Heat transfer system

Abstract

A heat transfer device 10, such as a heat exchanger, has dimensions and flow speed such that Reynolds number for the flow is in a range from 1 to 1000. The heat exchanger comprises an array of obstruc

Description

: FIELD AND BACKGROUND

[0001] This disclosure is concerned with heat exchange and with working fluids for apparatus used in management of heat energy by storing heat, absorbing heat or transferring heat energy from one location to another. In the following description, the terms “Floerger”, “Flopaam”, “Silverson” and “Mastersizer” are Registered Trade Marks (RTM).

[0002] Various forms of apparatus use a working fluid to absorb heat and transfer the heat to another location. An example is a heat exchange circuit. Another example is a solar water heating system in which solar energy heats a working fluid which in turn heats domestic hot water. A working fluid may also be used to receive and store heat energy when that energy is available and give up the heat at a later tune. There are also systems where heat is taken from a working fluid and the cooled fluid is used to absorb heat at a later time. Such working fluids are often water or an aqueous solution or may be some other single-phase liquid. SUMMARY

[0003] This summary is provided to introduce concepts that will be further elaborated and described below' in the detailed description. This summary' is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

[0004] One aspect of the present disclosure is a method of moving heat into or out of a flowing fluid, comprising pumping the fluid through a heat transfer device which comprises a chamber for through flow of fluid and wherein a chamber wall in contact with the flowing fluid is an interface through which heat energy is transferred to or from the flowing fluid, wherein:- the chamber contains an array of spaced obstructions compelling the streamlines of the flowing fluid to repeatedly change direction in order to flow through gaps between the obstructions; the viscosity of the fluid, the flow rate of the fluid within the chamber and the width of the gaps between obstructions gives a. Reynolds number (Re) for the flow which is in a. range from 1 to 1000, possibly 1 to 100, 1 to 250 or 1 to 500; the fluid contains a solute which enables the fluid to display elastic turbulence; and the flow rate of the fluid through the chamber is such that the flowing fluid is in a state of elastic turbulence.

[0005] A system for moving heat energy may comprise a heat transfer device including a chamber for through flow of fluid wherein a chamber wall is an interface through which heat energy is transferred to or from the flowing fluid, a fluid and a pump for pumping the fluid through the chamber, wherein: the chamber contains an array of spaced obstructions compelling the streamlines of flowing fluid to repeatedly change direction in order to flow through gaps between the obstructions; the fluid contains a solute which enables the fluid to display elastic turbulence; and the system is configured so that the viscosity of the fluid, the flow' rate of the fluid within the chamber and the width of the gaps between obstructions gives a Reynolds number (Re) for the flow' which is in a range from 1 to 1000, possibly 1 to 500, 1 to 250 or 1 to 100,

[0006] In some embodiments, the heat transfer device is part of a heat exchange system comprising a second heat transfer device at a different location, a pump and pipework connecting the pump and the heat exchange devices as a closed circuit containing the said fluid.

[0007] The obstructions may be a plurality of pillars extending across the chamber from the interface to another wall of the chamber. The pillars may be arranged so that flow' through gaps betw'een pillars in a row7 is compelled to change direction by pillars in an adjacent row'.

[0008] In another aspect, this disclosure provides a working fluid for a heat exchange system wherein the working fluid is a multi- phase system with a continuous phase and at least one suspended disperse phase which changes between solid and liquid at temperatures where the continuous phase is liquid and wherein die continuous phase is a solution containing a solute which enables the continuous phase, and thereby the overall working fluid composition, to display elastic turbulence. BRIEF DESCRIPTION OF DRAWINGS

[0009] Fig 1 is a diagrammatic view of a heat transfer system with two devices for heat transfer, both of which are shown as cross sections;

[0010] Fig 2 show's part of an array of pillars, as used in the heat transfer devices of Fig 1;

[0011] Fig 3 is a cross section of one heat transfer device, on line A - A of Fig 1;

[0012] Fig 4 is an enlargement of part of Fig 3;

[0013] Fig 5 is a similar view to Fig 4, showing pillars with a different cross section;

[0014] Fig 6 is a plot of experimental results showing onset of elastic turbulence;

