1

CHAPTER 1

INTRODUCTION

Heat exchangers are important, and used frequently in the process, heat and power, air-

conditioning and refrigeration, heat recovery, transportation and manufacturing industries. Such

equipment is also used in electronics cooling and for environmental issues like thermal pollution,

waste disposal and sustainable development. Various types of heat exchangers exist. The study

concerns plate heat exchangers (PHEs), which are one of the most common types in practice.

Plate heat exchangers are widely used in dairy, pharmaceutical and paper/pulp industry as well

as in HVAC applications. Flow of the substances to be heated and cooled takes place between

alternating metal sheets allowing heat transfer between the fluids. Gaskets are placed between

the plates to avoid mixing of the fluids. In the majority of the industrial applications, the plate

heat exchanger is the design of choice because of its many advantages. Among these are:

• Superior thermal performance; plate heat exchangers have heat transfer coefficients as

high as three to four times that of tubular types because of smaller hydraulic diameter.

The turbulent conditions are achieved at much lower Reynolds number hence higher heat

transfer coefficients.

• Compact design; the superior thermal performance of the plate heat exchanger and the

space efficient design of the plate arrangement results in a very compact piece of

equipment. Space requirements for the plate heat exchanger generally run 10% to 50%

that of a shell and tube unit for the same amount of heat transfer. In addition, tube

cleaning and replacing clearances are eliminated.

• Expandability and multiplex capability; the nature of the plate heat exchanger

construction permits expansion of the unit should heat transfer requirements increase

2

after installation. In addition, two or more heat exchangers can be housed in a single

frame, thus reducing space requirements and capital costs.

• Ease of maintenance; the construction of the heat exchanger is such that, upon

disassembly, all heat transfer areas are available for inspection and cleaning. Disassembly

consists only of loosening a small number of tie bolts.

• Availability of a wide variety of corrosion resistant alloys; since the heat transfer area is

constructed of thin plates, stainless steel or other high alloy construction is significantly

less costly than for a shell and tube exchanger of similar material.

1.1 Need Statement

A number of analytical and experimental studies have been conducted to study the heat transfer

and fluid flow characteristics of tubular heat exchangers. However a very limited work is found

in open literature regarding the heat transfer through plate heat exchangers. Computerized design

software has been developed by the manufacturers of plate heat exchangers but not a lot of data

are available for research purposes about the design of these heat exchangers. Therefore, there is

an urgent need for comprehensive and systematic research in this field.

1.2 Project Scope

In this project, to investigate the heat transfer characteristics and thermal performance of plate

heat exchangers, a series of experimentation were performed. The test rig was used to conduct

single phase experiments in order to develop Nusselt number correlation for the plate heat

exchanger with a mixed plate configuration. The operating range of flow rates and fluid

temperatures correspond to a maximum Reynolds number (Re) of 4500 and Prandtl number (Pr)

in the range of 5.6 to 8. The project was divided into five different phases:

1. Literature review of Nusselt number correlations

3

2. Writing the code for Modified Wilson Plot

3. Setting up the apparatus

4. Experimentation

5. Analysis of the result and conclusion

1.3 Some Important Definitions

1.3.1 Nusselt Number

Nusselt number is equal to the dimensionless temperature gradient at the surface, and it

essentially provides a measure of convective heat transfer.

(1)

The Nusselt number is to the thermal boundary layer what the friction coefficient is to velocity

boundary layer. Equation (1) implies that for a given geometry, the Nusselt number must be

some universal function of x*, Reynolds number and Prandtl number.

(2)

where:

= characteristic length (m)

= thermal conductivity of the fluid (W/m.K)

= convective heat transfer coefficient (W/m2.K)

Selection of the characteristic length should be in the direction of growth (or thickness) of the

boundary layer. Some examples of characteristic length are: the outer diameter of a cylinder in

(external) cross flow (perpendicular to the cylinder axis), the length of a vertical plate

undergoing natural convection, or the diameter of a sphere. For complex shapes, the length may

be defined as the volume of the fluid body divided by the surface area. The thermal conductivity

of the fluid is typically (but not always) evaluated at the film temperature, which for engineering

purposes may be calculated as the mean-average of the bulk fluid temperature and wall surface

4

temperature. For relations defined as a local Nusselt number, one should take the characteristic

length to be the distance from the surface boundary to the local point of interest. However, to

obtain an average Nusselt number, one must integrate said relation over the entire characteristic

length.

