Heat Exchangers Problems

General Equations, F-Tln, θ and , NTU methods

Problem 1.1 – The tubes of a water-water heat exchanger are 25mm outside diameter

with 2 mm thickness. The water inside the tubes has a flow rate of 20 ton/h enters at

35ºC and is heated until 55ºC by a flow rate of 10 ton/h outside the tubes entering at

100ºC. The heat exchanger has one passage in the shell and the velocity inside the

tubes should be larger than 0.5 m/s. The global heat transfer coefficient can be

assumed as 1200 W/m2

K. If the length of the tubes can not exceed three meters,

calculate:

a) The number of tubes per passage. (32)

b) The number of tubes passages. (2)

c) The lenght of the tubes. (2.6m)

Problem 1.2 – Consider a heat exchanger with concentric tubes that is very long or for

a fixed lenght that the global heat transfer coefficient is very high. The hot and cold

fluids have similar specific heat and enter at 80ºC and 20ºC, respectively. The hot

fluid flow rate is the double of the cold fluid. For the co and counter flow:

a) Sketch the temperature profiles of both fluids along the heat exchanger.

b) Determine the outlet temperature for each fluid.

c) Determine the efficiency of the heat exchangers.

Problem 1.3 – A shell and tube heat exchanger with respectively one and two

passages is designed to cool a flow rate of 15 kg/s of a fluid from 200ºC to 120º C

using a 37.5 kg/s flow rate of a fluid which increases its temperature from 60ºC to

80ºC. The specific heat of the hot and cold fluid is respectively 2500 and 4000 J/kg K.

The project global heat transfer coefficient is 500 W/m2 K considering a fouling heat

transfer resistance in the external tube side of 0.3 m2K/kW.

a) Calculate the heat transfer area of the heat exchanger. (72m2)

b) At the startup of the heat exchanger (with clean surfaces) what is the expected

outlet temperatures of both fluids. (114ºC, 82ºC)

c) Calculate the outlet temperatures of the fluids for the project conditions if the inlet

temperatures are modified to 190ºC and 70ºC. (122ºC, 87ºC)

d) In an emergency situation if the cooling flow is reduced to 30 kg/s the global heat

transfer coefficient is reduced to 450 W/m2K. What are the new values for the

outlet temperature of both fluids? (128ºC, 83ºC)

Heat Exchangers Associations

Problem 2.1 – With the objective of removing 25 kW from a water flow rate of

0.25kg/s initially at 80ºC using cold water flow rate of 0.125 kg/s to achieve a

maximum of 75 ºC, we want to know if it is possible to use heat exchangers (1x2) and

how many. The global heat transfer coefficient is assumed to be 400W/m2K.

a) Indicate the type of arrangement, the number of units and the area of each to

achieve the objectives.

b) If after a certain period the heat exchanged is reduced to 24 kW, estimate the

increase in heat transfer resistance due to fouling and compare with typical values.

Problem 2.2 – In an association in series of three shell and tube (2x1) heat exchangers

the cold fluid in the shell has the maximum heat capacity MaxC = 36 kW/K and the

heat capacity ration is r=0.5. The global heat transfer coefficient is 60 W/m2K and the

efficiency of the association is 0.9. The inlet temperatures are 20ºC and 280ºC.

a) Calculate the efficiency of each unit and the heat transfer area. (393m2)

b) Calculate the outlet temperatures from the association (46ºC, 137ºC)

c) Calculate the heat exchanged in the association. (4212kW)

d) Calculate all the intermediate temperatures between the units. (40, 86, 75 and

156ºC)

e) After some operation time the hot fluid outlet temperature is 70ºC. What are the

possible causes for this? Estimate the parameters that are modified.

f) Calculate the heat that would be exchanged if the three units were associated in

parallel and the global heat transfer coefficient was 40 W/m2K.

Problem 2.3 – An association of two shell and tube heat exchangers 4*2, with an

individual area of 96 m2 have a project efficiency of 83% when the inlet temperatures

are 25ºC and 140ºC. The project heat transfer resistance is 2 m2K / kW. The flow

rates and specific heat capacities are presented in the following table.

Fluid Flow rate (kg/s) Specific heat (kJ/kg K)

Hot 6 1.73

Cold 9 1.54

a) What is the project heat transfer coefficient. (190W/m2K)

b) Determine the outlet temperature and the temperature between the units.

