Abstract:
Heat pumps consume power in order to transfer heat from a source to a higher-temperature sink. This invention enables spontaneous heat transfer from a heat source to a small portion of the generally warmer working fluid that is cooled locally by the Bernoulli effect to a temperature below that of the heat source. The Bernoulli effect occurs in a Venturi shaped duct shaped to maintain attached flow. Heat-transfer efficiency is improved by restriction of the heat transfer to a small portion of the Venturi in which the flow temperature, velocity, pressure gradient and the Nusselt effect enhance heat transfer. Within this region, heat transfer is maximized by a thermally conducting grid extending across the Venturi neck.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This is a National Stage Application of PCT/US2006/024633, which claims priority to U.S. Provisional Patent Application No. 60/693,934, filed Jun. 24, 2005, now abandoned. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to heat pumps, devices that move heat from a heat source to a warmer heat sink. More specifically, it relates to Bernoulli heat pumps. 
         [0004]    2. Discussion of Related Art 
         [0005]    Heat engines are devices that move heat from a source to a sink. Heat engines can be divided into two fundamental classes distinguished by the direction in which heat moves. Heat spontaneously flows “downhill”, that is, toward lower temperatures. As with the flow of water, such “downhill” heat flow can be harnessed to produce mechanical work, as illustrated by internal-combustion engines, e.g. Devices that move heat “uphill”, that is, toward higher temperatures, are called heat pumps. Heat pumps necessarily consume power. Refrigerators and air conditioners are examples of heat pumps. Most heat pumps work by varying the temperature of a working fluid  1  over a range that includes the temperatures of the source and sink. In this way heat can flow spontaneously from the source into the portion of the working fluid in which the temperature is below that of the source. Similarly, heat flows spontaneously into the sink from the portion of the working fluid in which the temperature is above that of the sink. The required temperature variation of the working fluid is commonly effected by compression and expansion of the working fluid. 
         [0006]    By contrast, Bernoulli heat pumps accomplish the required working-fluid temperature variation by converting random molecular motion (reflected in the temperature and pressure of the fluid) into directed motion (reflected in macroscopic fluid flow). (The distinction between random and directed motion is particularly clear in the statistical distribution of molecular speeds. The random motion is the width of this distribution, whereas the directed flow is the mean of the same distribution.) A fluid spontaneously converts random molecular motion into directed motion when the cross sectional area of a flow is reduced, as when the flow passes through a nozzle or Venturi. The coupled variation of the temperature, density and pressure with cross-sectional area is called the Bernoulli principle. Whereas compression consumes power, Bernoulli conversion does not. The energy-conserving character of Bernoulli conversion is the fundamental efficiency exploited by the Bernoulli heat pump. 
         [0007]    The Bernoulli heat pump is contrasted with conventional heat pumps in  FIGS. 1   a  and  1   b . As indicated in  FIG. 1   a , a conventional heat pump consists of four fundamental components: a compressor  4 , and an expansion valve  7 , a low-temperature heat exchanger  3  and a high-temperature heat exchanger  2 .  FIG. 1   b  shows that the Bernoulli heat pump combines the roles played by the expansion valve  7  and the low-temperature heat exchanger  8  into a Venturi  8  capable of heat transfer. Whereas conventional systems require large pressure changes for a relatively small flux of working fluid, a Bernoulli heat pump requires smaller pressure changes in a larger flux of working fluid. Thus the compressor  4  component of conventional systems ( FIG. 1   a ) is replaced by a fan or blower  9  in a Bernoulli heat pump ( FIG. 1   b ). Conventional heat pumps, Bernoulli heat pumps, heat exchangers, compressors, blowers and Venturis have all been widely discussed. The present invention describes a new structure for the efficient transfer of heat  3  into a fluid flowing through a Venturi. The importance of the invention is the improved efficiency it provides Bernoulli heat pumps. The discussion below describes the problems with prior art in this context which are addressed and solved by the present invention. 
