Design of solar thermal systems utilizing pressurized hot waterstorage for industrial applications

Govind N. Kulkarni, Shireesh B. Kedare, Santanu Bandyopadhyay *

Energy Systems Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India

Abstract

A large number of industrial processes demand thermal energy in the temperature range of 80–240 �C. In this temperature range, solarthermal systems have a great scope of application. However, the challenge lies in the integration of a periodic, dilute and variable solarinput into a wide variety of industrial processes. Issues in the integration are selection of collectors, working fluid and sizing of compo-nents. Application specific configurations are required to be adopted and designed. Analysis presented in this paper lays an emphasis onthe component sizing. The same is done by developing a design procedure for a specific configuration. The specific configuration consistsof concentrating collectors, pressurized hot water storage and a load heat exchanger. The design procedure follows a methodology calleddesign space approach. In the design space approach a mathematical model is built for generation of the design space. In the generationof the design space, design variables of concern are collector area, storage volume, solar fraction, storage mass flow rate and heat exchan-ger size. Design space comprises of constant solar fraction curves traced on a collector area versus storage volume diagram. Results of thedesign variables study demonstrate that a higher maximum storage mass flow rates and a larger heat exchanger size are desired whilelimiting storage temperature should be as low as possible. An economic optimization is carried out to design the overall system. In eco-nomic optimization, total annualized cost of the overall system has been minimized. The proposed methodology is demonstrated throughan illustrative example. It has been shown that 23% reduction in the total system cost may be achieved as compared to the existing design.The proposed design tool offers flexibility to the designer in choosing a system configuration on the basis of desired performance andeconomy.

Keywords: Design space; Industrial applications; Pressurized hot water storage; System integration; Solar thermal; Optimization

1. Introduction

A large number of industrial processes demand thermalenergy in the temperature range of 80–240 �C (Proctorand Morse, 1977; Kalogirou, 2003). Solar thermal flat platecollectors are not suitable for very high temperature appli-cations. For high temperature applications, different solarconcentrators may be employed. A number of solar indus-

trial process heat systems are installed and operated onexperimental basis (ESTIF, 2004). Weiss and Rommel(2005) have reported the status of the development of med-ium temperature solar collectors for industrial applications.

The solar systems are in a developmental stage for med-ium temperature industrial applications and yet to achievea full commercialization (ESTIF, 2004). The challenge liesin the integration of a periodic, dilute and variable solarinput into a wide variety of industrial processes. Applica-tion-specific configurations are required to be adoptedand designed. Design issues in solar industrial process heatsystems involve:

Nomenclature

Ac collector area, m2

A heat exchanger area, m2

Ast surface area of the storage tank, m2

Ccoll collector cost coefficient including accessoriesand piping, Rs/m2

Chx capital cost of heat exchanger, US$/kW/�CCOM annual operation and maintenance cost, US$/yCF fuel price, US$/kgCpc specific heat of cold stream fluid, J/kg �CCph specific heat of hot stream fluid, J/kg �CCR cost function of auxiliary water heater, US$/kWCst storage system cost coefficient including piping

and insulation, US$/m2

CRFc capital recovery factor of collector and storagesystems, y�1

CRFaux capital recovery factor of auxiliary heater, y�1

CRFhx capital recovery factor of heat exchanger, y�1

(CV)F calorific value of fuel, J/kgDst average storage tank diameter, mF solar fraction over a specified time horizon, esti-

matedFs solar fraction over a specified time horizon, de-

siredFR collector heat removal factorh/d height to diameter ratio of the storage tankIbn beam normal solar radiation intensity, W/m2

IT solar radiation intensity on tilted surface, W/m2

k thermal conductivity of storage tank insulation,W/m K

mc cold stream mass flow rate of heat exchanger,kg/s

mh hot stream mass flow rate of heat exchanger, kg/smL desired load mass flow rate, kg/smst storage mass flow rate to heat exchanger, kg/sN number of transfer units of heat exchangern expected life of collectors and storage, ynL number of hours of load/daynaux expected life of auxiliary heater, yP cold or hot fluid temperature effectivenessPd storage tank design pressure, barPs saturation pressure corresponding to the limit-

ing storage temperature.Pmax maximum storage tank operating pressure, barqaux auxiliary energy required, WQaux auxiliary energy required over a specified time

horizon, JqL desired hot water load, WQL desired hot water load over a specified time hori-

