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Problem #$1$:

Given: Water flows inside a $2-$inch pipe at a velocity of $0\mathrm{.}25\frac{m}{s}.$ The temperature of the water is $96C.$ The exterior of the pipe is exposed to ambient condition $23C$ air.

Assume: The pipe is Sch $40$ black steel. No fouling is considered. $h_0=7\mathrm{.}9\frac{W}{m^2}K$

Find: The overall heat transfer coefficient, $U$ in units of $\frac{W}{K},$ for a $1$ m length.ECE $400$ Thermal System Components

Fall $2024$

Module $6$: Heat Exchanger Methods of Analysi

Problem #$1$:

Given: Water flows inside a $2-$inch pipe at a velocity of $0\mathrm{.}25\frac{m}{s}.$ The temperature of the water is $96C.$ The exterior of the pipe is exposed to ambient condition $23C$ air.

Assume: The pipe is Sch $40$ black steel. No fouling is considered. $h_0=7\mathrm{.}9\frac{W}{m^2}K$

Find: The overall heat transfer coefficient, $U$ in units of $\frac{W}{K},$ for a $1$ m length.

Problem #$2$:

Given: Water flowing at $1k\frac{g}{s}$ is warmed by oil in a double$-$pipe heat exchanger. The inlet temperatures of the water and oil are $25C$ and $120C,$ respectively. The outlet temperatures of the water and oil are $75C.$

Assume: The overall heat transfer coefficient is $325\frac{W}{m^{2\text{@}}}C.$

Find: Required area of the heat exchanger, $A$ in units of $m^2.$

Problem #$3$:

Given: The heat exchanger shown in the figure is to heat oil flowing through tubes using steam on the outside of the tubes. The mass flow rate of the oil is $0\mathrm{.}73k\frac{g}{s}.$ The inlet and outlet temperatures of the oil should be $20$ and $90C,$ respectively. The inlet and outlet temperatures of the steam are $135$ and $115C,$ respectively.

Assume: Specific heat of the oil and steam are $1\mathrm{.}91k\frac{J}{k}gC$ and $1\mathrm{.}85$

$k\frac{J}{k}gC,$ respectively. Overall heat transfer coefficient is

$U=280\frac{W}{m^{2\text{@}}}C$

Find: The required heat exchanger surface area, $A$ in units of $m^2,$ using the Log Mean Temperature Difference Method with Correction Factor.

Problem #$4$:

Repeat problem #$3$ using the Effectiveness$-$NTU method to find the required area, $A$ in units of $m^2.$