Two insulting materials of thermal conductivity $$K$$ and $$2K$$ are available for lagging a pipe carrying a hot fluid. If the radial thickness of each material is same

For air near atmospheric condition flowing over a flat plate the laminar thermal boundary layer is thicker than hydrodynamic boundary layer

When the fluid velocity is doubled the thermal time constant of a thermometer used for measuring the fluid temperature reduces by a factor of $$2$$

Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A.$$ The ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is