         [0008]      FIGS. 2 and 3  provide a basis for comparing prior art involving the Bernoulli heat pump to the present invention.  FIG. 1  shows the coupled variation of the temperature, density, pressure, flow speed and cross-sectional area of a compressible gas undergoing so-called one-dimensional flow. There is nothing new or contentious about this well known and much studied phenomenon. The coupled variation of these properties of a flowing compressible fluid is reproduced here because it provides a succinct basis for the comparison of earlier efforts to exploit Bernoulli conversion with one another and with the present invention. In one-dimensional flow, specification of any one of the four covarying quantities implies the values for the remaining three.  FIG. 2  shows the temperature, density, pressure and cross-sectional area implied by the (square of the) flow speed. The flow speed is labeled by the corresponding dimensionless Mach number. The linear decrease of the temperature with the square of the flow speed is a direct result of energy conservation, the conversion of random kinetic energy into directed kinetic energy. It is not surprising that the flow-speed scale over which the Bernoulli effect occurs is the Mach number, which is the ratio of the two speeds. The quantities shown in  FIG. 1  are normalized to their values in the stationary gas. 
         [0009]      FIG. 2  shows immediately the relationship of U.S. Pat. No. 3,049,891 to other inventions and to our invention. U.S. Pat. No. 3,049,891 requires that the flow be supersonic (Mach number values greater than one).  FIG. 2  shows that the gas temperature is indeed lower for supersonic flow. But,  FIG. 2  also shows that temperature reduction produced by subsonic flow is more than adequate for many practical purposes. Note, in this connection, that the temperature scale in  FIG. 2  is absolute. That is, at a flow speed of Mach 1, for example, the gas temperature has decreased by 25%. If, for example, the temperature of the gas at rest is 70 degrees F., then the temperature near the neck of the Venturi at Mach 1 is 60 degrees F. below zero. The numerical values shown in  FIG. 2  assume the isentropic flow of a perfect gas characterized by a specific-heat ratio of a monatomic gas, that is, 5/3. Thus, the challenge posed by the Bernoulli heat pump is not the generation of sufficiently low temperatures, but rather the efficient exploitation of the low temperatures found near the neck of the Venturi, even a subsonic Venturi. 
         [0010]    The second direct implication of  FIG. 2  is that the power required to maintain high-speed flow in the Venturi neck can be substantial. The pressure near the Venturi neck is approximately half that at the Venturi entrance. If this pressure drop is not recovered by means of a diffuser (expanding portion of the Venturi), then the potential efficiency of the Bernoulli heat pump is reduced. In addition to requiring a diffuser, efficiency requires the maintenance of unseparated flow in the diffuser. This requirement translates directly into diffusers characterized by very gradual expansion, that is, very asymmetric Venturis (Venturis with very different converging and diverging sections). The extensive literature associated with so-called “critical-flow Venturis” indicates that conical diffusers, for example, should be characterized by half angles (the angle between the cone wall and the symmetry axis) of less than ten degrees. The efficiency requirement of Venturi asymmetry is not addressed in While U.S. Pat. Nos. 2,325,036, 2,441,279 and 3,200,607 describe Bernoulli heat pumps they do not address efficiency and the role of the diffuser. The first two of these are envisioned as airplane technologies, where the power consumed by a short diffuser is a negligible fraction of the power available. 
