plase include all steps, unit converstion, equation used, or how equations used can be similar$3-$ Liquid nitrogen at $77$ K is stored in a cylindrical dewar flask having an inside diameter of $10$ cm $.$

The cylinder is made of glass $(k=1\mathrm{.}3\frac{W}{m}*K$ and the wall thickness is $0\mathrm{.}4$ cm $.$ Insulation is to

be added to the outer side of cylinder to reduce the nitrogen boil$-$off rate to $10\%$ of its value

without insulation. The insulation to be used has a thermal conductivity of $0\mathrm{.}13\frac{W}{m}*K.$ Energy

losses through the top and bottom of the cylinder are assumed to be negligible. What thickness of

insulation needs to be added if the convective heat transfer coefficient of the surrounding air is $10$

$\frac{W}{m^2}k$ and it is at room temperature $(300$ K $).$ Assume that the resistance to heat transfer from

the nitrogen to the inside wall of the cylinder is small. $($Hint: assume that the biol$-$off rate is

proportional to the heat flow.$)[25$ points$]$