Consider a hollow sphere designed to hold a cryogenic fluid. The fluid inside the sphere is at a uniform temperature, \(T_{i}\). Insulation with thermal conductivity, \(k\), is added to the outer surface. Convective heat loss to the environment is controlled by a heat transfer coefficient, \(h\). What is the critical insulation thickness for this geometry? With reference to the cylindrical geometry, is there a pattern that can be extended to dimensions higher than 3 ?