Laser interferometric studies of the control of heat transfer from flame gases by electric fields

COMBUSTION AND FLAME 25, 321-334 ( 1975)

321

Laser Interferometric Studies of the Control of Heat Transfer from Flame Gases by Electric Fields SARWAN S. SANDHU* and FELIX J. WEINBERG Imperial College, London, SW7, England

The effects of dc electric fields on heat transfer between flame gases and solid bodies are studied under three conditions: (1) Sub-breakdown fields are used to displace hot combustion gases relative to calorimetric probes. The case of maintaining a solid body cool by deflecting flame gases away from it is shown to be the most promising practical application. (2) Additional ions generated by corona discharges are used to induct cold air flow from outside the flame. This is relevant, for example, to improving the cooling of perforated walls of combustion chambers. (3) Corona discharges are generated within the boundary layers of tubular calorimetric probes. The results are relevant to modifying heat transfer between pipes and un-ionized gases. In each case, the analysis is based on calorimetric measurements and on data produced by a large area, double-exposure, laser interferometer that was designed for this purpose on the plan of a schlieren system. Theoretical correlations developed to account for heat transfer under the influence of fields and corona discharges show good agreement with the experimental results.

Introduction The possibility o f controlling heat transfer from flame gases to solid surfaces electrically was established some time ago [1, 2 ] . Any contribution to this effect due to increases in thermal conductivity caused by ions drifting in the field, and of recombination of ions on the surface to be heated was negligible, the major contribution being due to hot gas flow induced by the body force exerted by the field on unipolar space charges. It was further demonstrated that heat transfer to a body (e.g., a tube acting as a calorimeter) totally immersed in flame gases issuing from a small burner could not be increased by the application o f dc electric fields between the body and the burner. The present study (which is an expansion of a summary presented at the Combustion Institute European Symposium [3]) shows this to be due to the decrease in local gas temperature, which accompanies the increase in *Present address: Northern Research and Engineering Corporation, 219 Vassar Street, Cambridge, Massachusetts 02139, U.S.A.

flow rates because of the entrainment o f cold air, in the case o f small laboratory flames. In addition to the use o f flame ions under the influence of electric fields for controlling heat transfer, the production o f additional ions by local corona discharges is employed here. The latter makes it possible to induct cold, un-ionized gas for purposes o f cooling and for the disruption o f thermal boundary layers by generating ionic wind effects in selected regions within them.

Subtractive lnterferometry, The Determination of Temperature Distributions and Heat Transfer Rates The double exposure interferometer is an adaptation, conserving light for short exposures, of a more general device [4] and is described elsewhere [5, 6]. It uses the components o f a mirrorschlieren system in which the beam, after contraction to a small area, is made parallel again in order to be split, using front and rear surface reflections from a small-angle prism. The resulting fine fringe interferograms are converted to differential, infinite fringe records by the use of

Copyright © 1975 by The Combustion Institute Published by American Elsevier Publishing Company, Inc.

322

SARWAN S. SANDHU and FELIX J. WEINBERG

double exposures. The theory o f such interferometers is detailed in [4]. It subtracts not only aberrations and window effects but also end-effects, which otherwise introduce disproportionately large errors in the study of temperature distributions around hot test objects.

Copper tubes were used as heat transfer probes. Measuring inlet and outlet temperatures allowed the determination o f total heat transfer rates. These were compared with those calculated from double exposure interferograms giving reasonable agreement (differences less than 2%).

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6

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(c) Heat flux distribution around a copper tube with its axis normal to the flow of the flame gases, derived from (b).

CONTROL OF FLAME GASES BY ELECTRIC FIELDS Figure l(a) is an interferogram of a copper calorimeter immersed in flame gases. Figures l(b) and (c) are temperature and heat flux distributions, respectively, obtained from it. Heat Transfer Modification by the Effect of dc Electric Fields on Flame Ions The body forces generated by the application of dc electric fields to flame ions were employed to modify the flow patterns of hot flame gases, and consequently the heat transfer to a horizontal copper calorimeter initially positioned in (a) the thermal boundary, (b) outside, and (c) inside the flame gases of a premixed C H J a i r flame. The burners were of rectangular cross-section (longer side parallel to beam), and were provided with rectangular flametrap matrices.