[0015] Fig 7 is a diagrammatic view of apparatus to determine operating parameters for the system of Figs 1 to 3;

[0016] Figs 8 to 10 show' experimental results obtained with an embodiment of such apparatus; and

[0017] Figs 11, 12 and 13 show experimental results relating to elastic turbulence in a phase change emulsion. DETAILED DESCRIPTION

[0018] This detailed description refers to embodiments of the present disclosure and possibilities which may be used. It should be appreciated that features or possibilities described in combination may, where it is practical to do so, be used individually. Also, features or possibilities described in any embodiment may be used in any other embodiment, in so far as it is possible to do so.

[0019] The present disclosure uses the phenomenon of elastic turbulence. It is of course well known that Newtonian fluids such as water can undergo either laminar flow or turbulent flow. Such turbulent flow may be referred to as inertial turbulence. Conditions for laminar and turbulent flow are often expressed by Reynolds number which is a. ratio of inertial to viscous forces within a fluid. Reynolds number has no dimensions because it is a ratio. At Reynolds number above about 2000 there is inertial turbulent flow'. At Reynolds number below about 1500 a Newtonian fluid is in a state of laminar flow.

[0020] Elastic turbulence is a different physical phenomenon discovered at the end of the twentieth century. It has been observed at low' flow speeds where Reynolds number is low' and a Newtonian fluid would be in a state of laminar flow7. Elastic turbulence has sometimes been referred to using the older and more general term “elastic instability”,

[0021] A number of documents have mentioned possible use of elastic turbulence in microfluidics, w'here dimensions of flow7 paths and rates of flow are so small that apparatus has a volume below 10 ml and Reynolds number is vanishingly small, far below' one. In contrast with that, the present disclosure uses elastic turbulence in equipment where dimensions of the apparatus and rates of flow are large enough that Reynolds number is one or more but less than one thousand. When Reynolds number is in this range, the flow of a Newtonian fluid such as pure water is laminar. As already mentioned, a heat exchange device in accordance with this disclosure has a chamber for the through flow of a fluid which displays elastic turbulence as it flows through the chamber. The fluid volume within this chamber may be at least 50ml (possibly in experimental apparatus) and may be more, such as at least one litre or at least fifty litres in larger scale equipment.

[0022] The formula which may be used to determine Reynolds number for flow through a chamber containing obstructions so as to compel the flow stream lines to bend is: pUL Re = where p is density of the fluid in kilograms per cubic metre U is the flow velocity in metres per second L is the width of the gaps between the obstructions in the chamber q is the viscosity of the fluid in Pascal, sec. If the flow rate is measured as volume in unit time, the formula above becomes pQL Re 1]A where Q is the flow rate in cubic metres per second and A is the cross sectional area, transverse to the overall direction of flow, through which the flow passes.

[0023] Elastic turbulence occurs in solutions containing a solute which has a flexible structure. One category of material able to undergo elastic deformation and enable a solution to display elastic turbulence is a polymer containing long flexible linear chains. The number of monomer units in the polymer may be at least 5000 and may be considerably more such as at least 25,000. The monomer units may be present in linear chains of at least 1000 monomer units which may each be connected one to the next by a single covalent bond, so that one monomer unit can rotate relative to adjoining monomer units. Individual linear chains may be longer and a polymer may contain a linear chain of at least 5000 or even at least 10,000 monomer units. The mean molecular weight of the polymer may be 10° Daltons or more. The concentration of such long chain / high molecular weight polymer included in a solution for enabling elastic turbulence to occur may be under 5% by weight, for instance in a range from 0.05% or 0.1% up to 1% or 2% by weight.

[0024] A long chain polymer which enables elastic turbulence to occur may be a polymer of a single monomer or may be a copolymer of more than one monomer, for instance a block copolymer which is linear. A polymer may include side chains attached to a long chain of monomer units which are connected together by single covalent bonds. A polymer may include some chain branching, for instance at branch points where three or more chains, each of at least 1000 monomer units and possibly at least 2000 or 5000 monomer units, are connected together.

