A ship with a main engine of $8000$ kW power and $30\%$ thermal efficiency discharges $60\%$ of the total waste heat through the exhaust stack. Hot water at a temperature of $80\backslash$deg C is desired to be obtained from the exhaust gas. Distilled water is fed into the boiler at a temperature of $30\backslash$deg C$.$ The main engine exhaust gas exit temperature is $600\backslash$deg C$,$ and the atmospheric exit temperature from the stack is $220\backslash$deg C$.$ The boiler system is considered to have $2$ passes and $2-$stage plate separation. Assuming a body diameter of $150$ cm$,$ inner tube diameter of $10$ mm$,$ inner tube thickness of $2$ mm$,$ and a body length of $3$ meters, a$)$ Find the total heat transfer amount. b$)$ Find the overall heat transfer coefficient. c$)$ Find the number of tubes to be used. $(2$ passes $=1$ tube$).$ NOTE: $-$ Neglect the blocked area by the inner tubes when calculating the convection coefficient on the body side. $-$ Constants and properties: Cpwater$=4\mathrm{.}18$ kJ$/$kg$.$K$,$ Cpair$=1\mathrm{.}006$ kJ$/$kg$.$K$,$ kinner$=385$ W$/$mK$,$ kwater$=0\mathrm{.}65$ W$/$mK$,$ kair$=0\mathrm{.}026$ W$/$mK$,$ Prwater$=6\mathrm{.}7,$ Pair$=0\mathrm{.}7,$water$=8\mathrm{.}9$ x $10-4,$air$=1\mathrm{.}85$ x$10-5$ Pa$.$s$,\backslash$rho water$=997$ kg$/$m$3,\backslash$rho air$=1\mathrm{.}25$ kg$/$m$3.$