Optimizing Thermoelectric Cascades to Increase The

Efficiency of Thermoelectric Windows

Achille Messac,∗ Rhys-Sheffer Birthwright,†

Timothy Harren-Lewis,† and Sirisha Rangavajhala‡

Rensselaer Polytechnic Institute, Troy, NY, 12180

This paper presents a unique optimal design application. We optimize thermoelectric(TE) windows for applications in building structures. These windows use TE units toactively transfer heat to maintain the desired indoor conditions. TE units are solid statedevices that convert electrical energy into thermal energy, and are small enough to beintegrated into the frame of a window. The TE window is expected to compensate for itsown heat losses/gains. By layering the TE units in groups, called cascades, the system canperform with a coefficient of performance (COP) greater than that of conventional HVACsystems. In this paper, a method to optimize TE cascades is presented in the context of TEuse in a window design. The results are favorable for standard cooling conditions. Initialresults indicate that the cascades of TE units allow the system to compensate for windowheat gains substantially more efficiently than do traditional HVAC systems.

Nomenclature

A AreaCOP Coefficient of PerformanceG Geometry factor of a TE unitIsky Incident solar radiation on the windowI Electrical currentL Length of the heat sinkn Number of TE units in a single cascadeN Number of thermocouples in a single TE unitNcas Number of cascades in the TE windowP Electrical powerq Heat transfer rate per unitQ Total heat transfer rateR Thermal resistanceRaL Rayleigh number for a heat sink of length LSopt Optimal fin spacing for the heat sinkSHGC Solar heat gain coefficient of the windowT TemperatureVte Voltage across a TE unitU U-value of the windowwfr Width of the window frameZ Figure of merit for a TE unitα Seebeck coefficient of a TE unit∆T Temperature difference across a single TE unitκ Thermal conductivity of a TE unit

∗Professor, Department of Mechanical, Aerospace, and Nuclear Engineering, AIAA Fellow.†Graduate Student, Department of Mechanical, Aerospace, and Nuclear Engineering‡PhD, Mechanical Engineering

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49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference <br> 16t7 - 10 April 2008, Schaumburg, IL

AIAA 2008-1886

Copyright © 2008 by Achille Messac. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

ρ Resistivity of a TE unit

Subscripts

c Cold side of the TE unitcas Property of the cascadeh Hot side of the TE uniths Property of the heat sinkin Inside condition∞ Ambient conditionout Outside conditionpas Property of the passive window systemte Property of a single TE unitwin Property of the glass panes

I. Introduction

The current global demand for energy is unsustainable and often viewed as geopolitically destabilizing.This current global energy challenge will require new sources of energy production that rely less on dwindlingfossil fuels. Broadening the methods of energy production to include more reliance on “green” technologiesis expected to create more stability both geopolitically and environmentally. While green and renewablepower generation methods are rapidly gaining popularity, most continue to cost significantly more thanfossil fuels. Each new method of power generation entails long term uncertainties that could create otherunknown challenges. Alleviating the environmental and economic pressures caused by the global reliance onoil cannot be addressed by alternative energy production methods alone. In view of these realizations, anoverall reduction in the growth of energy consumption would have a great impact on these current challenges.

Energy for heating and cooling accounted for more than half of the energy consumption in US householdsin 2001.2 Research has shown that a large contributing factor to the thermal imbalance in residential andcommercial buildings is the unwanted heat flow through windows or glass facades.16 When compared to walls,ceilings, and floors of buildings, windows allow more heat transfer between outside and inside environmentsbecause of their low thermal resistance.18 Windows can contribute 25% to 30% of the heat gain/loss in ahome, even though they occupy only 10% to 15% of the floor area.18 Improving window technology has thepotential of significantly reducing energy consumption in buildings.

I.A. State of the Art Windows

The current standard in window energy efficiency is the “ENERGY STAR” qualification.3 The NationalFenestration Rating Council (NFRC)1 develops and administers ratings that allow a window to be ENERGYSTAR qualified for different geographic regions in the United States. These ENERGY STAR windowsare “passive” however; they do not actively respond with additional power to changes in environmentalconditions. Windows operating against environmental conditions to enhance their energy performance havebeen considered in the literature, and are appropriately called “active windows”. Moving beyond currentENERGY STAR standards, these active windows are what we consider the most promising next generationin window technology.