[0025] The flexibility of the polymer chains enables the polymer molecules to become entangled. The flexibility of polymer chains can be described by means of a mathematical model. The freely jointed chain model is commonly used and the flexibility of a particular polymer can be indicated by parameters of an equivalent freely jointed chain (itself a mathematical model). A description of this approach is provided by Chapter 2 of “Polymer Physics” by Rubinstein and Colby, 2003, Oxford University Press. An equivalent freely jointed chain has the same meansquare end-to-end distance and the same maximum end-to-end distance as the actual polymer but is considered to consist of so-called Kuhn monomers which are freely rotatable relative to each other. These model monomers have a length, termed the Kuhn length, and a molar mass.

[0026] Polymers which enable elastic turbulence to occur may contain at least one flexible polymer chain with length and composition represented by at least 1000 Kuhn monomers having a Kuhn length not more than 100 Angstroms (lOnm) and possibly not more than 50 Angstroms. If a polymer is a single, unbranched chain its length and composition may be represented by at least 5,000 Kuhn monomers having a Kuhn length not more than 100 Angstroms and possibly considerably more, such as at least 20,000 Kuhn monomers of such Kuhn length.

[0027] Elastic turbulence has been observed with several different long chain polymers in solution. One such polymer is polyacrylamide, which may be hydrolysed or partially hydrolysed. Experimental evidence for elastic turbulence in a solution of high molecular weight polyacrylamide was given by Groisman and Steinberg in “Elastic Turbulence in a polymer solution flow” Nature, Vol 45 p53 (2000). Other instances of long chain polymers reported to give rise to elastic turbulence include polyisobutylene of molecular weight 4 to 6 Megadaltons dissolved in an organic solvent (Dris and Shaqfeh, J. Non-Newtonian Fluid Meeh. Vol 80 pages 1 to58 (1998)), polystyrene of molecular weight 18 Megadaltons in an organic solvent (Magda and Larson, J. NonNewtonian Fluid Meeh. Vol 30 pages 1-19 (1988)) and polyethylene oxide of molecular weight 4 MegaDaltons in an aqueous solution (Davoodi et al, J.Fluid Meeh. Vol 857, pages 823-850 (2018)). Kuhn lengths for polystyrene and polyethylene oxide given by Rubinstein and Colby, page 53 are 18 Angstoms and 11 Angstroms. Kuhn length for polyacrylamides has been reported as 15 to 25 Angstoms (Fetters, Lohse and Colby, Chain Dimensions and Entanglement Spacings. In Physical Properties of Polymers Handbook; Mark,J.E.,Ed.;Springer:NewYork, 2007;pages 447-454).

[0028] When using a long chain linear polymer to enable elastic turbulence to occur, it is desirable to include a. biocide to protect the polymer from biodegradation.

[0029] Long chain partially hydrolysed polyacrylamide linear polymers with a molecular weight of more than 1 MegaDalton are available from SNF Floerger, whose headquarters are in Andrezieux, France.

[0030] Elastic turbulence has also been observed with solutions containing a surfactant which forms worm-like micelles in solution. An example, using cetyl trimethyl bromide as the surfactant, is mentioned by Favolin et al in Physical Review Letters Vol 104 178303 (2010).

[0031] When a solution contains a substance able to cause elastic turbulence, the phenomenon of elastic turbulence occurs if the solution is flowing at a sufficient flow velocity (which may be a low velocity) and the path of flow causes the streamlines of the flow to curve. Consequently, one known possibility for a flow' path which induces elastic turbulence is a serpentine channel. Another possibility is described below with reference to the drawings. A detailed discussion of elastic turbulence is provided by Steinberg in Annual Review' of Fluid Mechanics, vol 53, pages 27-58 (2021).

[0032] The ability of a fluid composition to display elastic turbulence can be demonstrated with laboratory apparatus, as mentioned below. A flow' rate through a heat exchange device which is sufficient for a selected fluid composition to display elastic turbulence can be found by experiment, as is also shown below'.

[0033] In the present disclosure, the elastic turbulence mixes the working fluid as it flow's over a solid interface through which heat is transferred into or out of the working fluid. As a consequence of the elastic turbulence, the rate of heat transfer is increased because the heat transfer to or from the interface is not restricted to the conduction of heat through the working fluid.

