at its centre is used to determine the thermal conductivity of an insulating material. The inner and outer radij of the sphere are $0\mathrm{.}1$ and $0\mathrm{.}125$ m$,$ respectively. In a particular test,a spherical shell of an insulating material of $75$ mm thickness was applied on the outer surface of the sphere, In the steady state,the temperature at the inmer surface ofthe aluminum wall was recorded as $200\text{'}$C$.$ The system is expused to room air at $30$C and the convective heat transfer coefficient is estimated to be $20$W$/($m$2$K$).$What is the thermal conductivity of the insulation'?Neglect heat los by radiation and contact resistance