1.3.2 Nusselt Number Correlation

Generally, for single phase heat transfer, Nu is represented by an empirical expression of the

form:

(3)

where C, m, and n are independent of the nature of fluid used. The last term in the expression

accounts for the variable viscosity effect.

1.3.3 Prandtl Number

The Prandtl number Pr is a dimensionless number approximating the ratio of momentum

diffusivity (kinematic viscosity) and thermal diffusivity.

(4)

where:

: dynamic viscosity, (Pa s)

: thermal conductivity of the fluid, (W/m.K)

: specific heat, (J/kg.K)

Note that whereas the Reynolds number is subscripted with a length scale variable, Prandtl

number contains no such length scale in its definition and is dependent only on the fluid and the

fluid state. As such, Prandtl number is often found in property tables alongside other properties

such as viscosity and thermal conductivity. This number essentially delineates a ratio which is

5

the thickness of the momentum boundary layer to the thermal boundary layer. When Pr is small,

it means that the heat diffuses very quickly compared to the velocity (momentum). This means

that for liquid metals the thickness of the thermal boundary layer is much bigger than the

velocity boundary layer.

1.3.3 Reynolds Number

Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial

forces to viscous forces and consequently quantifies the relative importance of these two types of

forces for given flow conditions.

(5)

where:

is the mean fluid velocity, (m/s)

is a characteristic linear dimension, (m)

is the dynamic viscosity of the fluid, (Pa·s or N·s/m² or kg/m·s)

is the density of the fluid, (kg/m³)

Reynolds number can be defined for a number of different situations where a fluid is in relative

motion to a surface (the definition of the Reynolds number is not to be confused with the

Reynolds Equation or lubrication equation). These definitions generally include the fluid

properties of density and viscosity, plus a velocity and a characteristic length or characteristic

dimension. For flow in a pipe or a sphere moving in a fluid the internal diameter is generally

used today. Other shapes (such as rectangular pipes or non-spherical objects) have an equivalent

diameter defined.

6

CHAPTER 2

MODIFIED WILSON PLOT

Modified Wilson Plot Technique is used to determine the value of multiplier and exponent of Reynolds

Number in the Nusselt Number Correlation.

The heat transfer coefficients for the cold and hot sides of plate heat exchanger are obtained by the

following equations respectively

(1)

(2)

The following basic relation (3) is algebraically manipulated in two different ways to obtain two

equations, which are subsequently used for obtaining the Modified Wilson Plot:

(3)

2.1 Linear Modification

Substituting equation (1) and (2) into the basic relation (3):

7

(4)

The above equation (4) is a linear modification of the basic relation and it is of the form:

Where,

Slope:

Intercept:

An initial guess ‘p’ is used to obtain a plot between X1 and Y1 .This plot yields Cc and Ch

2.2 Logarithmic Modification

Given below is the logarithmic modification of (3):

8

=

(5)

Eq. (5) is also of linear form

Slope:

Intercept:

A plot between X2 and Y2 provides the iterated value of p and Cc

2.3 Iterative Procedure

Steps for the iterative procedure are as follows:

• The value of Ch obtained from the linear plot (X1, Y1) coupled with the initial guess value of ‘p’ is

used to obtain a logarithmic plot (X2, Y2) as delineated by the logarithmically modified version

(5)

• The gradient of the logarithmic equation is the new value of ‘p’

• Reinsert ‘p’ obtained from the second plot (X2, Y2) into (4) to acquire yet another value of ‘p’ in

the second plot. The new value approaches closer and closer to the root (i.e. converges)

• Repeat this procedure until the difference between consecutive values of “p” tends to a value

smaller than the prescribed error

9

CHAPTER 3

EXPERIMENTAL PARAMETERS AND APPARATUS

The literature review has established that the general form of the Nusselt number correlation for

plate type heat exchangers is in the form of power law and given by:

Where, C and m are constants which were evaluated by experimentation. The purpose of the

experimental setup is to provide a means to control certain dimensionless parameters which are

explained below.

3.1 Experimental Parameters

3.1.1 Reynolds Number:

In the case of the plate heat exchangers, the hydraulic diameter is very small, of the order of mm,

so the turbulent conditions are achieved quite early i.e., at a very low value of Reynolds number.