         [0011]    The focus of the present invention is a third aspect of  FIG. 2  not addressed by any of the four patents referenced. The relationship indicated in  FIG. 2  between the flow speed and the cross-sectional area of the flow, especially for flow speeds near Mach 1, shows that the inverse area passes through a maximum with increasing flow speed. This maximum is the basis of the Laval nozzle. Another implication of this maximum is that, considered as functions of distance along the Venturi axis, the temperature, density and pressure all exhibit narrow dips near the Venturi neck (the maximum of the inverse area). That is,  FIG. 2  shows that, near Mach 1, the temperature, density, and flow speed all vary significantly while the cross-sectional area varies little. Thus, considered as functions of distance along the Venturi axis, or equivalently, as a function of the cross-sectional area, the temperature, density and pressure all exhibit a strong dip at the neck of the Venturi. The variation of the temperature for a specific and much studied Venturi shape  11  is shown in  FIG. 3 . (The variation of the temperature, density, pressure and flow speed along the Venturi axis is given (implicitly) by  FIG. 2  by specifying the cross-sectional area as a function of distance along the axis of the Venturi.  FIG. 3  is obtained by taking the area variation of the cross-sectional area to be that of a so-called “toroidal critical-flow Venturi. In these devices, the converging portion of the Venturi is a torus, and the diverging portion is a cone.) If the Venturi wall is thermally conducting outside the region of the dip shown in  FIG. 3 , then the Venturi wall provides a thermal path for heat transfer from elsewhere in the working-fluid flow to the cold neck of the same flow. That is, heat transferred to the neck portion of the working-fluid flow has come from elsewhere in same working-fluid flow, with no net benefit. While there is no benefit, there is a cost. Since the heat transferred to the working-fluid flow is the sum of the heat transferred from the heat-source flow (the desired effect) and that transferred from elsewhere in the working-fluid flow, we see that the desired heat transfer is directly reduced by heat transfer outside the dip. Restricting heat transfer between the working fluid and the Venturi wall to the region of the dip shown in  FIG. 3  is a focus of the present invention. This restriction is not addressed in the earlier patents. 
         [0012]    The importance of this effect is modified and amplified by four additional effects: the so-called Nusselt effect and three effects associated with the boundary layer. The Nusselt effect is the enhancement of heat transfer at a fluid-solid interface by the convection provided by fluid flow. Because the flow speed vanishes at the interface, heat transfer into the working fluid from the solid depends on thermal conduction. But, the flow of the working fluid beyond the boundary layer sweeps away (convection) heat transferred into the boundary layer by conduction. Convection is generally much more effective than conduction. At flow speeds near Mach 1, the Nusselt effect is large. For example, if the source of heat is a fluid flowing at a lower speed, then the area through which heat is transferred into the working fluid can be much smaller than the area through which heat is transferred out of the heat-source flow. 
         [0013]    Two additional effects involve the variation of the thickness of the boundary layer along the Venturi wall. Heat transferred into the working fluid at the Venturi wall must pass through the boundary layer of the working-fluid flow. The boundary layer is the region of a fluid that is flowing adjacent to the solid-fluid interface. Because the flow speed vanishes at the interface, the speed of the working-fluid flow must change rapidly near the interface. The narrow region in which this change occurs is called the boundary layer. The temperature gradient and therefore the conductive heat transfer are significantly enhanced where the boundary layer is thin. The thickness of the boundary layer is strongly affected by the gradient of the pressure along the direction of the working-fluid flow. 
         [0014]    The first of the two boundary-layer effects concerns the sign of the pressure gradient. It is well known that a so-called “adverse” (that is, positive) pressure gradient thickens the boundary layer. The pressure gradient is “adverse” in the diverging (diffuser) portion of the Venturi. 
         [0015]    In the converging portion of the Venturi, where the axial pressure gradient has the favorable sign, general arguments following directly from the Navier-Stokes equations show that the thickness of the boundary layer is inversely proportional to the square root of the axial pressure gradient. The axial pressure gradient increases sharply in the region of the temperature dip. This additional thinning of the boundary layer within the region of the temperature dip represents a fourth motivation for restricting heat transfer to this region. 
