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bagirrra123 [75]
2 years ago
7

A counter-flow double pipe heat exchanger is heat heat water from 20 degrees Celsius to 80 degrees Celsius at the rate of 1.2 kg

/s. The heating is to be accomplished by geothermal water available at 160 degrees Celsius at a mass flow rate of 2 kg/s. The inner tube is thin-walled and has a diameter of 1.5 cm. if the overall heat transfer coefficient of the heat exchanger is 649 W/m2K, determine the length of the heat exchanger required to achieve the desired heating.
Engineering
1 answer:
lakkis [162]2 years ago
7 0

Answer:

L=107.6m

Explanation:

Cold water in: m_{c}=1.2kg/s, C_{c}=4.18kJ/kg\°C, T_{c,in}=20\°C, T_{c,out}=80\°C

Hot water in: m_{h}=2kg/s, C_{h}=4.18kJ/kg\°C, T_{h,in}=160\°C, T_{h,out}=?\°C

D=1.5cm=0.015m, U=649W/m^{2}K, LMTD=?\°C, A_{s}=?m^{2},L=?m

Step 1: Determine the rate of heat transfer in the heat exchanger

Q=m_{c}C_{c}(T_{c,out}-T_{c,in})

Q=1.2*4.18*(80-20)

Q=1.2*4.18*(80-20)

Q=300.96kW

Step 2: Determine outlet temperature of hot water

Q=m_{h}C_{h}(T_{h,in}-T_{h,out})

300.96=2*4.18*(160-T_{h,out})

T_{h,out}=124\°C

Step 3: Determine the Logarithmic Mean Temperature Difference (LMTD)

dT_{1}=T_{h,in}-T_{c,out}

dT_{1}=160-80

dT_{1}=80\°C

dT_{2}=T_{h,out}-T_{c,in}

dT_{2}=124-20

dT_{2}=104\°C

LMTD = \frac{dT_{2}-dT_{1}}{ln(\frac{dT_{2}}{dT_{1}})}

LMTD = \frac{104-80}{ln(\frac{104}{80})}

LMTD = \frac{24}{ln(1.3)}

LMTD = 91.48\°C

Step 4: Determine required surface area of heat exchanger

Q=UA_{s}LMTD

300.96*10^{3}=649*A_{s}*91.48

A_{s}=5.07m^{2}

Step 5: Determine length of heat exchanger

A_{s}=piDL

5.07=pi*0.015*L

L=107.57m

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