TheoreticalConsiderations The basic concept of modifying heat transfer simply by displacing hot flame gases towards or away from the calorimeter is a considerable oversimplification. The gases accelerate under the influence of the body force transmitted by the ions to the neutral gas [2] and this increases heat

323

transfer. However, in incompressible flow, gases cannot accelerate without entraining ambient gas which, being cold in the case of small unconfined flames, produces the opposite effect. Thus even in the simplest case - that of an applied potential between the burner and an upper electrode at a fixed distance, (Fig. 2 (a)) above the reaction zone - two competing influences are at work. The body force acting on the gas per unit volume due to the electric field is the current density divided by the ionic mobility, j/K [2], and the momentum flux is pv 2 , where/9 = density of the gas, and v = its velocity. Viscous, buoyancy and pressure forces also operate but, being very much smaller, are neglected in this analysis. (Thus the maximum value off/K has been shown [2] to be 800 × greater than the maximum convective body force). By conservation of momentum for a one dimensional case in x, constant K, and using the hot boundary (subscript b) above a flat flame for reference (i.e., x = 0, p = Pb' v = Vb) _

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324

SARWAN S. SANDHU and FELIX J. WEINBERG

Since Pb Vb = Pu Su in one dimension,

where A = Pu Su' and

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In the limiting case of a thin flame such that all the entrained gas is cold air (subscript a), the final state is given by mbC-b(Tb - T) = m a c a ( T - Ta), where T = temperature and c- -- average specific heat at constant pressure. After substitution for m b and m a this equation can be solved for temperature. For 0-b / ~ - 1.0, for example, T-T Tb-T

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I E~

Z

( B ) l/z_ A

where C = ~ - B . Thus, since both T and v can be calculated as functions of x/a, local average heat transfer coefficients for a cylinder immersed in hot gases flowing normal to it can be computed. Using gas properties for air, the diameter of the cylinder = 1 cm; T -293 °K; T b = 2222 °K for stoichiometric CH4/air flame and S u = 35 cm sec "1 , heat transfer coefficients were calculated at various distances and field strengths. The method described in [7] was employed using data from [8]. Figure 2(b) shows temperatures, velocities, heat transfer coefficients and heat fluxes plotted against x/a for two values of field strength, E e. It will be seen that for a fixed E e, the dependence of heat flux on T is greater than that on v and hence the heat transfer from flame gases to a cold body initially immersed in them cannot be increased by the application of electric fields unless the gas entrained is also hot (as found in [1, 2]). The above type of unidimensional analysis becomes more complex when applied to the geometrical configurations shown in Fig. 5, band c, where flame gases are deflected towards or away from a heat sink by the application of electric fields, especially when the effects of different temperatures on entrainment rates are considered. There is of course no particular problem about keeping surfaces cool by deflecting flame gases away from them, provided there is a sufficient reservoir of cold air. In the converse case, where an object normally outside the flame is to be heated, it will be apparent that values o f E e greater than that for which the heat sink is completely immersed in flame gases do not cause an increase in heat flux, unless the gas entrained are hot. In general, electrically induced increases in heat transfer to

CONTROL OF FLAME GASES BY ELECTRIC FIELDS bodies completely immersed in flame gases can be produced, but only away from boundaries, in flames of large cross sections. Experimental To study heat transfer in greater detail, and in geometrically complex situations, the apparatus sketched in Fig. 3(a) was used. The burner was made of brass. The streamlining matrix was of plane and corrugated cupro-nickel strips compressed together to form a rectangular section. The body of the burner was filled with glass balls to randomize the flow. It was supported on ebonite legs for electrical insulation. The autoprotective circuit, A, for measuring current was designed to avoid damage to the microammeter due to any sudden current surge. This would be absorbed by the capacitor and discharged through the neon lamp, thereby bypassing the microammeter and giving a warning signal. Water was sprayed into the reservoir to avoid conduction between the water pipeline and the apparatus. The copper calorimeter is shown in Fig. 3(b). Copper-constantan thermocouples (36 S.W.G.) insulated with P.V.C. sleevings were employed to measure temperatures in the positions shown. The copper tube was filled with tiny balls to randomize the water flow.