Simpson reported that the turbulent condition can be achieved at Reynolds numbers as low as

150 [8]. Reynolds number is a function of fluid flow rate. In the experimental setup, the

Reynolds number is varied by changing the fluid flow rate. Variable frequency drive (VFD)

along with bypass loops and valves were used to vary the flow rate of water. Fluid flow through

the heat exchanger was varied by the mutual adjustment of these valves and the settings on the

VFD, allowing the desired amount of fluid to flow through the heat exchanger.

3.1.2 Prandtl number

Prandtl number is defined as the ratio of the momentum boundary layer to the thermal boundary

layer in heat transfer problems. Mathematically, it is important to note that the Prandtl number is

10

only a function of fluid properties. These fluid properties depend upon the nature of fluid and the

fluid temperature. In our experimental setup, the Prandtl number was varied by changing the

fluid temperature.

3.2 Experimental Apparatus

Fig.3.1: Photograph of the Experimental Setup

Fig. 3.2: Schematic of the Apparatus [1]

11

A schematic of the experimental apparatus is shown in Fig.3.2. The central piece of equipment is

the plate heat exchanger. The setup consists of a hot fluid loop and a cold fluid loop. The hot

fluid loop consists of a hot fluid tank and a pump that is pumping hot fluid from the tank to the

heat exchanger. The hot fluid tank has the capacity of 150 US gallons and is equipped with 8

electric immersion heaters. One of the heaters is attached to a temperature controller and

magnetic contactor. When the desired temperature is reached in the hot fluid tank, the controller

sends a signal to the magnetic contactor which acts as a relay and disconnects the supply from

the heater. The cold fluid loop consists of a cold fluid tank and a pump that is pumping cold fluid

from the cold fluid tank to the heat exchanger. The cold fluid tank has the capacity of 35 US

gallons. Temperatures are measured at the inlet and exit of the plate heat exchangers for both the

hot and cold streams. Temperatures are measured at various locations using the Resistance

Temperature Device (RTDs). The fluid is cooled by a 2 TR Packaged Air Cooled Water Chiller.

R22 is used as the refrigerant for chilling the fluid in the chiller.

The desired temperatures of the cold and hot fluids were achieved and the fluids of both the

loops were pumped into the Plate heat exchanger where they exchanged heat. The hot fluid

flowed from top to bottom within a channel of the plate heat exchanger while the cold fluid

flowed from bottom to the top of the channel achieving counter-flow. Flow rate measurements

were taken by the conventional bucket and stop watch method. Reynolds number was varied by

changing the fluid flow rate through variable frequency drives and bypass valves. Prandtl

number was varied by changing the temperature of the fluid using chiller, heaters and

temperature controllers. Experiments were conducted at various temperatures and flow rates of

hot and cold fluids using plates of a fixed chevron angle, β = 45o. Such plate configuration was

achieved using a combination of 30o and 60o plates. The system was allowed to reach the steady

state before any reading was made.

12

3.2.1 Equipment Details

The following table lists the equipment used in our experiment and their specifications:

Table 3.1: Details of the Equipment [7]

13

3.3 Plate Heat Exchanger

In order to completely understand the plate heat exchanger, it is very important to understand the

plate geometry. Discussions of various parameters that define the plate geometry are provided

below.

Fig 3.3: Plate Geometry [4]

Different geometric parameters of plate heat exchangers are defined below

Chevron Angle

Usually termed β and varies between 22◦–65◦. This angle also defines the thermal hydraulic

softness (low thermal efficiency and pressure drop) and hardness (high thermal efficiency and

pressure drop).

Enlargement Factor

This factor φ is the ratio of the developed length to the protracted length.

14

Mean Flow Channel Gap

This is defined as the actual gap available for the flow.

b = p – t

Channel Flow Area

This is the actual flow area defined as:

Ax = b*w

Channel Equivalent Diameter

Defined as:

Dh = 4Ax/P

where P = 2(b + φw) = 2φw.