         [0016]    A fifth and final consideration affecting the efficiency of the Bernoulli heat pump is addressed by the present invention. The portion of the Venturi labeled “heat-transfer slice” in  FIG. 3  identifies the portion of the Venturi axis in which the conditions for heat transfer are favorable. These are all properties of the bulk of working-fluid flow. That is, the temperature and axial pressure gradient are properties of the entire cross section of the working-fluid flow—except for the thin boundary layer at the periphery of the cross section. The viscous losses occurring outside the region of the temperature dip represents costs devoid of benefits. A focus of the present invention is the exploitation of the properties of the thin section  10  of the Venturi axis labeled the “heat-transfer” in  FIG. 3 , without incurring the viscous losses associated with those portions of the Venturi lying outside the dip region of  FIG. 3 . There are thus five issues associated with the dip region of  FIG. 3  that are not addressed in the prior art. These are: 
         [0017]    1. The Nusselt enhancement of heat transfer through the neck portion of the Venturi boundary layer 
         [0018]    2. Undesirable heat transfer into the dip region from elsewhere in the working-fluid flow. 
         [0019]    3. Unfavorable sign of the axial pressure gradient in the diffuser 
         [0020]    4. Magnitude of the favorable pressure gradient in the portion of the dip region that is within the convergent portion of the Venturi 
         [0021]    5. Efficiency reductions due to viscous losses in the portion of the boundary layer lying outside the temperature-dip region of  FIG. 3 . None of these five challenges is addressed in the prior art. 
         [0022]    We note in closing the discussion of related art that, while it is true that Bernoulli conversion is energy conserving (consumes no power), it is also true that the Bernoulli heat pump is not a perpetual-motion device. It consumes power in two ways. First, as required by the 2nd Law of Thermodynamics, when heat is added 3 to and removed 2 from the working-fluid flow at different temperatures there is a net increase in entropy that must be compensated by reversible work. This 2nd-Law effect is the reason that the “heat Out” arrows in  FIGS. 1   a  and  1   b  are larger than the corresponding “Heat In” arrows. The power required to compensate for this entropy generation is proportional to the difference in temperatures at which heat is added and removed. Second, and more quantitatively important, the flow-speed variation across the boundary layer implies viscous dissipation that must also be compensated by reversible work. If the first effect were the principal challenge, then Carnot efficiency would be approachable. The greater challenge is that stemming from the viscous dissipation in the boundary layer. 
       SUMMARY OF THE INVENTION 
       [0023]    The present invention is a structure that exploits the “heat-transfer” section identified in  FIG. 3  and systems exploiting that structure. The structure is a Venturi designed specifically for effective transfer of heat into the fluid passing through the Venturi. The invention consists of two types of exploitation of the “heat-transfer” section. First, heat transfer is restricted to the heat-transfer section. Second, heat transfer within the heat-transfer section is maximized by the use of specialized fins within the heat-transfer section. 
         [0024]    According to another aspect of the invention, the source of the heat transferred to the working fluid can be a flowing fluid, gas or liquid, or it can be non-fluid, as in the case of heat-generating electrical components. For both fluid and non-fluid heat sources, the critical requirement is a thermal conductor connecting the heat source to the narrow portion of the Venturi axis designated in  FIG. 3  as the “heat-transfer” section. 
         [0025]    According to another aspect of the invention the power consumed is reduced by making the divergence of the diffuser very gradual, with the objective of maintaining attached flow. 
         [0026]    According to another aspect of the invention multiple Venturis are staged to obtain either greater capacity or greater temperature difference. 
         [0027]    According to another aspect of the invention corrugation of the Venturi wall creates multiple “heat-transfer slices” within a single Venturi. 
         [0028]    According to another aspect of the invention, the rate of heat transfer to the working fluid can be varied continuously by variation of the flow speed through the Venturi. 
         [0029]    According to another aspect of the invention, systems based on the heat-transfer Venturi can be open or closed. That is, systems can exhaust the working fluid to which heat has been added, or circulate a working fluid optimized for heat transfer or other properties. 
         [0030]    According to another aspect of the invention, systems based on the heat-transfer Venturi can be used to pump heat “downhill”. That is, a heat source at a higher temperature than the working fluid when stationary will cool by conduction. Causing the working fluid to flow exploits the Nusselt effect and convection. Causing the working fluid to flow through a Venturi further enhances the cooling. Causing the working fluid to flow through a heat-transfer Venturi further enhances the cooling. 
