A Bakelite \((k=1.4 \mathrm{~W} / \mathrm{mK})\) coating is to be used with a \(10 \mathrm{~mm}\) diameter conducting rod whose surface is maintained at \(200^{\circ} \mathrm{C}\) by passage of an electric current. The rod is immersed in a fluid at \(25^{\circ} \mathrm{C}\) and the convection coefficient is \(140 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\).

a. What is the critical insulation thickness for the coating?

b. What is the heat transfer rate per unit length of the bare rod?

c. What is the heat transfer rate for the coated rod whose coating corresponds to the critical insulation thickness?

d. How thick should the Bakelite coating be to reduce the heat transfer rate associated with the bare rod by \(25 \%\) ?