$2.$ A double$-$pipe heat ex$-$changer is constructed of copper $($k $=380$ W$/$m $$ K$)$ inner tube of internal diameter Di$=1\mathrm{.}2$ cm and external diameter Do $=1\mathrm{.}6$ cm and an outer tube of di ameter $3\mathrm{.}0$ cm$.$ The convection heat transfer coefficient is reported to be hi $=700$ W$/$m$2$K on the inner surface of the tube and ho $=1400$ W$/$m$2$K on its outer surface. For a fouling factor Rf$,$i$=0\mathrm{.}0005$ m$2$ K$/$W on the tube side and Rf$,$o$=0\mathrm{.}0002$ m$2$ K$/$W on the shell side, determine $($a$)$ The thermal resistance of the heat exchanger per unit length. $[$Ans: $0\mathrm{.}0837$ K$/$W$]($b$)$ Overall heat transfer coefficients Ui and Uo based on the inner and outer surface areas of the tube, respectively.$[$Ans: $317$ W$/$m$2$K $,238$ W$/$m$2$K