Since b << w,

Therefore; Dh = 2b/φ

The plate specifications for the present study are shown below in Table 3.2:

Width w 185mmVertical distance b/w ports Lp 565 mmChannel spacing b 2.2 mmEffective Area A 0.095 m2

Surface enlargement factor φ 1.117Chevron angle β 45o (π/4 radian)

Table 3.2: Plate specifications for experimentation

15

CHAPTER 4

EXPERIMENTATION

4.1 Calibration of RTDs

Resistance Temperature Detectors (RTDs), are temperature sensors that exploit the predictable

change in electrical resistance of some materials with changing temperature. Our experimentation

required temperatures ranging from 12oC to 32oC. The RTDs used were PT100 A Class RTDs with

outer diameter of 6 mm. These RTDs provide stable output for long period of time with high

accuracy and are easy to recalibrate. A total of nine RTDs were calibrated relative to a reference

RTD. The selected reference was a brand new, factory calibrated RTD.

Plots for calibration of the RTDs with respect to the reference are shown below in Fig 4.1 and 4.2.

Fig 4.1: Calibration of RTDs

16

Fig 4.2: Calibration of RTDs

Those RTDs which showed an error of ±0.2oC were selected and installed in the experimental setup.

4.2 Experimental Procedure

The variable speed water pump was switched on, in order to start hot water circulation. The cold

water circulation was then started by switching on the cold water pump. A chiller was used to

maintain the desired cold water temperature. The heating of hot water side was initiated by switching

on the desired number of submerged water heaters in the hot water tank. The tank was provided with

eight submerged heating elements; six of them were of 3 kW capacities each while two of them were

rated at 2 kW each. The number of heaters used was dependent on the heat flux required for a

specific experiment. One of the 2 kW heaters was connected to the hot water inlet RTD through an

on/off switch and a digital thermostat which was capable of controlling the temperature within

±0.1oC. The hot water inlet temperature, set using a thermostat, was pre-selected based on the desired

value of Prandtl number. The hot water flow rate was adjusted by varying the speed of the pump

through the power inverter. The cold water flow rate was adjusted to desired settings by the flow

control valve. The experiments were conducted in a matrix of varying Reynolds number at a fixed

Prandtl number. Five different Reynolds numbers were used for our Prandtl number setting.

Sufficient time was given to the system to achieve steady state condition. The flow rates,

temperatures at all inlets and exits of the plate heat exchanger and energy balance were monitored.

The goal of this experimentation was to determine the convection heat transfer coefficient.

17

4.3 Range of Experimentation and Data

Experimentation for a range of Reynolds number from 500 to 4500 were carried out while

maintaining a constant Prandtl number of 7.5 ± 5% on the cold side.

For a fixed Reynolds number, five data points were recorded by varying the heat flux on the hot

side of the heat exchanger. Five such experiments were carried out for Reynolds number in the

given range. Heat flux was varied by controlling the hot inlet temperature (Th,i) from 20oC to

32oC.

Table 4.1 shows the experimental data:

Table 4.1: Experimental Data

T h,i0C

T h,o0C

T c,i0C

T c,o0C

m hkg/s

m ckg/s

31.73 25.20 12.04 21.10 0.086 0.059

31.00 25.90 12.30 21.40 0.105 0.060

27.50 23.59 12.56 19.99 0.100 0.056

23.84 21.09 12.53 17.78 0.106 0.059

20.99 18.90 13.50 16.79 0.092 0.060

30.42 23.31 15.19 19.06 0.091 0.164

25.28 20.63 14.82 17.86 0.100 0.156

22.55 20.05 16.60 18.20 0.100 0.156

20.85 19.15 16.64 17.76 0.100 0.156

29.33 23.15 17.02 19.39 0.104 0.266

27.81 22.17 16.39 18.65 0.104 0.266

25.14 20.10 14.92 16.92 0.104 0.266

24.07 19.53 14.76 16.55 0.104 0.266

22.33 18.39 14.10 15.69 0.104 0.266

29.75 22.58 16.37 18.34 0.100 0.370

26.66 20.84 15.70 17.30 0.104 0.370

25.10 19.85 15.13 16.63 0.104 0.370

23.30 19.26 15.64 16.77 0.104 0.370

21.44 18.79 16.41 17.16 0.104 0.370

28.24 21.92 16.91 18.21 0.104 0.485

26.32 20.43 15.67 16.97 0.104 0.485

24.89 19.74 15.54 16.65 0.104 0.485

23.01 19.74 16.96 17.66 0.104 0.485

22.05 19.34 17.02 17.62 0.104 0.485

18

CHAPTER 5

ANALYSIS AND RESULTS

5.1 Analysis Technique

An analysis was performed for the given data using EXCEL and MATLAB code. Property tables

for water were incorporated into our MATLAB program for the ease of interpolation and

calculation of the fluid properties. The values of the measured flow rates and temperatures were

input to the Graphical User Interface (GUI) of the program, which provided the fluid properties.

