Physical properties of sea water solutions: thermal conductivity

PHYSICAL

PRUPERTlES

OF

SEA

WATER

SOkUTlONSr

THERMAL

~~~~U~~V~TY

The thermal canductivity of sea water and its concentrates hasbeen measured in the temperature range 0 to f 75 “C using a relative hot-wire method. An equation is given which fits the measured values of thermal conductivity to within their claimed experimental accuracies.

Physicat properties data are required for the design uf almost all process plant especially those involving heat transfer, Sea water is a commonly used fiuid but for many purposes adeyuatz data are not available. This is particuh&y true ti*ith dist;Ilatjon plant for desaljnation purposes, At present flash evaporators operate at temperatures of 120°C or lower, and for the higher tem~~t~r~s thermai conductivity data has been obtained by estimation andfor extrapolation. When the problems associated with scale formatjo~t have been sofved higher maximum temperatures will be used and in anticipation of this, measurements of vapour pressure, density, visco&ty, thermal conductivity and heat capacity have been made in the National Eo~n~~ng Laboratory at temperatures up to about 180°C for sea water solutions ranging in concentration from I to S times that of natural ~a water- The present article gives the resufts of measurements of thermal conductivity. 2. EXISTiNG DATA The therma! eonduetivity of sea water was determined by [a) Nukiyama (I) for naturaf sea water between 10 and 70°C using a paralfeX plate apparatus based on a comparison method involving a standard grass plate_ The values are believed to be accurate to within about f 5 per teat. (b) Tufeu (2) for natural sea water between 0 and 80°C using an absolute concentric cylinder apparatus. The values are believed to be accurate to within about rf: 5 per cent.

D. T. JAMIESON AND J. S. TUDHOPE

394

(c) Fabuss (3) fcr sea water and sea water concentrates between 25 and 150°C using a D.C. transient hot-wire apparatus. The authors observed Stray currents in tests with electrically conducting liquids and the values are believed to be in error by an amount that increases with temperature. Fabuss stated in his report that “the data given in this table should be considered as tentative values until further experimental measurements”. Data from existing literature are given in Tables I-Ill. TABLE I SIJWAMA*S(‘) DATA THERMAL cm~~ucnwr~

___ ____-___-..-

TN

-

mW m-lK-’ .-.-

Distillpd water

7emperature f “Cl -

-___.

. 1--

--_ __----.

._. .__.._l..

-

---

10

580

s&i

70

648

639

---

TABLE II

DATA THERMAL CONDUCTIVIN

7”emprulure (“C) 0

-_-

.

~FELl’S~~

20 40 60 80

.-

Nafural sea water

3rd

DisMed

mW m-aK-l water

---

Natural sea water

-_-_I 565.0 598.5 627.0 649.5 665.5

~----

565.0 5%.9 fi23.5 644.5 659.5

TABLE 211 FA?WSS’~s’ DATA THERMAL co.*pucrlvnY

m

mW m-‘K-1

103.3

25

594

50

609 606 585

125

I50

583 594 583 549 493 414

574 584 569 531 473 384

568 577 561 521 457

369

_

Desalination,

568 576 J60 521 459

373

569 576 562 526 467

386

8 (1970)393-401

PHYSICAL PROPERTES

3.

SEA WATER

OF SEA WATER

395

X)I.UTIONS

SOLUTlONS

NEL a synthetic sea water from which catcium sulphate had beert deliberately omitted was used. Its eompusitjon is given in (4). Some tests were also performed using natural sea water obtained locally off the coast of Scotland, The difference betweerl synthetic and natural sea water is insignificant with respect to such properties as thermal conductivity. Fur

4.

must

of

the

tests

at

EXPERI!@ENTAL

The method adopted was a relative one using the hot-wire principle. The cell, shown in Fig. 1. consists of a straight platinum wire filament of 0.075 mm

/

$lL,coNE

,fNtERNAt

RUBBER

SL4SS

SEikt

TEST uclulo,

MERClJf?Y PLUG

1

-

L,

PLATINUM -

FILAMENT

Fig. 1. cc& ~rsahatinnrion, 8 (1970) 393401

D. T. JAMIESON

396

diameter

AND

and 130 mm long, welded at either end to a thicker platinum

J. S. TtJDIiOPE

wire of 0.23

mm diameter and concentrically sealed in a Pyrex glass tube of about 5.1 mm internal diameter. Th= filament. which had a resistance of about 3R at 25°C was connected in either a DC. bridge or an A.C. bridge as shown in Figs. 2 and 3 respectively.

Fig. 2. U.C. hndge.

ACNULLDElECTOR

Fig:.3. A.C.

bridge.