         [0031]    As with other heat-pump technologies, the Bernoulli heat pump can be used for the purpose of heating or cooling. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]      FIG. 1   a  shows the components of a conventional heat pump. 
           [0033]      FIG. 1   b  shows the components of a Bernoulli heat pump. 
           [0034]      FIG. 2  shows a graph of the coupled variation of the flow speed, temperature, density, pressure and cross-sectional area of a laminar flow of compressible gas. 
           [0035]      FIG. 3  shows a graph of the axial variation of the temperature within the Venturi revealing the “heat-transfer” section of the Venturi. The dashed curve is the corresponding Venturi shape. 
           [0036]      FIG. 4  is a cross-sectional view of a heat-transfer Venturi according to an embodiment of the invention. 
           [0037]      FIG. 5   a  is a cross section of a rectangular Venturi taken through its “heat-transfer” section containing a grid of thermally conducting fins traversing the heat-transfer section of the Venturi according to an embodiment of the invention. 
           [0038]      FIG. 5   b  is a cross section of a non-rectangular Venturi taken through its “heat-transfer” section containing a grid of thermally conducting fins traversing the heat-transfer section of the Venturi according to an embodiment of the invention. 
           [0039]      FIG. 6   a  is a cross-sectional view of multiple heat-transfer Venturis staged in parallel in order to obtain increased capacity, according to an embodiment of the invention. 
           [0040]      FIG. 6   b  is a schematic view of multiple heat-transfer Venturis staged in serial in order to obtain increased capacity, according to an embodiment of the invention. 
           [0041]      FIG. 7  is a cross-sectional view of a Venturi containing a corrugated wall and multiple “heat-transfer” sections, according to an embodiment of the invention. 
       
    
    
     BRIEF DESCRIPTION OF THE REFERENCE NUMBERS 
       [0000]    
       
         
           
               1 . Working fluid, the fluid to which heat is added by the heat-transfer Venturi. 
               2 . Heat removed from the working fluid at the (higher) sink temperature. 
               3 . Heat added to the working fluid at the (lower) source temperature. 
               4 . Compressor that raises the temperature and pressure of the working fluid. 
               5 . High-temperature heat exchanger which transfers heat from the working fluid to the sink. 
               6 . Low-temperature heat exchanger which transfers heat to the working fluid from the source. 
               7 . Expansion valve which reduces the pressure of the working fluid. 
               8 . Venturi, a duct of varying cross-sectional area. 
               9 . Fan/blower that maintains the working-fluid flow. 
               10 . Cross-sectional portion of the Venturi where the pressure, temperature and density are low and the velocity and pressure gradient are large. 
               11 . Cross-sectional area of a common “critical-flow Venturi”. 
               12 . Slowly moving, relatively warm portion of working-fluid flow. 
               13 . Rapidly moving, relatively cold portion of working-fluid flow. 
               14 . Decelerating portion of working-fluid flow where pressure gradient is “unfavorable”. 
               15 . Portion of working-fluid flow as it exits the Venturi carrying the heat added in the “heat transfer” section of the Venturi. 
               16 . Venturi wall. 
               17 . Heat-source fluid flowing into or out of the plane of the figure. 
               18 . Thermal conductor that carries heat from the heat-source flow to the working-fluid flow. 
               19 . Thermally conducting fins that transfer heat from the Venturi to the working-fluid flow. 
           
         
       
     
       DETAILED DESCRIPTION 
       [0061]    The present invention provides an improved heat-transfer structure for use in a Bernoulli heat pump. Embodiments of the heat-transfer structure are illustrated in  FIGS. 4-7 . The embodiments all exploit the “heat-transfer” section of a Venturi identified in  FIG. 3 . The heat-transfer section is exploited in two fundamental ways. First, heat transfer to the working fluid passing through the Venturi is restricted to the “heat-transfer” section  10 . Second, heat transfer within the “heat-transfer” section  10  is maximized by the introduction of thermally conducting fins that serve to increase the surface area available for heat transfer within the “heat-transfer” section of the Venturi. 