[0034] As an example embodiment of this disclosure, the drawings show' a heat transfer system for transferring heat energy from a heat source to a volume of water. The device 10 at the left of Fig 1 is exposed so as to be heated by the sun. The device 12 at the right of Fig 1 is immersed in a body of water. The two devices 10, 12 are joined by piping 14 for circulating working fluid which is pumped around the circuit by pump 16. The section of piping which carries hot working fluid is surrounded by heat insulation 24. The devices 10 and 12, along with piping 14 and pump 16 form a heat exchange circuit for transferring solar heat energy received at the surface 20 to the water surrounding the device 12.

[0035] The device 10 has a cuboidal casing defining a chamber through which the working fluid is pumped. The casing face 20 which is exposed to the heat of the sun is the interface between the working fluid inside the casing and the source of heat. This is made o f a thermally conductive material, such as copper or aluminium. The opposite surface 22 has heat insulation 24 against it to reduce heat loss.

[0036] Inside the casing of the device 10 is an array of pillars 30 formed by bars which extend from the casing face 20 across the internal chamber to the opposite face 24. Fig 2 illustrates the arrangement of such pillars 30 as as a perspective view from one side, without the enclosing casing 20. Fig 3 which is a cross section on line A-A of Fig 1 also shows the arrangement of the pillars 30. As shown by Fig 3 and the enlargement which is Fig 4 the pillars 30 have a square cross section with flat faces 32 meeting at corner edges 33 and 34. The width of a flat face 32 is indicated as “a” in Fig 4 and the spacing between the faces 32 of adjacent pillars is indicated as “b” The width of the gap between two confronting edges 34 is given by Pythagoras theorem as \'2b As shown in Fig 3, the edges of the array are completed with pillars 31 which have a triangular cross section. Each pillar 30 is positioned so that the diagonal across the square cross section between corner edges 33 is aligned with the overall direction of flow', ie. this diagonal is aligned parallel to an imaginary line from the inlet 26 to the outlet 28. The flat feces 32 of each pillar are inclined to this overall direction of flow. As shown by the enlarged view in Fig 4, wmrking fluid flows through the gaps between confronting edges 34 of adjacent pillars 30, but is then compelled to turn by another pillar. Thus the array of pillars 30 obstructs straight line flow' of working fluid, causing the streamlines of the flow indicated with broken lines in Fig 4 to bend repeatedly.

[0037] The heat exchange device 12, which is immersed in water to be heated, has a cuboidal casing 40 w'hich is the interface through which heat energy leaves the working fluid. Fins 42 projecting from the casing 40 assist the conduction of heat from the casing 40 to the surrounding water.

[0038] The interior of the device 12 is similar to the interior of the device 10. The casing 40 defines a chamber for the through flow of working fluid. Bars which extend across the interior chamber from one side face to the other provide an array of pillars 30 obstructing flow just as described for the device 10.

[0039] Fig 5 shows another possible cross section for pillars 30. The surfaces 54 have convex curvature and intersect concave surfaces 55 at edges 56. Fluid flows through the gaps between edges 56 as shown by the broken lines and is compelled by the arrangement of pillars to change direction as it does so.

[0040] The working fluid circulated through the heat exchange devices 10 and 12 may be an aqueous solution of a long chain partially hydrolysed polyacrylamide linear polymer with a molecular weight of more thanl MegaDalton and possibly more than 3, or 5 or 10 MegaDaltons. Its concentration may be no more than 5% by weight and may possibly be no more than 1% by weight. Such polymers are available from SNF Floerger, whose headquarters are in Andrezieux, France. The working fluid also contains a small concentration of a biocide to prevent biological degradation of this polymer.

[0041] The circulating pump 16 propels the working fluid at a flow rate such that flow entering at the device 10 at its inlet 26 is laminar and flow entering the device 12 is also laminar. This flow' rate is such that as the working fluid flow's through the arrays of pillars within the devices 10 and 12 it is in a state of elastic turbulence. In the device 10 this has the effect of transferring heat energy from the casing surface 20 to the working fluid more rapidly than would be transmitted by conduction under conditions of laminar flow without elastic turbulence. Similarly, in the device 12, elastic turbulence increases the rate of transfer of heat from the working fluid to the casing 40 of the device 12, from which the heat energy passes on to the water surrounding the device 12.