For temperatures of 75°C and below the cell was immersed in a constant temperature bath. For temperatures above 75°C the cell was placed in a stirred pressure vessel filled with oil and the pressure vessel was immersed in a constant temperature bath. Tests below 75°C using the A-C. bridge were also stied out in the pressure vessel. In the pressure vessel the ceil was maintained at about I5 bar with compressed nitrogen. The constant temperature bath could be controlled for tha duration of the experiment to within jt 0.005”C. With both bridges the experimental technique consists essentially of passing known currents through the filament and measuring the corresponding resistances when ‘fte temperatures are steady. The 4x41 resistance was measured to O.t3OOOlQ Desahufion,

8 (1970)

393-401

PHYSICAL

PROPERTiES

OF SE4 WA7?iR

SOLUTIONS

397

using variable resistance D. the usual allowance being made for ceii lead resistance. With a A.C. bridge the reactance had also to be matched using the variable capacitor C. Values of thermal conductivity were calculated from the equation I_=

m -

AS]lG

where i, and I_, are the thermal conductivities of the liquid and glass respectively and A and B are constants depending on the cell dimensions.

B

_

Intrelri)

2nL where r, and rl are the external and internal diameters of the glass tube, rf and L the diameter and length of the filament respectively, m is the rate cf change of filament temperature T with power input P. T = To + mP.

In practice it is more convenient to obtain m from a least-squares analysis of the experimental values of the cell resistance and the power input in the equation, R = R, -I- m,P

(1)

where R,, is the resistance of the cell with zero current. A minimEm of seven different values of P were zxsed. The vaiues of nz and m, are identical at the calibration temperature_ VaJues of 1)1may be obtained from HZ~at other temperatures by multiplying by a factor which allows- for the non-linearity of the temperature coefficient of the electrical resistance of platinum but for this work the cell was calibrated directly st each temperature. The values of A and R were obtained by calibrating the ccl1 with water and tolue;le whose thermal conductivities are accurately known ($6). Linearity of Eq. (I) was checked for each test and this was used as proof

that, if convective currents were present in the ceil, they were small and had no more than a negligitle effect on the rate of transfer of heat from the filament. Since the thermal conductivity is derived from the resistance of the platinum filament, it is essential that the change from an electrically insulating liquid to an electrically conducting salt solution should not cause a measureable change in the overall ceil resistance. According to reference (7) the change in celi resistances caused by the salt solutions will be too small to be detected. Jn order to check this experimentally the zero current resistance was measured with the cell filled with water. mineral oil, 33 per cent sulphuric acid and with a saturated solution of scsdium chloride. No cha?ge in the resistance of the cell was detected. Desalination. 8 (1970) 39.3401

398

D. T. JAMIESON AND 1. S. TUDHDPE

At temperatures below 75°C the cell performed well with both the DC. and A.C. bridges. At temperatures above 75’42 stray and random voltages occurred with the DC.

circuit.

These voltages

remain

unexplained

but are probably

cause

by an ekctrochemioal reaction. Jt was not possible to obtain accurate results at temperatures greater than about 75°C with the DC. bridge and aft subsequent measurements were made using an AC. bridge. Practically any frequency above about 500 Hz eliminated the effects of stray voltages and all measurements were made with the A-C. bridge at I.5 kHz.

but

Measurements were made over a range of salinities using the D.C. bridge the accuracy of measurement was not enough to merit measurement at

TABLE

IV

EXPlTRIMF_N7AL THERMAL

DATA

-

mNDlJmm

D.C. IN

~---

-

Temperature

Saiinity ~--__ Natural sea ICuter

ICC1 --__--

‘33.82 g/kg

0 25 _w 75

361.0 661.5

BRIDGE IIIW

m-‘K-1 _--

~----

_ArtijSriol sea water

. 33.57 gj&-------

--~----

555.3 607.4 Mt.8 66I.3

(avcragc of 3)

--153.56 g/kg --

65.55 g/kg

I IO.88 g/kg

564.7 z::

555.7

555.6 593.8

627.6 661.1

620-O

(average of 2)

(avcragc of 2) .I-

654.0 (avcragc of 3)

-

652.0

TABLE V

Snliniry Artificial seo water*

153146 g/kc 53 75 loo 125 150 175

---

630.0(awzage of 2) 669.6 (average of 3) 676.6 (avaage of 4) 701.8 (average of 5) 728.0 (average of 4) 697.5 (avetagc of 5)