Active window technologies include a wide variety of systems that change the thermodynamic propertiesof the window in response to the prevailing environmental conditions. Some are “smart” technologies thatincorporate systems that dynamically change the window’s optical and thermal properties for optimal per-formance. These window designs are claimed to have the potential to reduce peak electric loads by 20% to30% in many commercial buildings.13 A few examples of these active windows include:

1. Active control of motorized shading systems:12 These systems seek to limit the solar heat gain throughwindows by physically blocking the sunlight. A central control automatically adjusts a system ofinternal or external shades to regulate the incident solar radiation. Lee12 discusses performance char-acteristics of these systems, and strategies to implement this technology in existing and new buildings.

2. Switchable window coatings:10, 11 This technology differs from the shading systems by using non-mechanical means to reduce solar heat gains. Electrochromic or gasochromic glazing can be controlled

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to induce a dark tinted state with an applied voltage or influx of gas. This technology is similar tothat of Transitions R© lenses.

3. Heat extraction double skin facades:13 This type of technology seeks to reduce the solar heat gainthrough better thermal management rather than blocking the incident radiation. The incident radiationis absorbed by a between-pane shading system; and is drawn out of the intermediate space by ventilativemeans.

4. Airflow windows:6, 8 This technology is similar to extraction facades, but may include airflow betweenthe indoor and outdoor environment. These windows reduce passive heat transmission by allowing airto flow through the gap between the panes (either by forced or natural convection).

5. Thermoelectric Windows: In our current and previous work, we have investigated the feasibility of usingthermoelectric technology in windows. These thermoelectric units are integrated into the window frameto transfer heat against the passive heat flow through the glass panes.

In our present work, we expand our novel use of thermoelectric technology in windows. We present awindow design that employs sets of TE units within the frame of the window. TE units are solid state devicesthat convert electrical energy into thermal energy, and vice versa. By using sets of TE units layered into“cascades”, the system can achieve significantly greater efficiency than can a single TE unit. TE units operatewith no moving parts and no recurring costs, thereby making large scale commercialization economicallypromising. We intend the proposed TE window to actively compensate for its own heat gains, and to doso with a better coefficient of performance (defined later) than do conventional HVAC (heating, ventilation,and air-conditioning) systems.

In this paper, we develop a TE window design that addresses the heat transfer requirements in an optimalmanner. In section II, we present the requisite analytical developments. The optimization of the cascaded TEunits is formulated in section III. The performance results of the design optimization, and the implicationsof those results, are presented in section IV. Concluding remarks are presented in section V.

II. Modeling TE Windows

A simplified schematic of the TE window is shown in Fig. 1. The TE units in the window frame enforceheat flow (solid arrows) in the direction opposite to the passive heat flow through the window panes (dashedarrow) as shown in Fig. 1(b). These TE units are lodged within the frame of the window; and will removeheat, from the room, for summer conditions. This design can be integrated into any glazing system once theframing is modified to accommodate the TE units.

The viability of TE windows rests on their ability to compensate for the passive heat flow through thewindow pane, among other factors. A brief overview of the heat transfer model of passive windows is outlinedin the following section.

II.A. Heat Transfer through Passive Windows

A passive window’s thermal performance is described in terms of its ability to insulate the indoor environ-ment. This insulating quality is defined by three factors; namely: (1) the U-value, (2) the solar heat gaincoefficient, and (3) the air leakage.16

(1) The U-value (U) of a window is a measure of the air-to-air heat transmission (heat loss or gain)due to the difference between indoor and outdoor temperatures.18 The U-value accounts for heat transferdue to conductance, which entails conduction, convection, and hemispherical radiation through the window.(2) The solar heat gain coefficient (SHGC) is the fraction of solar radiation directly transmitted across awindow into a building; typically, an optical property of the window panes used. (3) The air leakage resultsfrom pressure gradients across the window and is primarily dependant on the quality of the installation.We assume that the air leakage is negligible in the present study. The total passive heat transfer through awindow, Qpas, is approximated as

Qpas =[

U(Tout − Tin) + SHGC (Isky)]

(Awin) (1)

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Ncas TE cascades located

in window frame

wfr

Panes

hwin

wwin

A A

(a) Schematic of the TE Window

Passive heatflow through

Heat compensationvia TE unitsin the frame

window pane

(b) Heat transfer process taking place throughTE window

1.21

Thermoelectric Cascade

Finned Heat sink

Air

Pane

n TE units

(c) Enlarged cross-section view of A-A showing TECascade in window frame.