zon, JqLs load met by solar energy or energy extracted

from the storage, WQLs load met by solar energy over a specified time

horizon, J

qs solar useful heat gain rate, WQs solar useful heat gain over a specified time hori-

zon, Jqstl storage heat losses, WR heat capacity flow rate ratio of heat exchangerRa auxiliary heater rating, WRb tilt factorr discount rate, %T time horizon of analysisTAC total annualized cost, US$Ta ambient temperature, �CTci cold stream inlet temperature, �CTco cold stream outlet temperature, �CTco,min minimum cold stream outlet temperature re-

quired meet the entire demand, �CThi hot stream inlet temperature, �CTho hot stream outlet temperature, �CTL desired process heat or load (hot water) temper-

ature, �CTR make up water temperature, �CTst storage temperature at any instant of time, �CTsti storage temperature at the beginning of the time

step, �CTstf storage temperature at the end of the time step,

�Ct time step in the analysis, stins storage tank insulation thickness, mtt storage tank wall thickness, mtca corrosion allowance for storage tank wall thick-

ness, mUA heat exchanger size characterization parameter,

W/�CUst storage heat loss coefficient, W/m2 �CUL collector overall heat loss coefficient, W/m2 �CVst storage volume, m3

Greek symbols

h incident anglegaux efficiency of auxiliary heatergo average optical efficiency of the concentratorq density of working fluid, kg/m3

qt density of storage tank material, kg/m3

rd design hoop stress for storage tank material,MPa

(sa) average transmittance absorptance product

Abbreviations

AUX auxiliaryHX heat exchangerISO organization for international standardsLDO light diesel oilLMTD logarithmic mean temperature differenceUS$ united states dollar

687

Storage Tank

Tst

Load

Make up water

Pump

Flat plate Solar Collectors

Load pump

Fig. 1. Schematic of a solar water heating system.

688

� selection of appropriate type of collector and the work-ing fluid, and� optimal system sizing i.e., to determine the appropriate

collector area, required storage volume and the size ofthe heat exchanger.

As far as selection of appropriate type of collector is con-cerned, thermal efficiency at the desired temperature, energyyield, cost and space occupied are the deciding factors.Water, as a working fluid, is the preferred choice for low tem-perature applications on the basis of thermal capacity, avail-ability, storage convenience and cost. However, for processheat applications above 100 �C, water must be pressurized.Storage cost rises sharply with increasing system pressure.Commercially available mineral oils are also used for med-ium temperature (above 100 �C) applications. However,applicability of these oils is restricted due to cost, tendencyof cracking and oxidation.

An important design issue in solar thermal system forindustrial applications is the optimal sizing of the systemi.e., appropriate sizing of the collectors, storage and heatexchanger. Different guidelines and methodologies areavailable to design solar thermal systems operating up to100 �C (Klein et al., 1976; Klein and Beckman, 1979; Par-eira et al., 1984; Abdel-Dayem and Mohamad, 2001; Kal-ogirou, 2004). For systems operating above 100 �C,detailed simulation programs such as TRNSYS (Kleinet al., 1975) and SOLIPH (Kutscher et al., 1982) have beenapplied. However, there is a scope for developing generaldesign guidelines for solar industrial process heat systemsfor medium temperature applications (Clark, 1982; Eskin,2000; Weiss, 2003). In this paper, a methodology is devel-oped to design and optimize a solar thermal system withpressurized water for medium temperature industrial appli-cations. The analysis is carried out by applying the designspace concept (Kulkarni et al., 2007). The design space isrepresented by tracing constant solar fraction lines on acollector area vs. storage volume diagram for a specifiedload. In this approach, all possible and feasible designs ofa solar water heating system can be identified. Investiga-tions in this paper comprise a design variable study andsystem optimization. Effects of different design variableson the collector area; storage volume and system perfor-mance are studied with the help of identified design space.The study is commenced by fixing the variables one by one.To consider the combined effects of additional design vari-ables such as heat exchanger size and maximum storageoperating pressure, economic optimization is needed. Aglobal economic optimum is obtained for the givenconfiguration.

The proposed procedure is demonstrated through anillustrative case study of integrating solar concentratorwith pressurized hot water storage to deliver 45000 l ofhot water to pasteurize 30 000 l of milk per day. Comparedto the existing system, the optimum design, obtained usingthe proposed methodology, offers 23% reduction in thetotal annualized cost.

