e$)$ A heat exchanger transfers heat from hot carbon dioxide to superheated steam.

The steam flows inside tubes and the gas flows over the outside in a parallel direction.

The steam is at $150$ bar pressure absolute and is heated from $375\backslash$deg C to $450\backslash$deg C respectively.

The carbon dioxide $($at atmospheric pressure$)$ is cooled from $620\backslash$deg C to $500\backslash$deg C and flows at $0\mathrm{.}5$ kg$/$s$.$

The tubes are thin walled and $50$ mm diameter. The total length is $150$ m$.$

Calculate the following heat transfer performances of the system.

i$)$ The flow rate of the steam.

ii$)$ The arithmetic mean temperature difference $($AMTD$)$ & the log mean temperature difference $($LMTD$).$

iii$)$ The effective heat transfer coefficient for the unit for the AMTD & LMTD

iv$)$ Which of the values of heat transfer coefficient is more accurate and explain why.

v$)$ A process change takes place reducing the steam outlet requirement to $405$oC and pressure to $75$ bar, the steam inlet temperature has dropped to $320$oC and pressure also is $75$ bar. Given the same CO$2$ heat source what flow rate of steam can now be produced by the heat exchanger.

For this question you will need to find data for carbon dioxide & steam. Use reliable data and reference your sources.