         [0062]      FIG. 4  illustrates a first embodiment of the heat-transfer structure in the shape of an asymmetric Venturi  16  (Venturi possessing different shapes in the converging-and diverging sections). The working fluid undergoing Bernoulli conversion. Arrow length is intended to indicate flow speed, with longer arrows indicating higher speeds. When the working fluid enters the Venturi  12 , the gas is slowly moving, relatively warm and relatively dense. As the cross-sectional area decreases, the flow speed must increase in order to maintain a constant mass flux. The energy required for this increase in flow speed is, as shown in  FIG. 2 , obtained from the random kinetic energy reflected in temperature. (The temperature decrease is proportional to the change in the square of the flow speed, that is, the Bernoulli effect.) So, as the gas proceeds through the Venturi, the flow speed increases until it reaches a maximum  13  at the minimum cross-sectional area. (The axial variation of the flow speed is the mirror image of the variation of the temperature shown in  FIG. 3 .) As the cross-sectional area begins to increase in the diffuser portion of the Venturi, the flow speed decreases  14  as the gas proceeds to the Venturi exit  15 , where the gas is warmed to the extent that heat has been transferred from the heat-source flow  17  through the thermally conducting material  18 . It is a critical aspect of the invention that the exposure of thermal conductor  18  to the working fluid is restricted to the “heat-transfer” section  10  identified in  FIG. 3 . The Venturi wall  16  is insulating everywhere outside of the “heat-transfer” section  10 . In particular, this structure eliminates unwanted heat transfer into the “heat-transfer” section  10  of the working fluid from other regions of the working fluid. 
         [0063]    The heat source shown in  FIG. 4  is a flowing fluid, chosen as an illustration. The nature of the heat source and its thermal coupling to the thermal conductor  18  is quite arbitrary. It is the restriction of heat transfer into the working fluid to the “heat-transfer” section  10  that is specific to this invention. 
         [0064]    The second fundamental component of this invention is the additional structures shown in the enlarged cross-sectional views of the “heat-transfer” section of the Venturi in  FIG. 5 . Note that, In contrast to  FIG. 4 , in  FIG. 5  the “heat-transfer” section of the Venturi lies in the plane of the figure. Here, heat transfer into the working fluid is increased by thermally conducting fins  19  extending from the Venturi wall  20  into the working-fluid flow. The use of fins to increase heat exchange is common. What is unusual here, beyond the context, is the limited extent of the fins in the direction of the flow, that is, parallel to the axis of the Venturi. Here, the fins are confined to the “heat-transfer” section  10 . The pattern of fins used is quite arbitrary.  FIGS. 5   a  and  5   b  show fins extending across the Venturi, and intersecting to form a grid  19  within the “heat-transfer” section  10 . Useful visualizations of the structure of such grids are provided by tennis rackets, apple corers and (planar) tea strainers.  FIGS. 5   a  and  5   b  also serve to emphasize the arbitrariness of the cross-sectional shape of the Venturi. Many Venturis possess cylindrical symmetry, but this is not a requirement. 
         [0065]    Another aspect of the invention is the cross-sectional shape of the thermally-conducting fins. Their cross-sectional shape is that of an airfoil, and is designed to minimize aerodynamic drag on the working-fluid flow by the fins. The normally larger component of drag, the so-called “pressure” component, is rendered negligibly small by the aerodynamic cross-sectional shape of the fins. Unlike more common airfoils our thermally conducting fins need not provide lift and need not change their angle of attack. Thus, they can be thin and oriented along streamlines of the working-fluid flow to further reduce drag. In this connection, arrays of fixed airfoils are often used to suppress turbulence in duct flow. 
         [0066]    Another degree of design freedom with regard to the grid elements is the variation of their cross section with distance from the Venturi wall. This degree of freedom represents a tradeoff between heat conductance and structural strength. Structural strength calls for increasing area with increasing distance from the Venturi wall. Heat conductance calls for the reverse. The appropriate balance depends on the material chosen for the grid element. 