water spray ~ constant ~ ~e',,e~ ~

The various positions of the calorimeter and the electrodes are shown in Fig. 5(a, b, c). In addition to the calorimetric data, double exposure interferograms (free of aberrations and window effects) were recorded for the various potentials applied to the burner at a constant fuel/air composition of the flame. Results and Discussion

Theory [1, 2] is confirmed by experimental results in an interesting manner. The heat transfer curves of Fig. 4(a, b, c) correspond to the temperature distributions revealed by the interferograms of Fig. 5(a, b, c) in which the fields are applied to a probe already within the hot gas stream - (a); so as to deflect the flame gases towards a probe initially outside it - (b); and away from a probe normally within it - (c). It is not possible within the space available to correlate the interferograms with heat transfer results [6] in detail, but it should be borne in mind that crowding of fringes in the vicinity of the calorimeter probe is a measure of the compression of isotherms and hence of increased heat conduction at right angles to them. It will be seen that the above theory is borne out, in that even before the onset of breakdown

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326

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[ 1, 2] the heat transfer falls - e.g., beyond 8 kV, Fig. 4(b) - when entrainment of cold air into hot combustion products becomes important. By 12 kV, the heat flux has fallen to about 1/3 of its value at 8 kV. In general, the parameter (j/K) determines the result. This encompasses current increasing with potential, current at a given potential increasing with fuel/air ratio and hence ionization (e.g., in Fig. 4(a) improvement in heat transfer at 5 kV is about 2.7× greater for a fuel/air ratio of 0.094 than for 0.072) and changes in mobility, K. The

latter is accurately illustrated in Fig. 4(d), when currents for positive and negative polarities may be compared at constant heat fluxes. The point is that, since the aerodynamic and heat transfer pattern for a single geometry and fuel/air ratio depends on the body-force alone, iso-heat-flux lines should represent constant (j/K). Hence, average mobilities of positive and negative charge carriers can be compared; they should be in the proportion of currents for the two polarities. Although it will be seen that K ~ K+ the ratio is not very large - confirming that the over-

CONTROL OF FLAME GASES BY ELECTRIC FIELDS

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(a) (b) (c) Fig. 5. Interferograms illustrating three geometries of flame gases displaced under the influence of electric fields.

whelming majority of the electrons (the original negative charge carriers) become attached to form negative ions on their way to the positive electrode. In all the configurations used, and again in accordance with theory [2], power consumed was negligible in comparison with the modification brought about in the total heat transfer from flame gases. The Use of Ions from a Corona Discharge Generating free charges in place of using those produced by chemi-ionization is more expensive in terms of power dissipation. A corona discharge requires electrical breakdown of the gas, locally, whereas the application of a field to a flame causes separation of existing free charges which, in the absence of the field, would recombine uselessly. However, the latter is confined to hot flame gases, whereas a corona discharge can be induced anywhere irrespective of conditions. Two potentially useful situations were studied. In order to maintain an object, such as the walls of a combustion chamber, cool in an environment of flame gases, it is desirable to generate charge carriers in cold air. The body force acting when a field is applied can then be used to pump cooling air. The work described under this heading

shows cooling caused by blowing corona-induced winds to shield surfaces from hot combustion products, either by inducing cold flow through apertures in the surface or by "blowing on it." Theoretical Considerations Such a generalized unidirectional flow, however. does not lend itself to the disruption of boundary layers. Since corona discharges are readily generated by sharp points of very small dimensions, it becomes possible to induce very large flow changes over very small regions - particularly within the relatively stagnant boundary layers around a body - and thereby profoundly modify heat transfer to it. The unidirectional flow model is amenable to a simple theoretical analysis, especially in the unidimensional case. Here it is required to produce a localized corona discharge at one electrode and, to achieve this at the lowest possible potential, it is desirable to use an assembly of regions of high local curvature (in practice sharp points). The convergence of isopotential surfaces near such regions increases local field intensity, which results in breakdown. Once such a discharge is initiated, then a space charge distribution exists between the emitting and collecting electrodes. For example, when an assembly of pinpoints is used as a plane source electrode,

