REPORT TO DEPARTMENT OF CHEMICAL ENGINEERING

MIDDLE EAST TECHNICAL UNIVERSITY

FOR COURSE: CHE-327 HEAT AND MASS TRANSFER OPERATIONS

PLATE TYPE HEAT EXCHANGER DESIGNGROUP MEMBERS:

ALARA MELISA AYDIN

COŞKU MOLER

RESKY SAPUTRA

METU

(25.05.2016)

Ankara, TURKEY

1

ABSTRACT

This design project aims to propose a plate type heat exchanger that can meet given heat

duty and find the number of plates required. Plate type heat exchanger uses metal plates to

transfer heat between two fluids. Starting point of this design is to define given properties. It is

asked us to cool the inlet fluid which is waste stream from 65 oC to 40 oC using cooling water at

15 oC. Several information of the inlet and outlet streams are given such as the inlet and outlet

temperature of waste stream, mass flow rate of inlet stream, physical properties of waste and

other constructional data for the similar heat exchanger; vertical, horizontal distances, plate

thickness, length, effective channel width, enlargement factor, chevron angle etc. Several

calculations are done in 2 parts. The first one is geometry analysis used in order to find the

required number of plates. The second one is heat transfer analysis in order to find the required

heat duty for both streams and actual heat duties for clean and fouled involving trial-error

solution. Some correlations is needed such as heat transfer coefficient calculation, correlation of

Nusselt number and Reynold number in which the empirical equation needed. Assumptions are

regarded at the beginning of the design. Finally, the required heat duty for cold and hot streams

are found 1.47 x 107 W and the actual heat duties for clean and fouled are 2.62 x 107 W and 2.32

x 107 W, respectively. The total required number of plates are also found as 105 plates.

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TABLE OF CONTENT

TABLE OF CONTENTS

NOMENCLATURE…………………………………………………………………………1

1. INTRODUCTION …………………………………………………………………..3

1.1. Problem Statement……………………………………………………………...4

1.2. The Calculation Method………………………………………………………..5

1.3. Assumptions……………………………………………………………………..8

2. SAMPLE CALCULATIONS…………………………………………………………10

2.1. Geometry Analysis………………………………………………………………10

2.2. Heat Transfer Analysis………………………………………………………….11

3. RESULT AND DISCUSSIONS……………………………………………………….14

4. CONCLUSIONS……………………………………………………………………….16

5. REFERENCES…………………………………………………………………………17

3

NOMENCLATURE

Thi : inlet hot stream temperature 0c

Tho : outlet hot stream temperature 0c

Tci : inlet cold stream temperature 0c

Tco : outlet cold stream temperature 0c

mc : cold stream mass flow rate kg/s

mh : hot stream mass flow rate kg/s

Gc : The cold channel mass velocity kg/m2s

Gh : The hot channel mass velocity kg/m2s

Ch : steam heat capacity J/kg.K

Cc : ipa-water mixture heat capacity J/kg.K

Qc : Amount of heat transfer under clean condition W

Qf : Amount of heat transfer under fouled condition W

Uf : Fouled overall heat transfer coefficient W/m2K

Uc : overall heat transfer coefficient W/m2K

Ae : Actual effective area m2

A1 : Single plate efective area m2

A1p : Single plate projected area m2

Nt : total number of plates

Ne : The effective number of plates

Np : Number of passes

Ncp : the total number of channels per pass

Lv : Vertical distance m

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Lh : Horizontal distance m

t : Plate thickness m

Lc : Plate pack length m

Lw : Effective channel width m

p : The plate pitch m

b : the mean channel spacing m

Dh : The hydraulic diameter of the channel m

∅ : The enlargement factor

β : Chevron angle o

µh : viscocity of hot fluid N.s/m2

µc : viscocity of cold fluid N.s/m2

Pr : prandalt number

Re : reynolds number

Nu : nusselt number

hc : convective heat transfer coefficient on clod fluid W.m2/K

hh : convective heat transfer coefficient on hot fluid W.m2/K

R fh : fouling factor for hot fluid m2.K/W

R fc : fouling factor for cold fluid m2.K/W

kw : thermal conductivity of the plate material W/m.K

1. INTRODUCTION

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Plate heat exchanger is a type of Heat Exchanger which consists of many corrugated

stainless-steel sheets separated by polymer gaskets and clamped into a steel frame. It transfers

heat by placing thin, corrugated metal sheets side by side and connecting them by gaskets. Flow

of the substances to be heated and cooled takes place between alternating sheets allowing heat to

transfer through the metal sheets.

Figure 1: Plate type heat exchanger

Some advantages using plate heat exchanger are high heat transfer area, high heat transfer

coefficient, having lower floor space requirements, multiple duties can be performed by a single

unit, most suitable type heat exchanger for lower flow rates and heat sensitive substances.

