water(Cp=4180J/kgoC)enter into the 2.5 cm internal diameter tube of a double pipe counter flow heat exchanger at 17oC at a rate of 3kg/s .Water is heated by steam condensing at 120oC (hfg= 2203kj/kg)in the shell .If overall heat transfer coefficient of the heat exchanger is 900W/m2oC ,determine the length of the tube required in order to heat the water to 80oC using LMTD n NTU method?

Question

Answer

Problem:

Water (Cp=4180J/kgoC) enters into the 2.5 cm internal diameter tube of a double pipe counter flow heat exchanger at 17oC at a rate of 3kg/s. Water is heated by steam condensing at 120oC (hfg= 2203kj/kg) in the shell. If the overall heat transfer coefficient of the heat exchanger is 900W/m2oC, determine the length of the tube required in order to heat the water to 80oC using LMTD and NTU method?

Solution:

Step 1: Determine the LMTD

LMTD (Logarithmic Mean Temperature Difference) is determined using the formula:

LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)

where ΔT1 = T1,in - T2,out and ΔT2 = T1,out - T2,in

Given:

T1,in = 17oC

T1,out = 80oC

T2,in = 120oC

T2,out = ? (unknown)

Using the formula to calculate ΔT1 and ΔT2:

ΔT1 = 17 - T2,out

ΔT2 = 120 - 80 = 40

Substituting the values in the LMTD formula:

LMTD = (17 - T2,out - 40) / ln((17 - T2,out) / 40)

LMTD = (57 - T2,out) / ln((17 - T2,out) / 40)

Step 2: Determine the NTU

NTU (Number of Transfer Units) is determined using the formula:

NTU = UA / Cp_min

where U is the overall heat transfer coefficient, A is the heat transfer area, and Cp_min is the minimum heat capacity.

Given:

U = 900 W/m2oC

A = πDL (where D is the inner diameter of the tube and L is the length of the tube)

Cp_min = 4180 J/kgoC (for water)

Substituting the values in the NTU formula:

NTU = (900 x π x 0.025 x L) / 4180

NTU = 0.017 x L

Step 3: Determine the Effectiveness

Effectiveness is determined using the formula:

ε = (1 - e^(-NTU(1 - C))) / (1 - C x e^(-NTU(1 - C)))

where C = (Cp_min,C / Cp_max,F) and Cp_max,F is the

Answer

Water (Cp = 4180 J/kg � �C) enters the 2.5-cm internaldiameter tube of a double-pipe counter-flow heat exchanger at 17�C at a rate of3 kg/s. It is heated by steam condensing at 120�C (hfg = 2203 kJ/kg) in theshell. If the overall heat transfer coefficient of the heat exchanger is 1500W/m² �C, determine the length of the tube required in order to heatthe water to 80�C.

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