A double$-$pipe $($shell$-$and$-$tube$)$ heat exchanger is constructed of a stainless steel $(k=15\mathrm{.}1\frac{W}{m}*K)$ inner tube of inner diameter $D_i=1\mathrm{.}5cm$ and outer diameter $D_0=1\mathrm{.}9cm$ and an outer shell of inner diameter $3\mathrm{.}2$ cm $.$ The convection heat transfer coefficient is given to be $h_i=800\frac{W}{m^2}*K$ on the inner surface of the tube and $h_0=1200\frac{W}{m^2}*K$ on the outer surface. For a fouling factor of $R_{f,i}=0\mathrm{.}0004m^2*\frac{K}{W}$ on the tube side and $R_{f,o}=0\mathrm{.}0001m^2*\frac{K}{W}$ on the shell side, determine $($a$)$ the thermal resistance of the heat exchanger per unit length and $(b)$ the overall heat transfer coefficients, $U_i$ and $U_o$ based on the inner and outer surface areas of the tube, respectively.