         [0067]    As with Bernoulli heat pumps not exploiting the “heat-transfer” section, multiple heat-transfer Venturis of the present invention can be configured in parallel to achieve greater capacity or in serial to achieve higher or lower temperatures. Such configurations are illustrated in  FIGS. 6   a  and  6   b.    
         [0068]    Just as the cross section of the fin-grid can be optimized to minimize turbulence and drag on the scale of the heat-transfer section, the shape of the entire Venturi, especially the diffuser, can be independently optimized to reduce drag and therefore the power required by the blower/fan mechanism  9  to maintain the working-fluid flow. The general requirement in this context is that, in order to maintain attached flow, the expansion of the cross-sectional area in the diffuser portion of the Venturi must be very gradual. Attached flow serves to minimize the largest component of aerodynamic drag, so-called pressure drag, leaving only the smaller component associated with viscous losses. The recovery of 95% of the pressure drop required to attain Mach 1 flow has been reported. 
         [0069]    Another design option concerns the flow speed at which the invention operates. In contrast to traditional heat pumps based on a change of phase in the working fluid, the operating conditions of Bernoulli heat pumps can be readily and continuously varied. In particular, the flow speed, and therefore the temperature, of the heat-sink flow can be varied by changing the power provided to the blower that maintains the heat-sink flow. One important implication of this degree of freedom is the inefficiency of conventional systems at startup. With Bernoulli heat pumps, including this invention, the rate of heat pumping is continuously variable, allowing startup transients and their inefficiencies to be effectively eliminated. For example, the blower maintaining the working-fluid flow can be thermostatically controlled. A second virtue of continuous variation and control is the increase in thermodynamically allowed efficiency at smaller temperature differences. (Carnot efficiency is inversely proportional to the temperature difference across which heat is pumped. Thus, the present invention offers an efficiency gain associated with longer operation over a smaller temperature difference. 
         [0070]    Finally, we show in  FIG. 7  the corrugation of the Venturi wall designed to produce multiple “heat-transfer sections within a single Venturi. That is, the Venturi wall is again thermally insulating outside the “heat-transfer” sections, but now there are multiple “heat-transfer” sections, as shown in  FIG. 7 . 
       DEFINITIONS 
       [0071]    Venturi: a fluid-flow duct or channel structure whose cross-sectional area varies along its axis. The variation of the cross-sectional area along the duct axis possesses at least one local minimum. Although most Venturis contain a diffuser section in which the cross-sectional area increases along the axis, we include in our definition of Venturi nozzles in which the diffuser section is either short or nonexistent. This extension thus extends the applicability of the invention to applications in which power consumption is not critical. 
         [0072]    Working Fluid: a fluid whose temperature is varied locally so as to permit spontaneous heat flow into and out of the working fluid. 
         [0073]    Working-fluid flow: the flow of the working fluid through the Venturi structure. 
         [0074]    Cross section: the area inside the closed curved formed by the intersection of the Venturi surface and a plane perpendicular to the Venturi axis. 
         [0075]    Heat-transfer section: The portion of the Venturi near its neck lying between two planes perpendicular to the Venturi axis and characterized by low temperature and high flow speed See  FIG. 3 . 
         [0076]    Fin: a structure consisting of high thermal conductivity material extending from a thermally conducting surface into a fluid flow adjacent to that surface whose objective is to increase the surface area available for heat transfer between the surface and the fluid flow, while minimizing resistance to the flow. 
         [0077]    Diffuser: a portion of a Venturi characterized by monotonically increasing cross-sectional area along the axis and flow direction. 
         [0078]    Having disclosed at least one embodiment of the present invention, various adaptations, modifications, additions, and improvements will be readily apparent to those of ordinary skill in the art. Such adaptations, modifications, additions and improvements are considered part of the invention which is only limited by the several claims attached hereto.