Properties of the fluid on either side were evaluated at their respective mean fluid temperatures.

The program code was based on the Modified Wilson Plot Technique. Given the initial guess

value and experimental data, the program automatically performs iterations and generates plots

that can be used to find the value of ‘C’ and ‘m’ in the Nusselt number correlation.

Below is the screenshot of the MATLAB graphical user interface:

Fig 5.1: MATLAB GUI

19

5.2 Results

The initial guess value ‘p’ and fluid properties are used to generate a plot between X1 and Y1.

The slope and intercept of the linear plot along with the guess value and fluid properties generate

the logarithmic plot. The slope of the logarithmic plot gives the value of ‘p’ to be used for the

next iteration. This procedure is repeated until the slope of the logarithmic plot converges.

The following table and figures show the results of our analysis:

Table 5.1: Experimental Data and Analysis

T h,i0C

T h,o0C

T c,i0C

T c,o0C

m hkg/s

m ckg/s Re h Re c Pr h Pr c

UW/m2.K Nu h Nu c

31.73 25.20 12.04 21.10 0.086 0.059 1005 529 5.62 7.62 2082 44 29

31.00 25.90 12.30 21.40 0.105 0.060 1229 541 5.62 7.56 2053 52 29

27.50 23.59 12.56 19.99 0.100 0.056 1099 493 6.03 7.69 1881 49 27

23.84 21.09 12.53 17.78 0.106 0.059 1081 506 6.52 7.95 1768 49 28

20.99 18.90 13.50 16.79 0.092 0.060 882 516 6.97 7.95 1765 42 28

30.42 23.31 15.19 19.06 0.091 0.164 1030 1482 5.83 7.50 2948 45 70

25.28 20.63 14.82 17.86 0.100 0.156 1032 1379 6.44 7.67 3102 47 66

22.55 20.05 16.60 18.20 0.100 0.156 994 1416 6.72 7.45 2829 47 67

20.85 19.15 16.64 17.76 0.100 0.156 963 1410 6.96 7.49 2678 46 66

29.33 23.15 17.02 19.39 0.104 0.266 1159 2455 5.92 7.30 3583 51 108

27.81 22.17 16.39 18.65 0.104 0.266 1125 2417 6.12 7.43 3512 50 107

25.14 20.10 14.92 16.92 0.104 0.266 1067 2321 6.49 7.77 3502 49 105

24.07 19.53 14.76 16.55 0.104 0.266 1048 2305 6.63 7.83 3438 48 105

22.33 18.39 14.10 15.69 0.104 0.266 1011 2259 6.89 8.01 3353 48 103

29.75 22.58 16.37 18.34 0.100 0.370 1110 3353 5.94 7.46 3679 49 144

26.66 20.84 15.70 17.30 0.104 0.370 1094 3284 6.31 7.64 3780 49 142

25.10 19.85 15.13 16.63 0.104 0.370 1069 3229 6.52 7.78 3763 49 140

23.30 19.26 15.64 16.77 0.104 0.370 1034 3258 6.72 7.71 3748 48 141

21.44 18.79 16.41 17.16 0.104 0.370 1006 3310 6.94 7.57 3747 48 141

28.24 21.92 16.91 18.21 0.104 0.485 1127 4416 6.11 7.42 3995 50 182

26.32 20.43 15.67 16.97 0.104 0.485 1085 4283 6.37 7.68 3962 49 179

24.89 19.74 15.54 16.65 0.104 0.485 1060 4257 6.54 7.73 3930 49 179

23.01 19.74 16.96 17.66 0.104 0.485 1037 4391 6.70 7.47 3812 48 181

22.05 19.34 17.02 17.62 0.104 0.485 1020 4392 6.83 7.47 3802 48 181

20

Fig 5.2: Linear Plot

Fig 5.3: Logarithmic Plot

After successive iterations, the gradient and intercept of the logarithmic plot give:

m = 0.881

Cc = Ch = 0.0566

Hence the Nusselt number correlation is found to be:

