1. Derive the LMTD equation for a parallel flow heat exchanger? 2. Derive the LM
ID: 701811 • Letter: 1
Question
1. Derive the LMTD equation for a parallel flow heat exchanger? 2. Derive the LMTD equation for a counter flow heat exchanger? 3. Steam enters a counter flow heat exchanger dry saturated at 10 bar and leaves at 350°C. The mass flow of steam is 800 kg/min. The gas enters the heat exchanger at 650°C and mass flow rate is 1350 kg/min. If the tubes are 30 mm diameter and 3m long, determine the number of tubes required. Take for steam: tsat = 180°C (@l 0 bar); Cps = 2. 71 kJ/kg°C, h.-600 w/m. Take for gas: Cpg " 1 kJ/kg°C ; hg-250 w/C . What is the significance of Reynolds No. in determining the heat transfer coefficient in forced convection? 5. What is the significance of Nusselt No. in determining the heat transfer coefficient in forced convection? 6. Prove that Prandtl No and Reynolds No. is a dimensionless quantity. 7. Write a short note on occurrence of radiation heat transfer in a process equipment.Explanation / Answer
1)
In the heat exchanger, Consider a small area dA with dQ (heat transfer rate) occuring through this area
In this area,Temperature differences on hot fluid is dTh and cold fluid is dTc in length dx
Because, Heat removed from Hot side = Heat gained from Cold side = U*dA*T
U: Overall Heat transfer coefficient
=> dQ. =U dA T =-m.h cph dth = m.c cpc dtc =U dA (Th – Tc)
cph: Specific heat of Hot side
cpc: Specific heat of cold side
dth= – dQ. / m.h cph = dQ. /Ch
dtc= – dQ/ m.c cpc =dQ/Cc
where Ch = m.h cph = heat capacity of hot fluid
Cc = m.c cpc = heat capacity of cold fluid
dth - dtc =– dQ. (1/Ch + 1/Cc)
(dth -dtc = d)
d = - dQ. (1/Ch + 1/Cc)
d = -U dA (Th – Tc) (1/Ch + 1/Cc)
d = - U dA (1/Ch + 1/Cc)
d/ = –UdA(1/Ch + 1/Cc)
Integration on both side,
ln( 2/1) = -U A (1/Ch + 1/Cc)
2 = Th2-Tc2
1 = Th1-Tc1
But 1/Ch =Th1 –Th2/ Q. and 1/Cc =Tc1 –Tc2/ Q.
ln( 2/1) = -U A ( Th1 –Th2/ Q.+ Tc1 –Tc2/ Q )
ln( 2/1) = (U A/ Q) (( Th2 –Tc2)-( Th1 –Tc1) )
ln( 2/1) = (UA/ Q) (2-1)
Q. = U A (2- 1)/ ln( 2/1)
Q. = U A m
m = LMTD = (2-1)/ ln( 2/1)
LMTD = (max-min)/ ln( max/min)
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