(Tho=45ºC, Tco=97, Thb=83ºC, Tcb=54ºC)

c) Calculate the global heat transfer coefficient if the outlet temperature of the hot

fluid is 50ºC. (U=140W/m2K)

d) What is the fouling heat transfer resistance in that situation? (3.8 m2K / kW)

Problem 2.4 – Consider an association of two heat exchangers where the cold fluid

goes through the two units in series while the hot fluid passes in parallel. For a matter

of convenience of assembling one unit will work in co-flow while the other in

counter-flow.

a) Verify that the efficiency is independent of the order of the heat exchangers.

b) Deduce the equations for the efficiency as a function of r in the case of large heat

capacity NTU for the different cases that you can identify (1, 2A and 2B from

the theory) Compare the values of the efficiency for rG=0.0, 0.25, 0.5, 0.75 and 1.0.

c) Calcule a eficiência do conjunto para as diversas condições indicadas na tabela:

NTUGlobal 1.0 1.0 1.0 3 3 3

rGlobal 0.25 0.25 0.75 0.25 0.25 0.75

Fluid in parallel minC MáxC MáxC minC MáxC MáxC

Counter-flow

Co-flow

Global

Heat exchanger with intermediate fluid or solid matrix

Problem 3.1 – We want to plan the heating of combustion air from the flue gases but

the distance between the ducts is large so it is planned the instalation of a heat recover

system using an intermediate water circuit. Assume the following values:

Flue gases (FG): m =0.8 kg/s, cp=1.2 kJ/kg K, Thi=350ºC, Tho=245ºC.

Air: m =4 kg/s, cp=1 kJ/kg K, Tci=20ºC

Neglecting the heat losses in the pipes and from the heat exchangers:

a) Calculate the global efficiency of the regenerator (air/flue gases).

b) Assuming that the water flow rate is very large, calculate the efficiency of both

heat exchangers (Air/Water and FG/Water) considering that they are similar.

(If you do not calculate this consider 40%)

c) Calculate the average water temperature in this case.

d) If the water flow rate is finite ( m =2 kg/s, cp=4.2 kJ/kgK) calculate the minimum

and maximum water temperature indicating where they occur.

e) If the efficiency of the heat exchangers (Air/Water) and (FG/Water) are different

which one, should be larger to minimize the average water temperature.

Exemplify for a set of values.

3.2 Consider a solid matrix regenerator, 4 m in diameter with a height of 0.9m. The

matrix contains 5 ton of metal with a specific heat of 450 J/kg K and has a heat

transfer area of 3500 m2. 50 kg/s of flue gas enters at a temperature of 500ºC in one

side while a similar flow of air at 15ºC enters the other side in counter-flow. Consider

that both fluids have specific heat of cp=1.05 kJ/kgK and the heat transfer coefficient

between the gases and the solid matrix is 130 W/m2K.

a) Calculate which will be the average outlet temperature of air if the rotation

period is 40 s and 120 s? Compare the results obtained with the simplified

analysis and the results from the -NTU graphs. Pay attention to the

definitions of AU in both analysis.

b) Evaluate the effects of the axial conduction in the regenerator efficiency,

knowing that = 1850 kg/m3, k= 1.4 W/mK, = 7.1x 10

-7 m

2/s.

Problems on concentric tubes heat exchangers

Problem 4.1 – Dimension a concentric tube heat exchanger to promote the heat

transfer between two water streams with the following values: QVh= 3m3/h, Thi= 70ºC,

Tho= 64ºC, QVc= 4m3/h, Tci= 30ºC. For the pressure drop consider as criteria that the

pumping power for each fluid is lower than 0.5% of the heat exchanged.

Flue Gases Pre-heated air

Problem 4.2 The heat exchanger represented in the figure is used to heat a flow of 5

kg/s of Dowtherm fluid from 15 to 65 °C using water that is cooled from 95 to 75 ºC.

The hot water circulates inside while the heat transfer fluid circulates outside the

tubes due to the higher viscosity.

1) What is the length of the heat exchanger required to perform the duty required?

2) What is the pressure drop in the heat exchanger assuming sections of 1m.

3) What is the outlet temperature of the heat exchanger if the length is 50m.

4) What is the new heat exchange area if the water circulates in parallel in four sets.