2. The design space approach

Design space, introduced by Kulkarni et al. (2007) is theregion bounded by constant solar fraction curves traced onthe collector area vs. storage volume diagram. Designspace approach involves identification of the entire designspace i.e., all the feasible system sizes. The procedure ofdesign space generation is reviewed briefly in this sectionand illustrated with the help of an example.

Schematic of a flat plate solar water heating system isshown in Fig. 1. For such a system, energy balance forthe well mixed storage tank can be expressed as a differen-tial equation. Change in the internal energy of the storagetank is equal to the energy interactions taking place over atime step. The energy interactions are solar input, demandmet and the storage heat losses:

ðqCpV stÞdT st

dt¼ Ac½ITF RðsaÞ � F RULðT st � T aÞ�þ

� qLs � U stAstðT st � T aÞ ð1Þ

In Eq. (1), solar input is determined using Hottel–Whillier–Bliss equation (Duffie and Beckman, 1991) and ‘+’ signindicates that only positive values of solar input are to beconsidered. In estimating storage tank heat losses, surfacearea of the storage tank is assumed to be related to the stor-age volume by following relation, assuming equal height todiameter ratio (Kulkarni et al., 2007):

Ast ¼ 5:54ðV stÞ2=3 ð2Þ

Solution of differential equation (1) enables one to calcu-late the storage temperature (Tstf) at the end of a time step:

AcITF RðsaÞ � AcF RU LðT stf � T aÞ � qLs � U stAstðT stf � T aÞ½ �AcITF RðsaÞ � AcF RULðT sti � T aÞ � qLs � U stAstðT sti � T aÞ½ �

¼ exp �ðAcF RUL þ U stAstÞtðqCpV stÞ

� �

ð3Þ

For a given type of collector, storage and load characteris-tics, Eq. (3) uniquely predicts the storage temperature overa period of time. The storage temperature is a function ofcollector area and storage volume. In this analysis, it is

0

20

40

60

80

100

120

0 10 12 14 16 18 20 22 24Time,h

Stor

age

tem

pera

ture

, °C

Limiting temperature line

Storage temperature profile for unity solar fraction

ISOLoadprofile

LoadTemp.60 ºC

2 4 6 8

Fig. 2. Load and storage temperature profile over a typical day.

0.1

1

10

100

1000

10000

50 75 100 125 150 175 200 225 250Collector area,sq.m

Sto

rage

vol

ume,

cu.m

a

b

m o

A min

Vmin

Load temperature constraint

Limiting storage temperature line

Feasible design region (Design space)

Volume limits for a given area

Area limits for a given volume

Fig. 3. Design space for F = 1.

689

assumed that change in the thermal energy of the storageover the time horizon (a day, a month or a year) is zero:Z T

0

qCpV st

dT st

dt

� �dt ¼ 0 ð4Þ

By varying the collector area and the storage volume, dif-ferent feasible designs may be obtained. For illustration,a case of unity solar fraction is described. Unity solar frac-tion suggests that the entire thermal demand has to be metby the solar energy. For satisfying the entire thermal de-mand, storage tank temperature during the time of the de-mand must be greater than the desired load temperature:

T st P T L ð5Þ

Since, water at the atmospheric pressure, is used as a work-ing fluid, the storage tank temperature has to be less than100 �C:

T st 6 100 �C ð6Þ

An acceptable design must satisfy these constraints. For aspecified load, all possible combinations of collector areaand storage volume that satisfy these two constraints definethe design space. Generation of the design space is demon-strated through an example.

A single day (15th April) is chosen for illustration.Monthly mean values of hourly solar radiation (Mani,1981) are adopted for this example. The time step t is3600 s and time horizon is a single day. The system param-eters are given in Table 1. Fig. 2 shows the storage temper-ature profile with a typical collector area and storagevolume combination (Ac = 90 m2 and Vst = 3.7 m3). Limit-ing storage temperature constraint and the hot waterdemand profile are also shown in Fig. 2. The limiting stor-age temperature constraint is 100 �C while the load temper-ature constraint is 60 �C. The storage temperature profile isin between these two constraints (Fig. 2). This is a feasibledesign for unity solar fraction. The combinations of Ac andVst are varied to obtain all the feasible designs for unitysolar fraction. Combination of the collector area and thestorage volume that satisfy these constraints are identifiedand illustrated in Fig. 3. The region inside these curves rep-resents all possible design combinations that satisfy theunity solar fraction. This region represents the design spacefor unity solar fraction for the example. From Fig. 3, itmay be noted that the point ‘a’ represents a system withthe lowest possible storage volume requirement. Point ‘a’represents 2.6 m3 of storage volume and 111 m2 of collectorarea. Any reduction in storage volume will result in boilingof water in the storage tank. Point ‘m’ in Fig. 3 indicates a

