136 Integrated Systems for Agri-food Production ISAP’03

MATHEMATICAL MODEL AND PROGRAM FOR DIMENSIONING PLATE HEAT EXCHANGERS

Eng. P.I. Dron*, S.l. Dr. Chim. N.D. Miron*, S.l. D. Nistor*

* Organic Synthesis and Environment Laboratory - University of Bacau, Romania

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KEYWORDS: plate heat exchangers, heat transfer, flow

1. INTRODUCTION

The plate heat exchanger has been used since 1930, first only in food industry, then in some other industrial branches, being used mostly in those cases in which the heat transfer is necessary. Their wide range use is due to some important advantages: - reduced space - low costs (by diminishing with 50-60% the required heat exchange area) - big concentration of heat exchange surface (up to 200 m2/m3 per apparatus) - intense heat exchange due to the reduced thickness of the liquid film (max. 5 mm) and to the turbulence caused by the plate pattern - reduced hydraulic resistance to the liquids flow - work agents volume lower with about 10-20% - reduced weight due to the diminished heat exchange area and to the small volume of the work agents - easy to clean, absence of sediments, high adaptability to different purposes - units with big heat exchange areas can be easily made - heat exchange area can be modified by adding or eliminating a number of plates and by modifying the direction of the fluids flow - can be set up in series mounted zones to realize heat exchange in consecutive zones, obtaining 70-85% heat recovery, realizing both heat economy and heat exchange at small temperatures differences - easy to clean chemically (with washing solutions) and mechanically - reduced temperatures differences between the output of the warm fluid and the input of the cold fluid, due to the countercurrent flow

- the possibility of removing the damaged plates - several heating and cooling processes can be made in the same apparatus, separated in several sections - the degradation of one of the two gasket is immediately shown by the liquid leaking out of the apparatus - the cooling water demand is reduced when the plate heat exchanger is used for cooling, due to its high thermal efficiency

The disadvantages of the plate heat exchanger are: - reduced pressure of operation - suspensions are not allowed in the fluids

2. MATERIALS AND METHODS

The apparatus contains metallic framework that supports the plates which are packaged by a tightening device (Figure 1).

Figure 1. Plate heat exchanger

The plates are made of stainless steel or other materials with suitable corrosion resistance. All the plates in the heat exchanger have the same exterior size, the same grooves or apertures for the lying on the framework bars.

The faces of the current plates have a series of corrugations which increase the heat exchange area, helping the directing of the liquid flow under the form of a film and the intensification of the turbulence which is necessary to increase the heat exchange ratio (Figure 2.) On the face of each plate there is a groove on its whole perimeter, in which is introduced a gasket made of synthetic rubber.

The gasket has to seal from the exterior the channel formed by two plates, to prevent the leaking of the working fluids.

The extremity plates thicker and they have only one face corrugated, the inner one, and only two apertures through which the fluids enter and go out. The

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intermediary plates have also a special construction and have the function of dividing the plate package and to ensure the liquid passage from one group of plates to the next one.

Figure 2. Plate types

On the basis of the mathematical relations[1,2] for the thermal transfer calculus of the working liquids and of the holding time in the apparatus it has been developed a mathematical model[3] for the technological dimensioning of the plate type heat exchanger.

3. RELATIONS AND TABLES

The following mathematical relations will be used for the developed mathematical model of the calculating program[1].

Flow to be processed: mp= w·S·m � >NJ�V@ (1) The flow depends on the nature of the fluid, the admissible pressure downfall

and temperature regime. Number of plates in zone i: ni=Ai/f (2) Number of packages in zone i: zi=ni/(2·ch) (3) Pressure losses: p=zi·Eu· ·w2, [kPa] Eu=4100·Re-0.55 (4) Criteria equations: Re=we/v (5) Nu=c·Rem·Prn· (6) Nu= ·de/ (7) Pr=cp· / (8)

Total heat transfer ratio:

211

11

1

αλδ

α++

=

∑=

m

j j

j

K ,

⋅ Km

W2

(9)