[0042] The ability of a solution to display elastic turbulence can be shown experimentally. In a cone and plate rheometer cell, the onset of elastic instability with application of increasing shear is observed as an apparent increase in viscosity at a particular shear rate associated with an abrupt increase in the noise in the measured torque signal. This has been described by D.O. Olagunju, “Instabilit ies and bifurcations of von Karman similarity solutions in swirling viscoelastic flow'”, Z angew Math Phys, 46 (1995) 224-238 and also by E. Tran, A. Clarke, “The relaxation time of entangled HPAM solutions in flow'”, Journal of Non-Newtonian Fluid Mechanics, 311 (2023) 104954.).

[0043] Fig 6 is a plot of viscosity against increasing shear rate for two aqueous solutions containing 0.456 wt% sodium chloride, a small percentage of a. linear polyacrylamide with molecular weight above 10 MegaDaltons and a few' drops of a biocide consisting of isopropanol and thiourea. In one of these aqueous solutions the polyacrylamide was 0.24wt% of Flopaam3630 from SNF Floerger which has mean molecular weight of 18 to 20 MegaDaltons. In the other aqueous solution the polyacrylamide was 0.2wt% of Flopaam 6040, also from SNF Floerger, with of mean molecular weight between 25 and 30 MegaDaltons. For both solutions, the onset of elastic turbulence with increasing shear rate can be seen as the change in slope of the plotted curve at about 150s1. (With heat transfer devices shown in Figs 1 to 4, the shear rate for the onset of elastic turbulence would be less).

[0044] A minimum flow rate required to cause elastic turbulence in a heat exchange device and the rate of heat transfer to or from the circulating working fluid can both be determined experimentally. Apparatus for this is shown in Fig 7. In this apparatus the heat exchange device 10 (or a preliminary model for such a device) is connected to a pump 60 which delivers liquid from a tank 62 which is maintained at a fixed temperature. Pressure sensors 64, 65 and temperature sensors 66, 67 are fitted at the inlet and outlet of the device 10. The temperature sensors 66, 67 may be thermocouples. The outlet 28 from the device 10 is connected to a graduated vessel 68 for measuring volume of liquid which has been pumped through the device 10 in a chosen interval of time, and thereby determining the flow rate.

[0045] When liquid from the tank 62 is pumped through the device 10 there will be a pressure drop between the inlet pressure sensor 64 and the outlet pressure sensor 65. When the flow rate through the device 10 is very low', the flow will be laminar, without any elastic turbulence. The minimum flow rate to cause elastic turbulence in the device 10 can be found by progressively increasing the pump speed to increase the flow rate and plotting the pressure drop against flow rate. This plot will show' a change in slope on reaching the flow rate at which elastic turbulence begins.

[0046] This is illustra ted by the following description of experiment al work with appara tus as shown in Fig 7. The results of the experiments are shown in Figs 8 and 9. An initial calibration determined relationships between pump speed and flow rate. The tank 62 was filled with water. The pump was used to propel water through the device 10 at progressively increasing flow rate. The pump speeds and the flow rates measured downstream of the device 10 were recorded and are shown in Fig 8 (triangle points). This calibration procedure was then repeated with an aqueous solution containing 0.1 wt% of Flopaam 3630 polyacrylamide in the tank 62. This gave the nonlinear' plot also shown in Fig 8 (circular points).

[0047] Fig 9 show's the measured pressure drops plotted against flow' rate. With water the plot was approximately linear (as would be expected because water is a Newtonian fluid) but with the polyacrylamide solution there was a very sharp change in the slope of the plot at the point 70, indicating that the flow' rate at this point was the minimum required to cause elastic turbulence with that polyacrylamide solution and device 10.