Figure 1. Schematic of TE window

where Awin is the area of the window pane; Isky is the incident solar radiation; and Tout and Tin are theoutside and inside ambient temperatures, respectively. Using Eq. 1, the total heat transfer across the windowpane can be determined for given window properties and environmental conditions.

II.B. Heat Transfer through TE Windows

We propose using TE units in the frame of the window to compensate for the passive heat flow definedby Eq. 1. We now describe the model of the TE window frame. We can use the formulation of the heattransfer rate, q, based on a given temperature gradient, ∆T , and a thermal resistance (R). Generically, thisis expressed as

q =∆T

R(2)

Tout

Rout Rte

Th Tc

Rin

Tin

Figure 2. Thermal circuitry of TE window (Summer Condition)

The heat transfer model of the TE window frame between the indoor and outdoor environments is depictedin Fig. 2 in terms of the thermal resistances. In Fig. 2, Tc and Th represent the TE unit’s cold side and hot side

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temperatures, respectively; and Tout and Tin are the ambient outside and inside temperatures, respectively.The thermal resistances between the ends of the TE units and the respective ambient environments areexpressed as

Rout =1

houtAhs

(3a)

Rin =1

hinAhs

(3b)

where hout and hin are the outdoor and indoor convective heat transfer coefficients, respectively; and Ahs

is the surface area across which the heat transfer is taking place. In this TE window analysis, we use air asthe ambient gas surrounding the TE units. The convection heat transfer coefficient of air inside and outsidethe building enclosure is a function of the air’s thermal and aerodynamical properties. We assume that thethermal properties of air do not vary with environmental conditions. However, we consider differences in itshydrodynamical properties indoors and outdoors. We propose increasing the effective heat exchange area ofthe TE window frame by using fins. Increasing the heat exchange area will reduce the thermal resistancewithout using additional power.

Properly designing fins for the TE window requires determining the optimal spacing and geometry foreach fin placed on the frame of the window. We use vertically oriented fins on the window frame (see Fig. 1).For vertically oriented fins of height, L, Bar-Cohen and Rohsenow derived a relation that defines an optimalfin spacing, Sopt, that maximizes the natural convection from the finned surface.5 This is given as

Sopt = 2.714L

Ra0.25L

(4)

where RaL is the Rayleigh number, which is further expressed as

RaL =gβ(Ts − T∞)L3

ν2(5)

In Eq. 5, g is the gravitational acceleration; β is the thermal expansion coefficient of the air; Ts and T∞

are the temperatures of the solid and ambient fluid, respectively; and ν is the kinematic viscosity of the fluid.For a given surface, only a certain number of fins, Nfin, can be placed with optimal spacing within the

geometry. With this number of fins, the total thermal resistance, Rfin,tot, of that surface area is given as

Rfin,tot =Rfin

Nfin

(6)

where Rfin is the thermal resistance of a single fin, defined as

Rfin =1

tanh (mH)√

hpkAc

(7)

In Eq. 7, h is the convection heat transfer coefficient; p, k, and Ac are the perimeter, thermal conductivityand cross sectional area of the fin, respectively; and H is the depth of the fin. We note that since h isdifferent for inside and outside, so is Rfin, so is Rfin,tot, and so will be Rfin,te. The fin property m is furtherdefined as

m =

√

hp

kAc

(8)

We use the fin relations, Eqs. 4 through 8 in the design of the fins for the TE window. Knowing the totalfin resistance, Rfin,tot, of the window frame, the thermal fin resistance on any side of a TE unit, Rfin,te isgiven as

Rfin,te = Rfin,tot

Atot

Ate

(9)

where Atot is the area of the window frame, without the fins; and Ate is the area of a single TE unit. Asdiscussed above Rfin,te is different for inside and outside.

As discussed above, increasing the heat transfer from the window frame system to the outdoor or indoorenvironment can be accomplished using finned heat sinks. Increasing the efficiency of the TE units is a morecomplex matter. TE units work most effectively in layers. First, we outline the heat transfer and efficiencycharacteristics of a single unit. We then discuss the changes needed to account for the system of layered TEunits (i.e. cascades).