* The accuracy of measurementswas not enough to merit measurementsat salinitiesbetween 0 and 153 gikg Desulinafion. 8 (1970) 393-401

PHYSICAL

PROPERTIES OF SEA WATER

salinities between 0 and 160 g/kg. At made with only distilled water and sea The average experimental values sea water soilrtions using the D.C. and respectively.

In previous

work

399

SOLUTIONS

higher

temperatures

measurements

were

water of 153 g/kg salinity. obtained for the thermal conductivity of AC bridges are given in Tables IV and V

(8) the standard

deviation

from

the average

of a

large number of repeat tests was shown to be I.2 per cent and an accuracy of 2 3 per cent was therefore claimed for the apparatus. An accuracy of f 3 per cent is claimed for the values reported in Tables IV and V. The following

equation

was fitted to these values 0.333

ini, = in(i., + X) + where

i., = thermal

(

2.3 - -$

conductivity

1 -

y

T

T

)(

E

of distiii?d

water

) (5) at the critical

point

(240

mWm-‘K-‘j,T,= critical temperature of distiiied waker (5) (647X), X = salinity x 0.0002, Y = salinity x 0.03. and G = 343.5 + (salinity x 0.37). The critical or pseudocritiwi zmpexature of the test liquid (T, + Y) was obtained from the boiling points of distilled water and sea water solutions assuming that the ratio b/?/T, is constant. The values of G, X and Y were obtained by optimization

using

the experimental

thermal

conductivity

data.

Eq. (2) fits the experimentat data to within the claimed experimental accuracy of 2 3 per cent. For the case of distilled water it represents the data right up to the critical temperature (T, = 647.3”K) with an error not greater than 1.3 per cent. Smoothed values of the thermal conductivity of sea water solutions are given in Table VI and compared with the literature data in Fig. 4. The values from (3) TABLE

VI

VALUES OF TK~RMAL CONOUCllVlN

0 20 40

60 a0 100 I20 140 160 180

l

569 603 631

653 670 681 687 688 684 677

571 603 630

IN

mw

568 601 628

650 650 665 666 676 677 682 , 684 683 686 680 684 673

678

m-‘K-l

565 599 627

649 666 678 685 688 686 681

565 599 627

649 666 678 686 689 687 682

561 596 625

648 66’6 679 688 691 690 686

JSI 593 623

647 666 680 689 694 694 689

553 590 621

646 666 681 691 696 697 693

549 587 619

645 666 681 692 638 699 6%

545 584 617

541 581 614

700

703

644 665 682 693 700 702

642 665 682 694 702 705

Best literature data for distilled water. Desalination, 8 (1970) 393-401

are assumed to be incorrect. They are similar to our preliminary resufts obtained using rbe i3.C. circuit at high temperatures when stray voltages were observed. Table VI was cor~structedfrom Eq. (2), The best literature data (3) for distikd water (zero salinity) are afscr given.

This paper is published by pert&&m of the Director of the National Engineering Laboratory, Alinistry of Technology. It is Crown copyright and is reproduced by permission of the Controkr of H.M. Stationery Ofice,

&sakiamion,8 (1970) 393-W

PHYSICAL

PROPERTIES OF SEA WATER

SOLLJTIONS

401

Thcrmai conductivhia of water. sea water and sowater 1. S. NUKIYAMAmD Y. YOSH~ZAWA. soiuti~ns. J_ !I&_ mr,k Etzrs., fopon, 37 (206) (1934) 347-350 (English translation 5-4244). ASD P. ~OHAWVIX, Thermal conductivity of certain liquids (in 2. R. Tr;nu, B. Lr N~DRE Frcncl~), Compr. Rend., 262B (1966) 229-23I_ 3. B. M. FABVSSASD A. KOROSI. Properties of sea water and solutions containing sodium chloride. po’vsium chloride, sodium sulphate and magnesium stllphate. Ofice of Saline Wurer Re3. Develop. Progr_ Rep;. No. 384. 1968. 4. n. T. JAMtFSDN, J. S. TUDHOPE. R. MORRXS ASD G. CARTWRIGHT. Physicai properties of sea water so!vtions: hmt Gtpacity. ~sal~r~a~~o~. 7 ( 1%9j70) 23-U). 6th int. Conf. on the Properties of Steam-Transport Properties 5. 3. KESTI~AXC J. H. Wwmuw, of Water Substances. 1. Engng_ Pm-r., es(l) (1966) 82-101. AND J. S. TUDHOPE. The thermal conductivity of liquids: a survey to 1963. 6. D. T. Jtit~sos JVEL Report Nu. 137, East Kilbtide. Glasgow: National Engineering Laboratory. 1964. 7. A. G. TUR~B~LL, TIN thermal conductivity of molten salts, Awfrufinn J. Appl. Sci.. 12( 1) (1361) 30-41. of binary &quid mixtures, 8. D. T. JAMFSO~AND E. H. HASTIXGS.The thermal conductkty T’kr~ Comfuctivify, 63 l-64 1, Bali Conjkrence on Thptmai Conductivity, Purdue Univ., l!W_

Desalination,

8 (1970) 393-401