[0048] A calculation of Reynolds number, at a flow rate giving elastic turbulence was as follows; The flat faces 32 of the pillars had a width “a” of 4mm and the height of the pillars was 7mm. The spacing “b” between the faces 32 of adjacent pillars was 2mm and so the gaps bet ween adjacent edges 34 was v'8 = 2.83mm. A full line of pillars transverse to the overall direction of flow' contained 12 pillars with 11 gaps between edges 34, d so the cross section available for flow' was 11x7 x2.83mm2 - 11 x 7.10"3 x 2.83.10"3 m2 1 5 3 1 Flow' rate was measured as 75 ml.sec = 7.5 x 10 ' nr sec . Density of the fluid was 1000kg / mJ; dynamic viscosity was 0.008Pa.sec. Putting these numbers into the formula mentioned above pQL '1000 x 7.5.10~s x 2.83.10~3 J^p ™ ------------- ™ ------------------------------------------------------------------------------------------ pA 8.10-3x 11x7.10-3x2.83. IO"3 which is Re = 12.17.

[0049] The apparatus of Fig 7 was also used to observe the rate of heat transfer through the surface 20 and into the device 10. For this, electrical resistors 72 serving as heating elements were fitted to the surface 20. The outlet 28 from the device 10 was connected to the tank 62 along a flow path partially indicated at 71, so that flow was in a closed circuit. A chiller was used to maintain the tank 62 at a fixed temperature.

[0050] Measurements were made with the Flopaam 3630 polyacrylamide solution in the flow circuit and also with water in this circuit. Measurements were made at a number of pump speeds. At each pump speed the electrical power to the resistors 72 was increased in steps and the temperature difference between the thermocouples 66, 67 was recorded. For each pump speed, this temperature difference was plotted against the electrical power supplied to the resistors 72. These plots were all linear and the slope of the line was a rate of heating the fluid flowing through the device 10. It was observed that when the flow rate was sufficient to cause elastic turbulence, the rate of heating was considerably increased. Without elastic turbulence the transfer of heat into the flowing fluid was solely conductive. When elastic turbulence was present, the transfer of heat included movement, brought about by the elastic turbulence, of heated fluid away from the surface 20 and into the body of the flowing fluid. In short, when there was elastic turbulence, the heat transfer was convective as well as conductive.

[0051] Calculations to show this quantitatively used the Nusselt number which is a dimensionless number indicating ratio of convective heat transfer to conductive heat transfer. The formula for a mean Nusselt number relating to heat transfer between a fluid and a flat, solid surface is where m is the mass flow' rate, k and C are the thermal conductivity and specific heat capacity respectively, zls and W are geometric parameters of the flow channel (surface area and width). Tmo and Tm,i are outlet and inlet temperatures respectively, and &Tlm is the log mean temperature difference defined as: ((jw ""Tm,o) - {Tw ■■■■ Tni)} ^lm “ r7 ~ V? LU ~ ltrw ■■■■ ^.1) j where Tw is the wall temperature, in this instance the temperature of plate 20 heated by the resistors 70. For each pump speed a ratio of the mean Nusselt number with polyacrylamide solution in the flow circuit and the mean Nusselt number with water in the flow circuit is given by the formula: Nu 1 “ polymer U water polymer w,polymer ,n,o,polymer ] ' w,polymer ‘m,I,polymer m water [ ^[7w,water .water] water ~ Tmwater] This ratio was calculated for each pump speed and the calculated ratios are shown in Fig 10. It can be seen that at pump speeds below 62 rpm, where there was no elastic turbulence the ratio was close to one, but above 62 rpm the ratio progressively increased with pump speed, confirming that elastic turbulence was considerably enhancing the rate of heat transfer into the fluid in the flow circuit.

[0052] In some embodiments of this disclosure, the working fluid is an emulsion or suspension where the disperse phase is able to melt and to freeze at temperatures where the continuous phase is liquid. Emulsions and suspensions are used extensively in a wide range of commercial products over a wide range of industries. Emulsions are liquid-in-liquid systems with small drops of one liquid (the dispersed phase) distributed within another liquid (the continuous phase). The two liquids may be (and usually are) immiscible. The dispersed phase may be stabilised against coalescence by a surfhetant in the composition or possibly by solid particles (smaller than the emulsion droplets) at the interface between the dispersed and continuous phases. An emulsion stabilized with solid particles is sometimes termed a Pickering emulsion. Suspensions have small particles of solid suspended within a continuous liquid phase.