328

SARWAN S. SANDHU and FELIX J. WEINBERG

there is little problem in ensuring that the field becomes essentially one-dimensional at quite a small distance from the charge-spraying electrode, so that the field lines become parallel. For a one dimensional system, the field distribution, E, is given [2] by

and the potential distribution, V, is:

K I(E + 12rrj K

)'/=

where j and K are current density and mobility of the charged particles. For ions produced in effectively unlimited numbers at the emitting electrode, it may be assumed that Eo becomes very small and can be neglected. Hence, E 2 = 8~jx K ' and V= 3.32 ( ~ )

1 (1 +/3/2) 1/2 '

and the consequent heat flux is PIlEB x/8rtp (1 + ~/2)

E 2 = E o: + 8rrjx/K,

v=

EB Vmax = (8¢rp) 1/2

1/2 x3/2

By momentum conservation and taking account of pressure loss due to permeable (in practice, gauze) electrodes, the velocity, v, for a single stage ionic wind generator is given as v = (j'x/pK) 1/2/(1 +/3/2) 1/2 where / 3 - - - ~ (--L-l-1),a 2

Cd being the discharge coefficient that depends on the Reynolds number at the orifice [9], and a, the fractional free projected area of the gauze electrode. In the above derivation, the velocity at the emitting electrode has been neglected. The maximum wind velocity is then given by the occurrence of breakdown (subscript B) at the collector electrode, as

where H is the local specific enthalpy. Practical values fall short of this maximum because of breakdown at lower mean field strengths brought on by protuberances on the collecting electrode such as the strands of the wire gauze or specks of impurities. To achieve higher flow rates without breakdown at the collecting electrode (caused by the space charge-induced rise in field) multistage ion pumps [10] can be used. Air flows generated in this way can be used to cool solid surfaces in contact with hot gases, such as products of combustion reactions, by displacing them away from the surfaces as well as diluting them. By contrast, the theory of individual points, or rows of points, within boundary layers tends to be very complex. The body force per unit volume is still//K, but the resulting flow pattern consequent upon aj-distribution partly determined by temperature variations which, in turn, are controlled by feedback of the flow pattern, defies detailed analysis. In view of its intractability, a dimensional analysis is probably the best form of correlation attainable. An example will be given after the discussion of experimental results.

Experimental A large number of configurations was studied, ranging from corona-induced transpiration-cooling of surfaces immersed in flame gases, to fitting cylindrical calorimeter probes in a flame gas environment with rows of "blowing" point-electrodes in various azimuthal positions with respect to the gas flow. Figure 6 shows one arrangement used for the study of unidirectional flow. The single stage ion pump, M, is composed of sharp stainless steel pins soldered on to a wire gauze (mesh 10) with their sharp ends pointing towards the collecting elec-

CONTROL OF FLAME GASES BY ELECTRIC FIELDS

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j calorimeter ~f thermocouple ion pump

I

4

2_ Fig. 6. End-on view of the apparatus to cool hot copper tubes (perpendicular to plane of diagram at P) simulating the walls of a combustion chamber provided with apertures. trode - another wire gauze. The calorimeter pipes (perpendicular to the figure) simulate the walls of a 2-dimensional combustion chamber, provided with apertures. Copper-constantan thermocouples (36 S.W.G) were employed to measure the inlet and outlet temperatures of the calorimetric fluid (silicone MS510). This flowed through the tubes under a constant hydrostatic head maintained in a reservoir. The corona discharge pumps were arranged behind the calorimeter to blow air over the calorimetric tubes in contact with the hot combustion products of a premixed flame stabilized on the burner, to push them away from the tubes. Fine wire gauzes of mesh 115 were arranged in between the probes and the pumps to calm the air flow so that an unblurred interferogram could be recorded in 1/150 sec. The interferograms are shown in Fig. 7(a, b) and reveal how the cooling of the probes arises by the effect of the induced gas flow on the temperature field. Heat transfer in this case was reduced by 18%. Figure 7(b) clearly indicates the compression of hot gases away from the walls of the simulated combustion chamber towards the axis. When the corona-induced ionic winds were directed to disrupting the thermal boundary layers by pointed electrodes within them, it seemed equally valid and much more convenient to use hot bodies in a cold atmosphere rather