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II.C. TE Model

The TE window design uses TE units to enforce heat flow from the cold to the hot side, given an electricalpower input. Each TE unit consists of thermocouples which, when subjected to a potential difference,induce heat flow in the direction of the current. This is known as the Peltier effect.7, 9, 17 This heat flow iscounteracted by heat induced due to the TE unit’s electrical resistance known as the Joules effect; which inturn creates a temperature difference across the TE unit, resulting in conduction from the hot side to thecold side.7, 9, 17 These effects create a net heat flow through the TE unit, given as

qte = 2N

[

αIteTc −I2teρ

2G− κ∆TteG

]

(10)

where N is the number of thermocouples; α is the Seebeck coefficient; Ite is the current; ρ is the resistivity;∆Tte is the temperature difference between the hot and cold sides of the TE unit, Th and Tc, respectively;κ is the thermal conductivity; and G is the geometry factor, which represents the area to thickness ratio ofthe thermocouple. These properties of the TE unit are generally known for given temperatures.

A proper means of comparison must be developed in order to contrast the efficiency of our system andthat of standard HVAC units. A standard HVAC unit is rated by its coefficient of performance (COP). TheCOP describes how much heat, q, can be transferred by a system for a given electrical power input, P . Thiscan be generically written as

COP =q

P(11)

The power used by a single TE unit is given as14

P = VteIte = 2NIte

[

Iteρ

G+ α∆Tte

]

(12)

where we used

Vte = 2N

[

Iteρ

G+ α∆Tte

]

(13)

From Eq. 10, it can be observed that the heat transfer capacity of a TE unit, qte, increases as thetemperature gradient, ∆Tte, decreases. Similar observation of Eqs. 12 and 13 shows that power consumptiondecreases with decreasing temperature gradient. Therefore, by decreasing ∆Tte we can increase qte and the

COP simultaneously. The difference in temperatures, between outdoors and indoors, will define the totaltemperature difference across the TE unit, ∆Tte, that is required to produce the heat flow for an energybalance to be satisfied. Before discussing a method to decrease ∆Tte across a given unit, the required ∆Tte

will be derived.Consider a single TE unit operating between different ambient temperatures, we define as

∆T∞ = Tout − Tin (14)

Balancing the energy flow through the system requires that the heat flowing from the indoor environmentto the TE unit, qin, to be the same as that flowing through the unit, qte; and also the same as that flowinginto the outdoor environment, qout. This balance can be expressed mathematically as

qout = qin = qte = q (15)

The quantities qout and qin are defined in terms of their thermal resistances as

qout =Th − Tout

Rout

(16a)

qin =Tin − Tc

Rin

(16b)

Solving for Th and Tc, and taking their difference gives the required temperature difference across the TEunits as

∆Tte = Th − Tc = qte(Rout + Rin) + ∆T∞ (17)

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A given TE unit’s performance is limited by the maximum operating current, Imax, and the maximumoperating temperature difference, ∆Tte,max, respectively given by

Imax =

(

κG

α

[

√

1 + 2ZTh − 1]

)

(18a)

∆Tte,max = Th −

[

(√

(1 + 2ZTh) − 1)

Z

]

(18b)

where Z is the figure of merit, a physical property of a TE unit.From Eq. 17, we observe that large ∆T∞ casllfor a correspondingly large ∆Tte, which we explained leads

to a low COP, i.e. low performance. By forming layers, or cascading the TE units, each unit is subjected tosmaller temperature gradients, which increases its COP/efficiency. The performance analysis presented inthis section is used in the following section to model cascaded TE system’s performance.

II.D. Cascaded TE Units

Consider the case of a single TE cascade under the same environmental conditions as the single TE unitanalyzed in the last section. Assuming there is no contact resistance between the TE units, the cold sidetemperature of one unit is equal to the hot side temperature of the previous unit. This is shown schematicallyin Fig. 3; and the orientation of the entire cascade in the window system is shown in Fig. 1(c). By electricallyconfiguring the TE units in series, the current through each unit, Ite, is the same. It follows from the energybalance, discussed previously, that the heat flow through one unit is the same as the that through any otherunit.

