In an aluminum melting furnace, $36\mathrm{.}6$ tons of aluminum is melted by burning $240$ Nm$3$ of natural gas per hour. The chimney of this stove As a result of the measurement, the flue gas temperature was measured as $410$ oC$.8,250$ kcal$/$Nm lower calorific value in the furnace natural gas is burned. As a result of preliminary calculations, the density of natural gas is $0\mathrm{.}757$ kg$/$Nm$3.$ air$/$fuel

The ratio is $25$ kgAir$/$kgDG$,$ the partial pressure of water vapor in the flue gas is $12\mathrm{.}35$ kPa and the specific heat value of the flue gas is It was determined that the temperature$-$dependent function was cp$($ToC$)=1\mathrm{.}1693+0\mathrm{.}0003$T $($kJ$/$kgK$).$ The company uses the thermal energy in the flue gas.

It searches for investments that will provide economic returns. The flue gas temperature is $25$oC above the dew point ORC $($Organic Rankine$)$ which has a thermal efficiency $($Electric Power$/$Thermal Power$)$ of $16\%$ with the thermal energy to be obtained by reducing the value to He wants to make an investment to produce electrical energy through conversion. The specific investment cost of the ORC system is $4500$ Offer was received in $$/$kWe$.20\%$ of the electricity produced in this system will be used for domestic consumption and the rest will be used in the business.

The specific value of Operation and Maintenance costs is determined as $4\mathrm{.}5$ $$/$MWeh$-$Year and the annual escalation is $26\%.$ mains electricity Its price is $4\mathrm{.}035$ TL$/$kWeh and its annual real escalation is $2\%.$ Inflation $50\%,$ dollar exchange rate $32\mathrm{.}2$ TL$,$ annual working hours of the Business Since it is $7,000$ hours and the economic life is $15$ years, calculate the payback rate of this investment using the combined values.

Since the real capital cost of the loan to be taken for investment is $5\%,$ investigate the suitability of the investment.