Table 1 – Technical characteristics for the plate heat exchanger

Characteristics Measuring

unit VX 03 VX 1 VX 3

Heat exchange surface area for a plate

m2 0.035 0.1 0.35

Connections mm Dn32 Dn65 Dn100 Total heat transfer ratio W/m2·K 2330 – 6000 Work temperature °C -10 … +140 (160) Maximum work pressure bar 16 16 16 Maximum work liquid flow

m3/h 15 63 150

Maximum heat flux that can be transferred in an equipment

MW 1.16 3.5 11.6

Table 2 – c, m, n and YDOXHV�IRU�GLIIHUHQW�SODWH�W\SHV Values Plate type

c m n Alfa-Lava plate -heating -cooling

0.314 0.314

0.65 0.65

0.4 0.3

11

APV plate -heating -cooling

0.14 0.14

0.65 0.65

0.4 0.3

11

Rosenblad plate 0.315 0.73 0.43 ( ) 25.0PrPr p

Alfa-Laval R II plate 0.0917 0.73 0.43 ( ) 25.0PrPr p

Tehnofrig plate 0.0645 0.78 0.46 ( ) 25.0PrPr p Prp=

1.05 – heating Prp=0.95 - cooling

PDN 1000 plate 0.1165 0.70 0.35 1 0.5G and 0.5E plate -for Re<50 -for 50<Re<20000

0.60

0.135

0.33 0.73

0.33 0.43

11

4. RESULTS AND DISCUSSIONS

To exemplify we consider a plate heat exchanger with the following characteristics: − heat exchanger plates 183 − product velocity in the heat exchanger 0.2 m/s − thermal agent velocity in the heat exchanger 0.361 m/s

According to the flow chart the following data are available (Figure 3): − give de product flow 57 kg/s − product input and output temperatures 80 K, 45 K

20-��������������7LPLúRDUD��5RPDQLD 139 140 Integrated Systems for Agri-food Production ISAP’03

− thermal agent input and output temperatures 20 K, 60 K − product density at average temperature 882.5 Kg/m3

− thermal agent density at average temperature 989 Kg/m3

− product specific heat at initial and final temperature 3450 and 3488 J/Kg·K − thermal agent specific heat at initial and final temp.: 4177.5 and 4174.7 J/Kg·K − product viscosity at initial and final temperature: 0.63 and 0.101 Pa·s − thermal agent viscosity at initial and final temperature:0.00097 and 0.00094 Pa·s − product heat transfer ratio at initial and final temperature:0.435 and 0.441 W/mK − thermal agent heat transfer ratio at initial and final temp.: 0.67 and 0.658 W/m K − type of the heat exchanger: 6

− plate dimensions and the material it is made from: 1.25/0.5/0.001 m, 17.5 W/m·k

− distance between the plates: 0.003 m

Figure 3. Algorithm

5. CONCLUSIONS

- the program realizes the calculus for the technological dimensioning of the plate heat exchangers. It makes the work easier both for those who frequently face those calculations and for students

- the possible improvements of the program may concern the formation of a data base, eliminating the necessity of introducing from a streamer the chemical and physical parameters. The user will only have to introduce the type of the desired plate type heat exchanger and the work parameters.

6. SYMBOLS ch / number of channels w – circulation velocity between the plates [m/s] S – flow section area for the considered plate type [m2]Ai – heat transfer area for zone i [m2]f – plate heat transfer area [m2]d – distance between plates [mm]

– thickness of the plates [mm] de – equivalent diameter [mm] K – total heat transfer ratio [W/m2·K]

– individual heat transfer ratio [W/m2·K] – viscosity [kg·s/m2]– thermal conductivity [W/m2·K] – density [kg/m3]

cp – specific heat [kg/m3·

7. REFERENCES [1]. Rasenescu I. “Operatii si aparate in industria alimentara”, Ed. Tehnica,

Bucuresti, 1972; [2]. Suciu, G. “Procese calorice si mecanice de separatie”, Ed. Didactica si

Pedagogica”, Bucuresti, 1962; [3]. Bucur F., Sdrula N., Medvedic C. “Revista de chimie”, 38, (10), 1987,p. 119-

121