The abovementioned empirical correlation is valid for following range of experimentation:

500 < Re < 4500

21

5.6 < Pr < 8.0

Chevron angle (β) = 45o, achieved using mixed plate configuration of 30o /60o

5.3 Comparison with Existing Literature

Fig 5.4: Nu Vs. Re, a comparison

We compared our correlation with those of other researchers which were applicable to our range

of experimentation. The results are comparable to those of Khan [1], Thonon [9], and Cooper

[10].

5.4 Investigating the effects of varying ‘n’

The following table demonstrates the effect of changing the exponent ‘n’ of the Prandtl number

on the multiplier ‘C’ and exponent ‘m’ in the Nusselt number correlation.

n C m0.30 0.060 0.8820.33 0.057 0.8810.35 0.055 0.8810.40 0.049 0.883

Table 5.2: Effect of ‘n’ on ‘C’ and ‘m’

22

Fig 5.5: ‘C’ vs. ‘n’ plot

Fig 5.6: ‘m’ vs. ‘n’ plot

Changing the value of exponent ‘n’ has negligible effect on the Nusselt number correlation. The

correlation is a strong function of Reynolds number and a weak function of Prandtl number.

Hence, n = 1/3 is a reasonable choice.

23

CHAPTER 6

CONCLUSION AND FUTURE WORK

Experiments were performed to investigate the thermal performance of a commercial plate heat

exchanger by developing an empirical single phase heat transfer correlation. After

experimentation, it was found that the Nusselt number correlations for hot and cold side are the

same because the multipliers in the correlation (i.e. CC and CH) were equal. Although

experimentation was performed with a fixed cold side Prandtl number, the above result means

that our correlation is valid for an extended range of Prandtl numbers. The presented correlation

is valid for 500 < Re < 4500 and 5.6 < Pr < 8.0 and β=45o.

The Nusselt number correlation obtained was comparable to the correlations in existing literature

Khan [1], Thonon [9], Cooper [10].

Nusselt number was found to be a strong function of Reynolds number. In contrast, changing the

value of the Prandtl exponent ‘n’ in the correlation has negligible effect on the Nusselt number.

Hence, a value of 1/3 is used in accordance with earlier research.

Following are suggestions for further work in this area:

- Extending the range of Reynolds number to investigate any changes in the correlation

- Broadening the range of heat flux over which the experiments are performed

- Using a viscous working fluid like ethylene glycol, thereby extending the range of

Prandtl number

- Repeating the experiment to take into account the effects of varying plate configuration

and plate geometry

- Eliminating the unsteady effects of the chiller by using municipal water

- Developing pressure drop correlations

24

BIBLIOGRAPHY

[1] T.S. Khan, M.S. Khan, Ming-C. Chyu, Z.H. Ayub, Experimental investigation of single

phase convective heat transfer coefficient in a corrugated plate heat exchanger for multiple plate

configurations, Applied Thermal Engineering 30 (2010) 1058–1065.

[2] Jose Fernandez-Seara, Francisco J. Uhia, Jaime Sieres, Antonio Campo, A General Review

of the Wilson Plot Method and its Modifications to Determine Convection Coefficients in Heat

Exchange Devices, Applied Thermal Engineering 27 (2007) 2745–2757.

[3] Pettersen, J., Rieberer, R., Tollak, S., Heat Transfer and Pressure Drop for Flow of

Supercritical and Subcritical CO2 in Microchannel Tubes, February 2000.

[4] Ayub, Z.H., Plate Heat Exchanger Literature Survey and New Heat Transfer and Pressure

Drop Correlations for Refrigerant Evaporators, Heat Transfer Engineering, 24(5): pp. 3–16,

2003.

[5] Hayes, N., Jokar, A., Study of Carbon Dioxide Condensation in Chevron Plate Exchangers,

pp. 46-52, ASHRAE 1394-RP, 2009.

[6] Frank P. Incropera, Fundamentals of Heat and Mass transfer, 5th edition, John Wiley & Sons,

2001.

