auxiliary time was $45$ minutes.

$[]$ Caculation $(25$ points$)$

$(16).$ Benzene is cooled from $100C$ to $60C$ with mass flow rate $3500k\frac{g}{h}$ in a double$-$pipe exchanger with inner pipe $483\mathrm{.}5mm.$ Cooling water is heated from $40C$ to $50C$ with specific heat $c_P=4\mathrm{.}174k\frac{J}{k}g*K$ through the annular space $().$ The heat transfer coefficient ho is $3490\frac{W}{m^2*K}.$ Assume the heat loss and the fouling factors on two sides can be ignored.

The physical properties of benzene at $]=[\frac{100+60}{2}$ :

$C_P=1\mathrm{.}9k\frac{J}{k}g*K,=0\mathrm{.}37{10}^{-3}Pa*s,=840k\frac{g}{m^3},=0\mathrm{.}138\frac{w}{m*K}$

The thermal conductivity $$ of pipe wall is $45\frac{W}{m*K}.$

What is the mass flow rate for cooling water?

What is the heat transfer coefficient $h_i$ between benzene and pipe wall?

What is the overall heat transfer coefficient based on the outer surface area of tube.

What is the logarithmic mean temperature difference $($LMTD$)$ and the length of the double$-$pipe when the two fluids flow in countercurrent flow?

When the exchanger is used for a year, it is found that it cannot meet the need of production, explain why?