329

than vice-versa. In this way natural as well as forced convection could be investigated. The various components of the flow and calorimetric apparatus were similar to those used hitherto, except that edges of a stainless steel fine wire gauze (mesh 170, wire dia. 0.061 ram; width of strip 1 mm) were used as emitting electrodes. Sharp ends of gauze strands in the edges acted as points. The calorimetric fluid used in the study was silicone (MS510) because of its high dielectric strength and resistance required at the high potentials and because it is nonflammable and could achieve the high temperatures required. The fluid was kept at a constant level to maintain a steady flow rate through the calorimeter, and at a constant initial temperature by the use of a thermostatically controlled bath. The average temperatures of the fluid at the inlet and outlet of the calorimeter were determined by using glass sheathed copper-constantan (36 S.W.G.) thermocouples. In the first phase of the study, the experiments were confined to free convection, but were repeated in forced flow of cold air by holding the calorimeter above the burner matrix through which air was pumped at a constant flow rate. From the calorimetric data the total heat loss was determined and corrected for radiative heat loss. In fact, the latter was found to be less than one percent of the total. Figures 8(a and b) show the various results obtained for cooling of the hot horizontal cylinder in free convection. Figures 8(c and d) show what happens to the structure of the thermal boundary around the cylinder under the effect of corona discharges. These interferograms show quite clearly that the effect of the electrical body-force is very much greater than that of the buoyant force (so much so that the hot air initially moving upwards has been diverted in the direction of the corona discharge) and that the thickness of the hot boundary around the cylinder has decreased quite considerably as large flow rates of cold air are induced. Figure 9(a) shows the calorimetric results obtained for cooling of a hot horizontal cylinder in forced flow of air of initial average velocity of 32.2 cm sec "~ just above the burner matrix. Figure 9(b) shows that here too the effect of coronainduced flows is overwhelming.

330

SARWAN S. SANDHU and FELIX J. WEINBERG

(a)

(b)

Fig. 7. Interferograms illustrating the cooling of solid surfaces in contact with hot flame gases by ion pumps. Discussion

Although calorimetric measurements reveal that large changes in heat transfer - greater than 100% - are attainable and interferograms show that local flows generated dwarf those due to the normal velocity distributions in those regions, even in forced convection, the power dissipated in the corona is not always negligible (in contrast to the case when only flame ions are involved). It will be apparent from the graphs that, from this point of view, the optimum use of the corona is at the lowest potential at which a discharge will occur. In Fig. 8(a), for example, while the heat transfer is doubled for a power dissipation of 3 watts, further increases in current produce much less improvement in relation to the additional power dissipated. The reason is that at low corona discharge current values, just above

the electrical breakdown of air at the emitting electrode, the flows are sufficient for the thermal boundary layer to be effectively modified. Higher corona discharge currents only increase flow rates of air at a rate proportional to (current density) 1/2 while power consumption rises steeply, and can rapidly exceed the increase in cooling. Multiple corona emitting electrodes with various geometrical orientation may be helpful - Fig. 8(b) shows higher rates of cooling per unit power consumption in the case of two corona discharge electrodes as compared with the case of a single corona discharge electrode, Fig. 8(a). The orientations are shown in the insets. The differences in cooling due to different angular positions of a corona-emitting electrode are caused by the interaction of the flow patterns set up under the effects of buoyancy and electrical

CONTROL OF FLAME GASES BY ELECTRIC FIELDS

331

3.0

Q 2.0

2.0

¼o 1.o

m

0

10

oC) ~

10

5

x0

15

watts

0

1

L

5

10

15

20

watts

(a)

(b)

(c)

(d)

i

Fig. 8. (a-b) Plots of h-/h-o (ratio of heat transfer coefficients vs power consumed (watts)); (c-d) Interfero~gram illustrating the effect of corona discharges on thermal boundary layer around hot horizontal cylinders. body forces. This may be expressed in terms of some function o f the ratio o f electrical to initial aerodynamic forces. Any such relation including the effect o f a corona discharge on heat transfer should reduce to the one in the absence o f a corona discharge for zero current. The heat trans-

fer relationship is, therefore, expressed as: h = h o (1 + F ( ~ ) ) , here h = average convection heat transfer coefficient and the subscript " 0 " represents the absence of an electric field,