Moreover, area of heat transfer of plate heat exchanger can be increased by increasing the

number of the plates.

1.1. Problem Statement

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In this problem, a plate heat exchanger is needed to be designed for a specific purpose. This heat

exchanger should be able to cool a waste from 65°C to 40°C using cooling water which enters

the heat exchanger at 15°C. The mass flow rate of the waste stream is 140 kg/s and its properties

may be approximated as follows:

ρ = 985 kg/m3

μ = 510 x 10-6 kg/m.s

k = 0.650 W/m.K

Pr = 3.3

Cp = 4200 J/kg.K

Fouling resistance ≡ Fouling resistance of water= 0.0000069 m2.K/W (taken from Heat

Exchanger: Selection, Rating and Thermal Design, table 10.4)

Moreover, we are going to propose a plate type heat exchanger that can meet this heat duty and

find the number of plats required for the heat exchanger.

Some constructional data for a similar heat exchanger are given as follows:

Total effective area (Ae)= 110 m2

Vertical distance (Lv) = 1.55 m

Horizontal distance (Lh)= 0.43 m

Plate thickness (t)= 0.6 mm

Plate pack length (Lc)= 0.38 m

Effective channel width (Lw)= 0.63 m

Enlargement factor (∅ )= 1.25

Chevron angle (β )= 45°

Plates are stainless steel (kw = 16.5 W/m.K, taken from heat exchangers selection, Rating and

thermal design, table 10.1)

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Figure 2: Main dimensions of a chevron plate and and developed and projected dimensions of a

chevron plate cross section normal to to the direction troughs.

1.2. The Calculation Method;

Calculation of this problem design are separated by 2 analysis.

The first one is geometry analysis. The channels increase the surface area of the plate as

compared to the original flat area. To express the increase of the developed length in relation to

the projected length, a surface enlargement factor,∅ , is the defined as the ratio of the developed

length to the flat or projected length

∅= Developed lengthProjected length = Actual effective area

projected plate area =A1/A1p

(1.1)

Where Actual effective area can be calculated as (1.2)

Actual effective area (Ae) = Lp * Lw (1.2)

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Or actual effective area can be calculated as Ae = A1 * Ne

Where the effective number of plates. Ne, can be estimated as Ne = Nt – 2

Also Lp and Lw can be estimated from the port distance Lv and Lh and port diameter Dp as

Lp ≈Lv - Dp (1.3)

Lw ≈ Lh + Dp (1.4)

The value of enlargement factor is calculated the effective flow path.

From (1.3 and 1.4) we can make a new equation to find Lp.

Lp = Lv – Lw + Lh (1.5)

Flow channel is the conduit formed by two adjacent plates between the gaskets. The cross

section of a corrugated surface being very complex, the mean channel spacing, b, is defined as

(1.6)

b = p –t (1.6)

The plate pitch (p) can be determined from the compressed plate pack length (Lc), which usually

specified.

p = Lc / Nt (1.7)

Where Nt is the total number of plates.

The hydraulic diameter of the channel (Dh) can be estimated as (1.8)

Dh ≈ 2b / ∅ (1.8)

Finding the total number of channels per pass (Ncp) is obtained from (1.9)

Ncp = (Nt – 1) / 2 *Np (1.9)

Where Nt is total number of plates and Np is the number of passes.

From those correlations we can find total number of plates required. With plate type heat

exchangers, heat transfer is enhanced. The heat transfer enhancement will strongly depend on the

chevron inclination angle (β) relative to flow direction. Moreover, the performance of a chevron

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plate will also depend upon the surface enlargement factor (∅ ¿, the channel profile, the mean

channel spacing (b), the temperature dependent physical properties, and especially the variable

viscosity effects.

The second one is heat transfer analysis. In order to find heat transfer coefficient (h),

correlation of Nusselt number (Nu) and Reynold number (Re) is needed. The Reynolds number

based on channel mass velocity and the hydraulic diameter of the channel is defined as (1.10)

Re = Gc * Dh / μ (1.10)

Where the channel mass velocity is given by (1.11)

Gc = mch / Ncp * b * Lw (1.11)

Correlation empirical equation is needed. The correlation in the form of (1.12) are proposed by

Kumar and the values of constants Ch and n are given in table 1.1 (Heat exchangers:Selection,

Rating and Thermal design 2nded, p. 395)

Nu = Ch * Ren * Pr * (μ

μw)0.17 (1.12)

Table 1.1. Constants for single-phase heat transfer and pressure loss calculation in gasketed-plate

heat exchanger (Heat exchangers:Selection, Rating and Thermal design 2nded, p. 394).