1

1

1

2

2

n

Tout Tin

Tc1

Tc1

Tc1

Th1

Th1

Th1

Th2

Th2

Thn−1Thn

Figure 3. TE unit configuration: single unit, two unit cascade, n unit cascade

Given the above observation, we now equate qte (Eq. 7) of the ith TE unit with that of the (i− 1)th TEunit. The resulting equation can be rewritten in terms of the temperature differences across the ith TE unit,∆Ttei

, and the (i − 1)th TE unit, ∆Ttei−1, given as

∆Ttei= ∆Ttei−1

+αIte∆Ttei−1

κG1 < i ≤ n (19)

where n is the number of TE units in the cascade. In general, for a cascaded system with n TE units, the

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analog of Eq. 17 can be written as

∆Tcas =

n∑

i=1

∆Ttei= q(Rout + Rin) + ∆T∞ (20)

With the TE units in thermal series, the heat flux, q, is constant through the entire cascade. We evaluateq based on the properties of the first unit. Eq. 12 defines the power used by each TE unit in series in acascade. Therefore, the COP of a cascade, of n units, is given by

COPcas =qte1

∑n

i=1 Pi

=αIteTc1

− I2

teρ

2G− κ∆Tte1

G∑n

i=1

(

Ite

[

IteρG

+ α∆Ttei

] ) (21)

We make the important observation that ∆Tte2through ∆Tten

are dependant on ∆Tte1and Tc1

. Thesevalues are used as design variables in the optimization problem formulated in the next section.

III. Optimizing Cascaded TE units

In section II.D, we stated that the performance of the cascaded design can be expressed in terms of theoperating performance of the first TE unit (or any other given TE unit). Optimizing the cascaded designfor optimal efficiency essentially requires optimization of only one TE unit. Here, we consider the first TEunit, defined as the TE unit that is on the side of the cascade absorbing heat.

For a given heat transfer rate, necessitated by the indoor and outdoor environmental conditions, thenecessary temperature difference across the cascade is given by Eq. 20. The temperature difference acrossthe cascade can be expressed in terms of the temperature difference across the first TE unit, ∆Tte1

, byEq. 19. We seek to transfer as much heat as possible, while maintaining a COP that is, at least, comparableto that of standard HVAC systems, denoted COPmin. The optimization problem formulation is as follows.

maxIte,Tc1

,∆Tte1

qte (22a)

such that

Ite ≤ Imax (22b)

COPcas ≥ COPmin (22c)

∆Tte1≤ ∆Tte,max1

(22d)n

∑

i=1

∆Ttei= ∆Ttecas

(22e)

Tc1= Tin − qteRin (22f)

qte = 2N

[

αIteTc −I2teρ

2G− κ∆TteG

]

(22g)

We explore the impact of cascading using the above optimization problem in the TE window application,by specifying varying values of COPmin. Results of this exploration are discussed next.

IV. Results and Discussion

In this section, we present the results of the optimization problems outlined in section III, and discuss theimplications of the optimization problem on the performance of TE windows. In our analysis, we consider a1 m2 window with a frame width, wfr, of 56 mm (see Fig. 1(a)). For the given value of wfr, the total framearea on either side of the window is 0.22 m2. Assuming that all the TE units are identical, the number ofcascades, Nc, in the window frame can be expressed as a function of the area of one TE unit as

Nc =0.22

Ate

(23)

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where Ate is the area of one TE unit. The TE units considered have an area of 16.4 mm2 resulting inNcas = 13409 as the maximum number of cascades. The thickness of the frame, 22 mm, dictates themaximum number of units in a single cascade, n. For this configuration, n = 22 is the maximum value.

To maximize our heat transfer potential, we use fins on the window frame. Using the optimal fin spacingrelation (section II.B), we evaluate the thermal resistance for the area of a single TE unit. This evaluationyields inside and outside fin resistances of 40.6 K/W and 20.9 K/W, respectively. We keep these valuesconstant throughout our analysis.

For comparison, the passive heat transfer through a tinted Pilkington OptifloatTMdouble pane glazing(U = 2.807 W/m2K, SHGC = 0.409) was considered, Qpas. This value was divided equally among all thecascades to obtain the heat gain per TE unit, qpas. This is expressed as

qpas =Qpas

Ncas

(24)

Each cascade must transfer this amount of heat, qpas, for the entire system to be thermally neutral. Theenvironmental conditions used are the NFRC 15 standard summer conditions, ambient outside and insidetemperatures of 305 K and 297 K, respectively; and incident solar radiation of 783 W/m2. For the summerconditions, the heat passive gain divided by the number of TE units is evaluated as qpas = 0.0256.