[7] Riaz, K.U., Ali, M.H., Javed, S., Design and Fabrication of an Experimental Setup to Develop

Nusselt Number Correlation for Single Phase Flow through Plate Heat Exchanger, Senior Design

Project, GIK Institute (2010).

[8] R. Simpson, and S. Almonacid, Plate Heat Exchanger, Encyclopedia of agricultural food and

biological engineering, 14 August 2003

25

[9] B. Thonon, Design method for plate evaporators and condensers, in: 1st International

Conference on Process Intensification for the Chemical Industry, BHR Group Conference Series

Publication 18, 1995, pp. 37–47.

[10] Cooper, A., Recover More Heat with Plate Heat Exchangers, The Chemical Engineer, no.

285, pp. 280–285, 1974.

26

APPENDIX A

MATLAB CODE

Given below is the MATLAB code for the program. To save space, only part of the code has

been written. Nevertheless, the reader is strongly recommended to run the CD included with this

report to gain access to the executable code and it’s GUI.

temp=[273.15 275 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 373.15];

rho=[1.00E+03 1.00E+03 1.00E+03 1.00E+03 9.99E+02 9.98E+02 9.97E+02 9.95E+02 9.93E+02 9.91E+02 9.89E+02

9.87E+02 9.84E+02 9.82E+02 9.79E+02 9.77E+02 9.74E+02 9.71E+02 9.67E+02 9.63E+02 9.61E+02 9.58E+02];

cp=[4217 4211 4198 4189 4184 4181 4179 4178 4178 4179 4180 4182 4184 4186 4188 4191 4195 4199 4203 4209 4214 4217];

muo=[1.75E-03 1.65E-03 1.42E-03 1.23E-03 1.08E-03 9.59E-04 8.55E-04 7.69E-04 6.95E-04 6.31E-04 5.77E-04 5.28E-04

4.89E-04 4.53E-04 4.20E-04 3.89E-04 3.65E-04 3.43E-04 3.24E-04 3.06E-04 2.89E-04 2.79E-04];

k=[5.69E-01 5.74E-01 5.82E-01 5.90E-01 5.98E-01 6.06E-01 6.13E-01 6.20E-01 6.28E-01 6.34E-01 6.40E-01 6.45E-01 6.50E-

01 6.56E-01 6.60E-01 6.68E-01 6.68E-01 6.71E-01 6.74E-01 6.77E-01 6.79E-01 6.80E-01];

b=0.0029;

w=0.185;

phi=1.117;

d_hyd=(2*b)/phi;

A=b*w;

A_h=0.095;

x=1;

handles.t_ho = handles.t_ho +273.15;

handles.t_hi = handles.t_hi +273.15;

handles.t_co = handles.t_co +273.15;

handles.t_ci = handles.t_ci +273.15;

t_avgh=(handles.t_ho+handles.t_hi)/2;

t_avgc=(handles.t_co+handles.t_ci)/2;

t_avgw=(handles.t_ho+handles.t_hi+handles.t_co+handles.t_ci)/4;

d=length(temp);

t=t_avgh;

for i=1:1:d

a=temp(1,i);

if(a<=t)

x=i;

27

end

end

t1=temp(1,x);

t2=temp(1,x+1);

c1=cp(1,x);

c2=cp(1,x+1);

muo1=muo(1,x);

muo2=muo(1,x+1);

k1=k(1,x);

k2=k(1,x+1);

rho1=rho(1,x);

rho2=rho(1,x+1);

rho_h = (( rho2 -rho1 ) * ( t - t1 ) / ( t2 - t1 )) + rho1;

cp_h = (( c2 - c1 ) * ( t - t1 ) / ( t2 - t1 )) + c1;

muo_h = (( muo2 - muo1 ) * ( t - t1 ) / ( t2 - t1 )) + muo1;

k_h = (( k2 - k1 ) * ( t - t1 ) / ( t2 - t1 )) + k1;

pr_h=(muo_h*cp_h)/k_h;

d=length(temp);

t=t_avgc;

for i=1:1:d

a=temp(1,i);

if(a<=t)

x=i;

end

end

t1=temp(1,x);

t2=temp(1,x+1);

c1=cp(1,x);

c2=cp(1,x+1);

muo1=muo(1,x);

muo2=muo(1,x+1);

k1=k(1,x);

k2=k(1,x+1);

rho1=rho(1,x);

rho2=rho(1,x+1);

cp_c = (( c2 - c1 ) * ( t - t1 ) / ( t2 - t1 )) + c1;

muo_c = (( muo2 - muo1 ) * ( t - t1 ) / ( t2 - t1 )) + muo1;