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Overall heat transfer coefficient under fouling conditions is calculated as (1.13)

1U f

= 1hh

+ 1hc

+ tkw

+Rfh+Rfc (1.13)

The required heat duty (Qr) for cold and hot streams is defined as (1.14)

Qr = (m∗Cp ¿c *(Tc2 – Tc1) = (m∗Cp ¿h * (Th1 – Th2) (1.14)

On the other hand, the actually obtained heat duty (Qf) for fouled conditions is defined as (1.15)

Qf = U*Ae*F*∆ T lm (1.15)

In order to find ∆ T lm, equation (1.16) is defined as

∆ T lm =¿¿ (1.16)

For heat transfer analysis we are not given T c ,out. So that physical properties of water cannot be

decided. Hereby trial-error solution is needed to find the correct T c ,out. To determine the correct

one we need to check both the required heat of hot and cold fluid. From energy balance analysis,

the required heat of hot and cold fluid must be same. The calculation for trial-error solution stops

until it reaches the equality of the required heat of hot and cold fluid.

1.3. Assumptions;

Physical properties are constant at 1 atm

Heat loses to or from the surrounding are negligible.

The kinetic and potential energy changes are negligible.

The heat exchanger operates at steady-state conditions.

No phase changes in the fluid streams.

Wall thermal resistances are distributed uniformly.

The velocity and temperature at the inlet of the heat exchanger on each fluid side are

uniform.

The heat transfer area (A) is distributed uniformly on each fluid side.

The cold and hot stream mass flow rate are same

Number of passes is one pass

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2. SAMPLE CALCULATIONS

2.1 Geometry Analysis

12

Ae 110m2 Lv 1.55m Lh 0.43m t 0.0006m Lc 0.38m Lw 0.63m

kw 16.5W

m K Np 1

The projected plate areaLp Lv Lw Lh 1.35mA1p Lp Lw 0.851m2Single plate heat transfer areaA1 A1p 1.063m2The effective number of platesNe

AeA1

103.469Total number of platesNt Ne 2 105.469The plate pitchp

LcNt

3.603 10 3 mthe mean channel flow gapb p t 3.003 10 3 mThe one channel flow areaAch b Lw 1.892 10 3 m2The channel hydraulic

Dh2 b

4.805 10 3 m

2.2 Heat Transfer Analysis

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Total number pf channel per pass

NcpNt 12 Np

52.234

(Trial-error method)

assumewater properties at 313/288 = 300.5 K 8.4 10 4 Pa s

k 0.611W

m K mc 140

kgs

PrCpc

k5.748 Rfwater 0.0000069

m2 KW

waste properties

Cpwaste 4200J

kg Kkwaste 0.650

Wm K

Prwaste 3.3waste 51010 6 Pa s

Rfwaste Rfwater 6.9 10 6s3 Kkg

mh mc 140kgs

The mass flow rate per channel

mchmc

Ncp2.68

kgs

GchmchAch

1.417 103kg

s m2 Gcc Gch 1.417 103

kg

s m2

for hot fluid for cold fluidReh

Gch Dhwaste

1.335 104 RecGcc Dh

8.103 103

Tco 40 273 313K

Tho 40 273 313K

Thi 65 273 338K

Tci 15 273 288K

Cpc 4185.847J

kg K

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Table 10.6 450 Reh 100 Rec 100

ch 0.3 n 0.663

hhotkwaste

Dhch Rehn

Prwaste

1

3 3.283 104

kg

s3 K or hhot= 3.283x104 W/m2K

or hcold=2.669x104 W/m2Khcold

kDh

ch Recn Pr

1

3 2.668 104kg

s3 K

The clean overall heat transfer coefficientUc1

1hcold

1hhot

t

kw

9.587 103kg

s3 K

or 9.587 103 W/m2K The fouled overall heat transfer coefficient

Uf1

1Uc

Rfwaste Rfwater8.467 103

kg

s3 K

T2 Tho Tci 25K T1 Thi Tco 25Kfor counter current flowLMTD 25Kthe actual heat duties for clean and fouled surfacesQc Uc Ae LMTD 2.636 107 WQf Uf Ae LMTD 2.328 107 WThe required heat Qrh mh Cpwaste Thi Tho( ) 1.47 107 W

Qrc mc Cpc Tco Tci( ) 1.465 107 W

Since Qrh and Qrc is almost same, then Tco assumption is acceptable

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The safety factor

CsQfQrh

1.584

The precent over surface design

OS 100Uc Rfwaste Rfwater( ) 13.23

The cleanliness factor

CFUfUc

0.883

3 RESULTS AND DISCUSSONS

Objective of this project was to design a proper plate type heat exchanger. Several assumptions

were made while making the calculations. These assumptions are constant physical properties at