332

SARWAN S. SANDHU and FELIX J. WEINBERG

F ( $ ) = some function of ~, where ~ = (electrical force)/(initial aerodynamic force). It is found that, in practice, F can be represented by q~ • ( $ ) n where $ and n are constants for the case of the hot cylinder initially being cooled by natural, as well as by forced, convection. In the natural convection case, ff may be expressed as:

p = density of air (the subscripts " 0 " and " t " represent room and mean thermal film temperatures, respectively); g = acceleration due to gravity (980 cm sec "2). For the forced convection case, ~ was expressed in terms of momentum flux: momentum flux due to field momentum flux at the tube surface with no field

body force generated by electric field per unit volume buoyancy force per unit volume f/K+ (No - P t ) g '

The momentum flux at tube surface was considered to be approximately proportional to that at the collecting electrode. Therefore, for inviscid flow in the absence of buoyancy, pv 2 oc]a/K, [2], where a = distance between emitting and collecting electrodes. Therefore,

where ] = current density based on surface area of the cylinder; K + - 1.8 c m 2 s e c "1 V -1 at n.t.p. --- mobility of positive ion in air (used because of the positive corona employed in the study);

$

=

(constant). ( "a..~2K), Pv o

where Vo = velocity in the absence of corona discharge, and the constant raised to the appropriate

&

1.0

O°

Q,,,

h/i,o , 0

S

10

watts

(a)

(b)

Fig. 9. (a) Plot of h/h-o vs power consumed (watts) to cool a hot horizontal cylinder (initially in forced convection) by the use of a corona discharge edge (pointing downward in (b))

CONTROL OF FLAME GASES BY ELECTRIC FIELDS power, n, may be absorbed into ¢. h o can be calculated from relations given in [7]. Thus, for every case

This theory is, of course, just a convenient way of correlating results, for each particular geometry, in terms of current and flow conditions (the difficulties of exact analytical solutions were discussed above). Nevertheless, such semiempirical correlations are useful for predicting convective heat transfer coefficients within the range of experimental data. As expected in this regime, the "downwind blowing corona" in the forced convection case has the largest effect, for a given current, as it aids normal convection. More interesting results may be expected in separated and turbulent flows, but this would be difficult to study interferometrically.

log [_-fi-h - 1 ] = n l o g [if] +log 1~5]. ho Plots of [(h/ho) - 1] vs ff on log-log scale are indeed straight lines (Fig. 10(a and b)) from which n and ~ may be deduced for each geometry. The results are given in Table 1. TABLE 1 Results of Plots of [(h/ho) - 1] vs t~ n

9

333

Configuration

Natural Convection Cooling 0.70 0.28 0.23 0.30

0.027 0.23 0.24 0.25

O O" 0 O-

One o f us (S. S. S.) is indebted to BISRA for a research bursary at Imperial College, and to NREC for financial assistance towards the production o f this paper.

O (~) Q

References 1. Payne, K. G., and Weinberg, F. J., Proc. Roy. Soc. A250, 316 (1959).

Forced Convection Cooling 0.448 0.697 0.198

0.180 0.022 0.195

0

x

(a)

<)

x

0.2 2O

)00

2

3

4

x

(b)

0;0

007

1

I

,

i

J

,

i

i

I 10o

i

Fig. 10. Effect of corona discharges on heat transfer.

S

334 2. Lawton, J., and Weinberg, F. J., ElectricalAspects of Combustion, Clarendon Press, Oxford, 1969, pp. 296,300, 324,327. 3. Sandhu, S. S., and Weinberg, F. J,, Combustion Institute European Symposium (F. J. Weinberg, Ed.), 1973, p. 316. 4. Jones, A. R., Sehwar, M. J. R., and Weinberg, F. J., Proc. Roy. Soc. A322, 119 (1971). 5. Sandhu, S. S., and Weinberg, F. J.,J. Sei. Instrum. 5, 1018 (1972). 6. Sandhu, S. S., Ph.D. Thesis, London University, 1973.

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Received 26 February 1975