5) What is the purpose of the 32 fins mounted on the external surface of the tube.

Proprerties Dowtherm Water at 40ºC

Density kg/m3 1044 969

Specific heat J/kgK 1622 4197

Condutivity W/mK 0.138 0.676

Viscosity Ns/m2 2.7x10

-3 3.11x10

-4

Problemas sobre heat exchangers de corpo and feixe tubular

Problem 5.1 - Consider a shell and tube heat exchanger with an internal diameter of

the shell of 31'' and 3m long tubes. This heat exchanger is to cool a flow rate of 10

kg/s of a hydrocarbon initially at 150 °C, using a flow rate of 13 kg/s of water at 30

°C. The hydrocarbon flows on the outer tubes while the water circulates inside the

tubes making two passes. The heat exchanger tubes have an outside diameter and

thickness of 2.1mm (BWG14) and are arranged in a square with a ratio pitch/diameter

of 1.25.

Proprieties of fluids: Water cp = 4.2 kJ/kg K = 0.0007 kg/m s

Hydrocarbon cp = 2.75 kJ/kg K = 0.031 kg/m s

a) Estimate the heat exchange area indicating the assumptions made.

(If you do not solve, consider the value of 100m2 for the rest of the problem)

b) Indicate the maximum number of baffles recommended for this heat exchanger

according to TEMA standards. (If you do not indicate consider 15)

c) Calculate the Reynolds number for flow inside and outside of the tubes that would

enable the calculation of the heat transfer.

d) Indicate the criteria that can be used to decide the flow of the hydrocarbon outside

and the water inside the tubes.

e) Considering that the hydrocarbon is cooled until 70ºC when the heat exchanger is

clean, calculate what is the expected outlet temperature assuming a heat transfer

resistance of 0.5 K m2

/ kW.

Problem 5.2 – A shell and tube heat exchanger of class C, has copper alloy tubes of

diameter 1" BWG14 with a length of 16 ft, arranged in a triangle with a spacing of 1"

¼. The heat exchanger body diameter is 25". The fluid that circulates in the tubes

makes two passages. The two currents are water the cold water with a flow rate of 1.3

kg /s entering at 15 º C, while the hot fluid flow rate is 1.8kg/s entering at 86 °C. The

convection coefficients and fouling resistances for the interior and exterior of the

tubes is estimated as

Inner fluid; h=552W/m2K and Rsuj m

2K/kW = 1.5.

Outside fluid h=427W/m2K and Rsuj =1.0 m

2K/kW.

a) What is the number of rods required and its diameter?

b) What is the recommended number of flow baffles?

c) What is the number of tubes and their heat transfer area?

d) Determine the overall coefficient of heat transfer.

e) What is the thermal power transferred under these conditions

Problem 5.3 – A shell and tube heat exchanger 2x1, has a shell diameter of 17"¼, the

tube bundle consists of tubes ¾" BWG16, with a length of 16ft, arranged in diamond

with a spacing of 1". The heat exchanger cools a water flow rate of 2kg/s from

seawater at 95°C at the expense of 1.5 kg/s of treated cooling water which is available

at 20ºC. The convection coefficients are 500 W/m2K for sea water and 600 W/m

2K

for treated cooling water.

a) What is the heat transfer area of the heat exchanger?

b) Is it possible to cool the sea water until at least 65 ° C in this heat exchanger?

c) What is the best solution if both fluids flow rates are doubled and the sea water has

to reach 60ºC?

Problem 5.4 – A shell and tube heat exchanger 2x1 is designed to cool a hydrocarbon

by water. The hydrocarbon circulates outside the tubes while the water circulates in a

total of 620 tubes ¾ "BWG16 steel. The tubes are arranged in diamond shape with a

pitch of 1 "and have a length of 2.4 m. There are seven baffles.

The known characteristics are shown in the table below.

Hidrocarbon Cooling Water

Flow rate (kg/s) 5 10

Inlet temperature (ºC) 210 25

Heat transfer resistance (m2K/kW) 0.35 0.17

Specific heat (kJ/kg K) 2.75 4.2

Viscosity (kg/ms) 0.03 0.0007

Density (kg/m3) 800 1000

a) Calculate the Reynolds number for both flows and comment the results.

b) Assuming that the global heat transfer coefficient for the design situation is

350W/m2K, calculate the efficiency of heat exchanger and the outlet temperature

of the hydrocarbon.

c) With clean surfaces, calculate the outlet temperature of the hydrocarbon.

d) In the case the hydrocarbon flow rate is doubled using the same flow of water,

compare the use of three alternatives: 1) two units in series, 2) two units in parallel

and 3) two units with the water in series and the hydrocarbon in parallel. Assume

that the heat transfer coefficient is similar and estimate the heat transfer efficiency

for each case. Comment on the expected variation of transfer coefficient and

pressure drop.