1 atm, negligible heat losses through the surroundings, negligible kinetic and potential energy

changes, operating at steady state, no phase changes, same mass flow rates and, uniform

temperature and velocity at the inlet of the heat exchanger. Calculation of this problem design

are separated by 2 analysis. The first one is geometry analysis and the second one is heat transfer

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analysis. Geometry is analyzed by the given datas and calculations were made according to these

given datas. First of all projected length was calculated as 1.35 m and then projected area was

determined as 0.851 m2, by using this value single plate heat transfer area was calculated by

enlargement factor times projected area, enlargement factor,∅ , is the defined as the ratio of the

developed length to the flat or projected length and found as 1.25. Up to here effective area and

single plate heat transfer area was calculated number of effective plates was found as 103.469 by

dividing effective area by single plate heat transfer area. Then total number of plates were found

as 105.469. After that plate pitch was determined as 3.603∗10−3 m and mean flow channel gap

was found by using that one as 3.003∗10−3 m. The one channel flow area was determined by

using mean flow channel gap and found as 1.892∗10−3 m2 hydraulic diameter was calculated by

2 mean flow channel gap divided by enlargement factor and found as 4.805∗10−3 m. Lastly total

number pf channel per pass was found as 52.234 and the geometry calculations were done. In the

heat transfer analyses in order to find heat transfer coefficient (h), correlation of Nusselt number

(Nu) and Reynold number (Re) is needed. The Reynolds number based on channel mass velocity

and the hydraulic diameter of the channel is defined as Re for hot fluid was determined as

1.335∗104and8.303∗103 for the cold fluid. Where the channel mass velocity is given by Gc

1.417∗103 kgm2∗s

for both hot and cold fluid. In calculation of Nusselt number Correlation

empirical equation is needed. The correlation in the form of (1.12) are proposed by Kumar and

the values of constants Ch and n are given in table 1.1. This correlation gave us the heat transfer

coefficients directly by using Nusselt number as 3.283∗104 Wm2∗K

for hot 2.668∗104 Wm2∗K

for

cold fluid. By using these heat transfer coefficients, the overall heat transfer coefficient for hot

clean and fouled heat exchangers were found 9.587∗103 Wm2∗K

, 8.467∗103 Wm2∗K

respectively.

In the determination of Qr and Qf ∆ T lm is required and for heat transfer analysis we are not

given T c ,out. So that physical properties of water cannot be decided. Therefore trial-error solution

is needed to find the correct T c ,out. To determine the correct one we need to check both the

required heat of hot and cold fluid. From energy balance analysis, the required heat of hot and

cold fluid must be same. The calculation for trial-error solution goes until it reaches the equality

of the required heat of hot and cold fluid. To be sure of the T c ,out value was acceptable Qrh and

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Qrc was determined and found as 1.47∗107 W and 1.465∗107W which is really close to each

other so that Tcout value that choosen is acceptable. After calculation of ∆ T lm Qr and Qf was

calculated as 2.637∗107 W , 2.328∗107W respectively. Lastly the safety factor was calculated by

dividing Qf to Qrh and found as 1.584 and cleanless factor as 0.883. According to the literature

Process heat transfer, 1950, typical design are based on safety factor of 1.6 which is closer to

1.58. Moreover, based on Heat Exchanger: Selection, Rating, and Thermal Design, 2nd , Typical

designs are based upon a cleanliness factor of 0.85 which is quite closer with our value.

4 CONCLUSION

After performing the required equations which are given in calculation part, it is seen that

each plate is corrugated to increase the surface area and maximize heat transfer. Within a plate

heat exchanger, the fluid paths alternate between plates allowing the two fluids to interact, but

not mix, several times in a small area. The data from the similar heat exchanger is used in order

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to define the heat exchanger that is used in the project. The goal of the project is to understand

the characteristics and design of a plate heat exchanger. By geometry and heat transfer analysis,

the total number of plates, the actual with fouled surface and required heat duty are found as 105

plates, 2.63 x 107 W and 2.32 x 107 W, respectively. It is considered that no heat loss to

surroundings however in reality there should be heat loss, therefore, error due to this assumption

must be considered in real life applications.

5 REFERENCES

Incropera, F. (2012). Principles of heat and mass transfer (7th ed.). Singapore: John

Wiley & Sons Singapore Pte.

Leib, T., & Pereira, C. (2008). Perry's chemical engineers' handbook (8th ed.). New York:

McGraw-Hill.

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Kakaç. S. (Sadik). Heal exchangers : selection, rating. and thermal design / Sadik Kakaç, Hongtan Liu.-. 2nd ed

Kern, “Process heat transfer”, McGraw Hill, 1950

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