Table 1. Assumed parametric values for the TE unit

Parameter Symbol Unit Summer

Seebeck coefficient α V/K 2.02 × 10−4

Resistivity ρ Ω/cm 1.01 × 10−3

Thermal conductivity κ W/cm K 1.51 × 10−2

Figure of merit Z 1/K 2.68 × 10−3

Geometry factor G 1/cm 0.024

Here, the optimization problem (Eqs. 22a through 22g) are solved for COP values ranging between 1and 4.75. The results are summarized Fig. 4. Table 1 summarizes the values of the TE parameters used inEq. 10. The passive heat transfer rate, qpas = 0.0256, is shown in Fig. 4 as the horizontal dashed line.

1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

COP

qcas

(W)

qpas

Figure 4. Effect of minimum COP on the heat transfer rate

The intersection of the COP (solid line) and qpas curves occurs at a COP of 4.58. At this intersection,the proposed TE window will compensate for for the entire heat gain through the window with a COPgreater than that of conventional HVAC systems. Table 2 shows the heat actively lost through the cascades,Qcas = qcas ×Ncas; and the heat passively gained through the pane, Qpas. This analysis considers the solarheat gain which is the largest component of heat transfer during summer conditions (see Eq. 1). With thisconfiguration, the TE window can compensate for the passive heat flow coming in through the window using34% less power than a standard HVAC system operating at a COP of 3.

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Table 2. Optimal window performance for a COP = 3

qcas (W) Ncas Qcas Qpas (W) COP Power Reduction

0.0766 13409 342.8 342.7 4.575 34.4%

To further demonstrate the benefits of a cascading, the optimization problem was modified to maximizeCOP values for a given qte using the same constraints, Eqs. 22b, 22d, 22e, 22f, and 22g. This maximumCOP problem was run for cascades of varying numbers of units. These benchmark results are shown in Fig.5 along with the passive heat transfer per cascade, qpas.

0 0.05 0.1 0.15 0.20

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

qcas (W)

CO

Pn = 1n = 5n = 10n = 20

qpas

Figure 5. Effect of cascading on the COP for given heat transfer rates

Figure 5 shows the relation that exists between the COPcas and heat transfer rate, qte, for differentnumbers of TE units in a cascaded design. The results of Fig. 5 were generated using a TE unit with Gfactor 0.024 cm, but similar trends exist for other TE units. This figure demonstrates that even a smallcascade of 5 units can increase the efficiency of the system by a factor of three. The results validate the useof the maximum number of units, allowed by the geometry, in the previous optimization problem. However,if another constraint were placed upon the number of TE units, the number of units would have to beconsidered as part of the optimization problem.

Figure 5 also shows that there exists a qte at which the TE unit will operate at its highest efficiency.While the optimal heat transfer is small for a cascade of any size, a large number of cascades can fit withinthe frame of a window, making the heat transfer capacity of the system viable.

If this system were able to harness some of the incident solar radiation to power the TE units, the systemwould very easily obtain a thermally neutral status at a very high COP. If 17 watts of solar energy couldbe converted to electrical energy for this system to use, the effective COP would be 6. This COP valueis comparable to specialized, non-traditional, HVAC units, such as geothermal cooling systems.4, 19 This17 watts is less than 3% of the incident solar radiation on a standard summer day. The integration of aphotovoltaic system into a window is beyond the scope of this paper’s work.

V. Concluding Remarks

In this paper, we investigated further improvement of the TE window concept. We observed that arrang-ing TE units in cascades enhances the efficiency of the system, to bring it to practical competitiveness. Weused an optimization formulation that helps us gain insights into the performance tradeoffs in the design.The results showed that the cascaded TE window design yielded a significant improvement in the perfor-mance when compared to the non-cascaded case, and when compared to a standard HVAC unit. Futherwork in this area could have significant global warming implications.

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Acknowledgments

Sponsorship of this work by the National Science Foundation through awards numbers ENG-CMMI-0533330 and ENG-CMMI-0333568 is gratefully acknowledged.

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