Problems on plate heat exchangers

Problem 6.1 – A plate heat exchanger has 11 thermal plates with an area of 0.04 m2

each. They are connected in U with a single passage for each fluid. The flow rates,

specific heat and inlet temperature of both fluids are in the following table. The

design fouling resistance for each side is 0.1 m2K/kW and the outlet temperature of

cold fluid is expected to be 65 °C.

Fluid Flow rate

(kg/s)

Specific heat

(kJ/kg K)

Inlet temperature

(ºC)

Hot 0.20 1.73 120

Cold 0.45 1.54 30

a) Draw the flow of the two streams in the heat exchanger and determine the total

number of plates, including the endplates.

b) What is the design overall heat transfer coefficient.

c) When the outlet temperature of the hot fluid is 60 ° C what is the value of the

fouling heat transfer resistances.

d) Determine the variation in the heat exchange if the hot fluid makes two passes in

the heat exchanger and if the heat transfer coefficient increases by 20%.

Problem 6.2 - In a heat exchanger type heat plate with thermal plates 19, the hot fluid

at a flow rate of 0.25 kg/s, makes a single pass through the heat exchanger. For its

part, the cold stream at a flow rate of 0.125 kg / s, makes two passes in the heat

exchanger. The permuted thermal power is 25 kW when the hot fluid enters at 90 ° C

and the cold fluid at 38 ° C. The two fluids have the same specific heat equal to 4.5

kJ/kgK.

a) If the heat transfer area of each plate is 0.1 m2, determine the global heat transfer

coefficient required for the operating conditions indicated.

b) If the cold fluid has only one passage and the global heat transfer coefficient is

reduce to 1 kW/m2K, calculate the new heat exchanger efficiency.

Problems on tube or plate finned heat exchangers.

Problem 7.1 - Consider a heat exchanger to heat water using the combustion products

of a Diesel engine. At full load the gas flow is 1 kg/s (cp = 1.05kJ/kg K, constant) at

530ºC warming a flow rate of 2 kg/s of water initially at 20°C. The heat exchanger is

made of 12 mm (outer diameter) tubes, arranged in a triangular pitch with longitudinal

and transverse pitch of 25 mm and 30 mm as depicted in the figure. The tubes have

250 fins per meter, which are continuous and have a thickness of 0.5 mm. The tubes

are 0.5m long and there are 8 rows in the direction of the flow with 16 tubes each.

a) Calculate the heat transfer area, dividing the contribution of the tubes and fins

and the hydraulic diameter for the gases. (20 m2)

b) Assuming a global heat transfer coefficient of 50 W/m2K calculate the outlet

water temperature if it circulates in parallel in all the tubes as shown in b).

c) In order to increase the water outlet temperature it is proposed to divide the

heat exchanger into two units with four rows of tubes each as shown in c).

For this case calculate the new outlet temperature of the water and the

intermediate temperature of the gases. Comment the results.

a) b) c)

Problem 7.2 – Consider a cross-flow heat exchanger consisting of finned plates with

overall dimensions shown in the figure. The plates have 2mm thickness and the fins,

mounted between the plates, have a height of (h = 8mm). The fins are off-set with a

step (x = 10mm) in the direction of flow, width (w = 1mm) and pitch (s = 10mm). For

this type of fins consider the following correlation:

D

BA

h31

Res

h*

d

x*C

PrRe

Nuj

with

The heat exchanger is used to heat an air flow rate of 0.2 kg/s from room temperature

(20ºC) using a flow rate of 0.7 kg/s of gases (cp =1.14 kJ/kgK) initially at 250 ºC.

a) Calculate the hydraulic diameter, the factor (ratio of passage area and frontal

area) and the total heat transfer area for one of the gas streams. (6 m2).

b) Discuss the consequences of the choice of direction for the flow of air and

gases in terms of the heat transfer coefficient and pressure drop.

c) Considering the air flowing through the section with larger frontal area,

calculate the convection coefficient.

d) Considering that the convection coefficient of the gas side is 200W/m2K,

calculate the overall coefficient of heat transfer.