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k_c = (( k2 - k1 ) * ( t - t1 ) / ( t2 - t1 )) + k1;

rho_c = (( rho2 -rho1 ) * ( t - t1 ) / ( t2 - t1 )) + rho1;

pr_c=(muo_c*cp_c)/k_c;

t=t_avgw;

for i=1:1:d

a=temp(1,i);

if(a<=t)

x=i;

end

end

t1=temp(1,x);

t2=temp(1,x+1);

muo1=muo(1,x);

muo2=muo(1,x+1);

muo_w= (( muo2 - muo1 ) * ( t - t1 ) / ( t2 - t1 )) + muo1;

%%%%%%%%%%%%%

dlt1=handles.t_hi-handles.t_ho;

dlt2=handles.t_co-handles.t_ci;

w1=handles.t_hi-handles.t_co;

w2=handles.t_ho-handles.t_ci;

w3=log(w1/w2);

w4=w1-w2;

LMTD=w4/w3;

m_h=handles.v_h*rho_h;

m_c=handles.v_c*rho_c;

Re_h=(rho_h*handles.v_h*d_hyd)/(muo_h*A);

Re_c=(rho_c*handles.v_c*d_hyd)/(muo_c*A);

muo_rh=muo_h/muo_w;

muo_rc=muo_c/muo_w;

q=m_h*cp_h*(handles.t_hi-handles.t_ho);

U=q/(A_h*LMTD);

load cfd.mat

d=[s.hint];

29

n=max(d);

X1=zeros(1,n);

Y1=zeros(1,n);

p=handles.p;

h=1;

while(h>=.0000001)

for t=1:n;

b=0.0029;

w=0.185;

phi=1.117;

d_hyd=(2*b)/phi;

A=b*w;

r_wall=0.0005/15.6;

e1=((1/U)-(r_wall));

e2=k_c/d_hyd;

e3=((rho_c*v_c*d_hyd)/(A*muo_c))^p;

e4=((cp_c*muo_c)/k_c)^.33333;

e5=(muo_rc)^0.14;

Y1(1,t)=e1*e2*e3*e4*e5;

f1=k_h/d_hyd;

f2=((d_hyd*rho_h*v_h)/(A*muo_h))^p;

f3=((cp_h*muo_h)/k_h)^.33333;

f4=(muo_rh)^0.14;

X1(1,t)=(e2*e3*e4*e5)/(f1*f2*f3*f4);

end

w1=(polyfit(X1,Y1,1));

p1=w1(1,1);

c1=w1(1,2);

load cfd.mat

d=[s.hint];

n=max(d);

X2=zeros(1,n);

Y2=zeros(1,n);

30

for t=1:n

b=0.0029;

phi=1.117;

d_hyd=(2*b)/phi;

r_wall=0.0005/15.6;

c_h = 1/p1;

c_c = 1/c1;

e1=((1/U)-(r_wall));

f1=k_h/d_hyd;

f2=k_c/d_hyd;

h_h=c_h*((Re_h)^p)*((pr_h)^.333)*((muo_rh)^.14)*f1;

h_c=c_c*((Re_c)^p)*((pr_c)^.333)*((muo_rc)^.14)*f2;

Y2(1,t)=log((e1-(1/(h_h)))*((pr_c)^.333)*f2*((muo_rc)^.14));

X2(1,t)=log(Re_c);

end

w = polyfit(X2,Y2,1);

p1 = abs(w(1,1));

h = abs(p1-p);

p = p1;

end

l=min(X1):0.001:max(X1);

l1=w1(1,1);

l2=w1(1,2);

set(handles.edit14,'string',p);

axes(handles.axes1)

plot(l,l1*l+l2)

xlabel('X1');

ylabel('Y1');

w = polyfit(X2,Y2,1);

d= min(X2):0.001:max(X2);

d1=w(1,1);

d2=w(1,2);

axes(handles.axes2)

plot(d,d1*d+d2)

xlabel('X2');

31

ylabel('Y2');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%