[0053] If melting and freezing of the disperse phase of an emulsion take place within a temperature range where the continuous phase is liquid, the disperse phase may freeze and remain as a. suspension of solid particles in the continuous phase. Because the continuous phase remains liquid, this suspension remains mobile, capable of flow and pumpable. Such a two-phase liquid is termed a phase change material emulsion (PCME). If a. PCME is used as a working fluid for heat exchange or heat storage, with temperatures such that the disperse phase undergoes melting or freezing, the heat-carrying capacity of the fluid includes the latent heat of fusion of the dispersed phase (or the latent heats of the disperse phases if two or more are present and change between solid and liquid) because this latent heat must be supplied to cause melting and is given out on freezing.

[0054] As an illustration of this, if a unit mass of water with specific heat capacity Cpvater is heated from temperature Tj to temperature T2 the enthalpy change is ^ater = ^ater If unit mass of an emulsion containing proportion d) of an oil is heated over the same temperature range, and the melting point of the oil is between Tj and 1'2, the enthalpy change is ae!"" = ^(r"+c°" (r2 -7;)) + (1-^)^(^-7]) where L01! is the latent heat of fusion of the oil and for simplicity it is assumed that the specific heat of the oil is the same for its frozen and liquid forms. In the case of a PCME containing 30vol% of hexadecane as the disperse phase in water as continuous phase, and with a tempera ture rise of 15° spanning the melting temperature of the hexadecane, the enthalpy change of the PCME calculated using published values for specific heats and latent heat is 1.97 times that of water alone.

[0055] The use of a PCME as working fluid and the use of a working fluid displaying elastic turbulence can work in co-operation with each other. Using a PCME may reduce the volume and / or the flow' rate of working fluid required to carry heat without directly altering the rate at which heat is transferred into or out of the working fluid. Indeed, use of a. PCME may even reduce the rate at which heat is transferred from or to the working fluid, because the PCME may have lower overall thermal conductivity than its continuous phase. Use of elastic turbulence improves heat transfer at the interface through w'hich heat is carried into or out of the working fluid, and so can reduce the size required for this interface or reduce the required flow' rate over this interface and in consequence reduce the required pumping power. Thus the use of a PCME as working fluid jointly with elastic turbulence at the point of heat transfer to or from the working fluid can reduce the size and / or power demand of equipment to transfer heat by means of a flowing working fluid.

[0056] The continuous phase used for the PCME may be an aqueous solution. However, it could be a non-aqueous liquid such as an organic solvent or a low' viscosity polydimethyl siloxane, commonly referred to as low viscosity silicone oil.

[0057] The disperse phase or phases of the PCME should not be agglomerated by interaction with the polymer w'hich enables elastic turbulence. A disperse phase may therefore be an organic compound without heteroatoms, such as a paraffinic hydrocarbon, or may be an organic compound in w'hich the only heteroatoms are oxygen atoms in ester or ether groups. It is also possible that a. disperse phase is a fluorocarbon.

[0058] A number of factors may destabilize emulsions. In particular, so called ‘creaming’ is a problem encountered when the disperse and continuous phases are of different densities. It refers to the migration of emu lsion droplets to the top of the emulsion, resul ting in the eventual separation of phases. Emulsions additionally suffer from coalescence, where droplets merge to form larger droplets unless kinetically arrested using surfactants. A polymer w'hich enables elastic turbulence may also stabilize against creaming. A further possibility is to incorporate a second polymer which does not by itself enable elastic turbulence to occur but does slightly enhance viscosity and thereby stabilize the PCME against creaming. More specifically a second polymer may be weakly associative so that a weak or critical gel is formed (i.e. giving the fluid solid-like properties) under quiescent conditions. As soon as flow starts the weak structure is broken and the emulsion flow's easily.

[0059] The amount of a second polymer included to stabilize the emulsion may be tinder 5% by weight, and may be in a range from 0.05% or 0.1 % up to 1% or 2% by weight.