C A B D Re

0.48 0.16 0.18 0.54 <1000

0.24 0.32 0.09 0.37 >1000

D=12mm

25

mm

30mm

d) Calculate the gas side outlet temperature and indicate an appropriate

temperature for calculating the properties of both fluids.

e) Describe qualitatively the influence of the cuts in the fins (off-set) compared

to continuous, with respect to pressure drop, heat transfer and efficiency.

Problem 7.3 - Compare two types of heat transfer surfaces whose characteristics are

presented in the figures. These surfaces are designed for a heat exchanger with a fixed

total volume where air (μ= 20x10-6

kg/m/s, ρ = 2kg/m3) should have a speed of 8 m/s.

a) Calculate the relative value of the convection coefficient and indicate which

surface allows for higher heat transfer, presenting the simplifications made.

b) Calculate the relative value of pressure losses and indicate which surface has a

higher ratio between heat transfer and ventilation power consumption.

Indicate the assumptions made and calculate relative values.

0.3 m

0.5 m

0.16

X

s

h

s=10mm

h=8mm

x=10mm

w=1mm

t=2mm

1.1 1.2

t

Problems about thermal integration of heat exchangers

Problem 8.1 - Consider the diagram below of the pinch point analysis based on the

accumulated heating and cooling currents. Based on these figures:

a) Identify the temperature at which the pinch point occurs and what is the

temperature difference at that point.

b) Identify how much heat must be supplied from outside and the heat that can be

exchanged among the various currents.

c) Apply the energy cascade method to solve the previous item again.

d) Calculate the heat exchanged by all the heat exchangers (1-3) identified in the

heating and the cooling streams at all points.

e) Indicate whether it is possible to change the order between the first and second heat

exchangers and the consequences.

F1

200ºC

Q1

40ºC

]/[ KWcm p

600

180ºC

1800

800

Q2

120ºC100ºC

30ºC

3

3

1

1

2

2

120ºCArrefecedor

Aquecedor110ºC

F1

200ºC

Q1

40ºC

]/[ KWcm p

600

180ºC

1800

800

Q2

120ºC100ºC

30ºC

3

3

1

1

2

2

120ºCArrefecedor

Aquecedor110ºC

]/[ KWcm p

]/[ KWcm p

Problem 8.2 - Consider the results of an integration analysis in order to use the

cooling of a hot current pcm = 1000 W/K between 180 and 40 ° C to heat two cold

currents. The values shown in the chart relate the enthalpy of the cold currents of the

warm and accumulated offset.

TEntrada [ºC] TSaída [ºC]

600 20 150

300 80 170

Accumulated enthalpy

TE [ºC] TS [ºC] Ha

[kW]

600 20 80 48

900 80 150 111

300 150 170 117

The test results indicate the method of installing four heat exchangers, two for each of

the cold currents, as indicated in the figure below:

600

180ºC

Q1

]/[ KWcm p

1000

170ºC300

234

150ºC2F1

F2 3

420ºC

Tq1Tq3Tq440ºC

80ºC

1

1

Tq2

Tf2i

Tf1i600

180ºC

Q1

]/[ KWcm p

1000

170ºC300

234

150ºC2F1

F2 3

420ºC

Tq1Tq3Tq440ºC

80ºC

1

1

Tq2

Tf2i

Tf1i

a) Calculate the heat that can be used in all the streams and the heat removal in

the additional cooler for the hot currents.

b) Considering Tf1i=70ºC and Tf2i=105ºC, calculate the heat exchanged in each

unit.

c) Considering that the difference in temperature between hot and cold must be

maintained consistently above 10 ºC, calculate the intermediate temperature of

the hot Tq1, Tq2, Tq3 and Tq4 and the cold Tf1i and Tf2i (Tf1i = 70ºC;Tf2i=105°C).

d) Calculate the heat exchanged in heat exchangers 1-4.

e) Based on the results of c) discuss the possibility of eliminating one of the

intermediate heat exchangers.

117

111

48

12

-23

117

0

50

100

150

200

-50 0 50 100 150

H (kW)T

(ºC

)

Fria Acumulada

Quente Deslocada