List of top Heat Transfer Questions on Heat exchangers process calculations

A perfectly insulated double pipe heat exchanger is operating at steady state. Saturated steam enters the inner pipe at 100 °C and leaves as saturated water at 100 °C. Cooling water enters the outer pipe at 75 °C and exits at 95 °C. The overall heat transfer coefficient is 1 kW m$^{-2}$ K$^{-1}$ and the heat transfer area is 1 m$^{2}$. The average specific heat capacity of water is 4.2 kJ kg$^{-1}$ K$^{-1}$. The required cooling water flow rate is \(\underline{\hspace{2cm}}\) kg s$^{-1}$ (rounded off to two decimal places).
In a double-pipe heat exchanger (10 m), hot fluid flows in annulus and cold fluid in inner pipe. Temperatures vary as:
$T_h(x) = 80 - 3x$,
$T_c(x) = 20 + 2x$,
where $T$ in °C and $x$ in m.
The logarithmic mean temperature difference (LMTD) is

For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as 250 W m$^{-2}$ K$^{-1}$ for a specific process condition. It is expected that the heat exchanger may be fouled during the operation, and a fouling resistance of 0.001 m$^{2}$ K W$^{-1}$ is prescribed. The dirt overall heat transfer coefficient is \(\underline{\hspace{2cm}}\) W m$^{-2}$ K$^{-1}$.