[0060] The following experimental work shows a PCME which displays elastic turbulence. The continuous phase was an oil-in-water emulsion containing the following materials Material Concentration Function Sodium Chloride 4.55 g / L Salinity modifier Xanthan 2.25 g / L Gelator Polyacrylamide (HPAM) 0.54 g / L Elasticity Sodium Dodecyl Sulfate 1.54 g / L Dispersant (SDS) Deionised Water balance solvent The polyacrylamide was Flopaam 3630 as mentioned above, with molecular weight 18-20 MegaDaltons. The disperse phase was hexadecane.

[0061] Preparation of the emulsion began with preparation of three compositions as follows: 1. Xanthan in brine. 0.5g of xanthan powder was added to 99.5g of 4.55 g / L NaCl brine. The xanthan was mixed for 5 - lOmin at 5000 rpm with a Silverson L5 lab mixer fitted with a general purpose disintegrating head. The mixed solution was heated to 80°C with hotplate and magnetic stirrer and then cooled. 2. Partially hydrolysed polyacrylamide (HPAM) in brine. 0.12g of Flopaam 3630S was added to 99.88g of 4.55g / I NaCl brine. The mixed solution was stirred with a magnetic stirrer at 200rpm overnight. 3. Hexadecane emulsion. 46.38g of hexadecane was added to 153.62g of a 2wt% sodium dodecyl sulfate (SDS) solution in 4.55g / L brine whilst shearing at 6000rpm in a Silverson L5 mixer fitted with a high shear screen. The droplet size distribution was measured in a Malvern Instruments Mastersizer 3000. The dso parameter for the emulsion droplets was .measured as 4.56 pm.

[0062] The xanthan solution and the HP AM solution were combined in a 1:1 by weight proportion. The combined solution exhibited elastic turbulence which was detected as a rheological flow instability observed with a cone and plate rheometer as mentioned above. Fig 11 is a plot of viscosity vs shear rate for this example HPAM / Xanthan mixture. In this measurement, made in a. rheometer cell, the onset of elastic turbulence with increasing shear rate can be seen at about 150s'3.

[0063] The PCME was then made by mixing the combined solution and the hexadecane emulsion. PCME’s containing 0.6vol%, 1.5vol% and 3vol% of the initial hexadecane emulsion were observed to be stable to creaming and each exhibited elastic turbulence when tested using a cone and plate rheometer as above. The onset of elastic turbulence on increasing shear rate was again seen at about 150s'1.

[0064] A sample portion of this PCME formulation was examined by differential scanning calorimetry. The results are shown by Fig 12. The measurement was started at 30°C and temperature was reduced at 1 °C / min. Freezing of the hexadecane droplets occurred at about 11°C. The sample was cooled to -10°C and was then heated (for this composition at this cooling rate the continuous phase did not freeze). The hexadecane then melted at 18°C.

[0065] As an example, a heat exchange circuit as in Figs 1 to 3 is used to heat a water supply with an incoming temperature of 5°C. The working fluid is as described above with hexadecane as disperse phase in an aqueous continuous phase containing polyacrylamide and xanthan. The heat exchange device 10 exposed to the sun raises the temperature of the working fluid to at least 25°C so that the disperse phase is emulsified liquid droplets as it leaves the device 10 through outlet 28 and as it enters the device 12. In the heat exchange device 12 the working fluid is cooled to 10°C, so that the hexadecane disperse phase freezes to suspended solid particles. The working fluid is then pumped again into the device 10 where the solar heat provides the latent heat to melt the frozen hexadecane droplets as well as raising the fluid temperature to 25°C. Consequently, the heat carried from the heat exchange device 10 to the device 12 and given out from the device 12 to the surrounding water comes both from the drop in temperature of the working fluid and the latent heat of fusion given out as the disperse phase solidifies. At the same time the elastic turbulence increases the rates at which heat is carried into and out of the working fluid. As a consequence of these, the heat exchange devices may be smaller than would otherwise be required and the energy used in pumping the working fluid may be less than would be required to pump a working fluid at a flow rate giving inertial turbulence.

[0066] The various embodiments of this disclosure which have been set out above are intended to assist understanding of this disclosure, but not to limit in any way the scope of this disclosure as defined by the following claims.

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