Table 1Solar system parameters

Location Pune, India (latitude �18.53�, longitude – 73.85�, ground reflectaLoad Domestic hot water for an apartment building, 4500 LPD at 60 �

(International Standards Organization, 1997)Collectors Flat plate collectors (single cover, selective coated, south facing TStorage Insulation: 0.14 m glass wool (k = 0.04 W/m K)

minimum collector area design. The design occurs at a col-lector area of 76 m2 and storage volume of 28 m3. Anydecrease in the collector area from ‘m’ will not meet thedesired hot water demand.

It may also be noted that there exists a minimum as wellas a maximum storage volume for a given collector area.For example, a constant collector area line (Ac = 111 m2)in Fig. 3 intersects the limiting curves at ‘a’ and ‘b’. Point‘a’ indicates a minimum limit on storage volume of2.6 m3,while point ‘b’ indicates a maximum limit of1227.2 m3. Beyond point ‘b’, thermal losses from the storagetank will dominate resulting into a loss of solar fraction.Similarly, there exists a minimum as well as a maximumcollector area for a given storage volume. It is illustratedin Fig. 3 through points ‘m’ and ‘o’. The line segment ‘m-a’ in Fig. 3 signifies the Pareto optimality curve.

The region bounded by the limiting curves includes allfeasible designs of the system and is called the design space(Kulkarni et al., 2007). Similar to the above procedure, thedesign space can be identified by tracing constant solar

nce = 0.2)C, Consumption pattern as per ISO 9459–3:1997(E)

ilt = 33.53�) Collector parameters FR(sa) = 0.675, FRUL = 5.656 W/m2 K.

690

fraction lines for other solar fractions. Any objective func-tion involving the capital and the operating costs of the sys-tem may be chosen for optimization of the overall system.A more elaborate treatment of design space is given byKulkarni et al. (2007). Application of the design spaceapproach has been demonstrated for solar thermal systemoperating up to 100 �C. A large number of industrial andcommercial applications demand solar thermal energybeyond 100 �C. Utility of the design space methodologyis therefore, improved and extended for systems operatingbeyond 100 �C.

3. The design space for pressurized water storage

In this section, the concept of design space is improvedand extended to a solar thermal system intended for indus-trial application beyond 100 �C.

3.1. System configuration

The general configuration of a solar thermal system sup-plying hot water beyond 100 �C is shown in Fig. 4. Thegeneral system comprises of a concentrating collector, apressurized hot water storage tank, a load heat exchangerand an auxiliary heater.

The beam solar radiation is converted into useful heatby the concentrating collector. Water from the storage tankis circulated through the absorber tubes of the receiver.Water absorbs the heat and is returned back to the storagetank. Heat is stored in the form of pressurized hot water.When heat is demanded by the process, hot water ispumped to the heat exchanger at a rate of mst. Hot waterat Thi from the storage tank is circulated through the heatexchanger. In the heat exchanger, heat is transferred to thecold stream. Water returns to the storage tank at a lowertemperature of Tho. The cold process stream is pumpedat a constant flow rate of mc. A minimum cold stream out-let temperature (Tco,min) is desired to meet the entiredemand. This limit can be determined on the basis of thedemand and the cold stream flow rate. Actual cold streamoutlet temperature (Tco) depends on the storage tempera-

SolarConcentrator

Pump

Pressurizedhot water Storage

Tst = Thi

Fig. 4. Schematic of a solar indust

ture Tst. Auxiliary heater is placed in the cold stream circuitin series with the heat exchanger. If Tco < Tco,min, auxiliaryheater is switched on and the cold stream is further heatedto the desired temperature.

The design variables for this generalized system are

� Collector area (Ac),� storage volume (Vst),� solar fraction (F),� maximum storage mass flow rate (mst,max),� heat exchanger sizing parameter (UA) and� limiting storage temperature (Tst,max).

The limiting storage temperature determines the maxi-mum operating pressure of the system and the thicknessof the storage tank. For simplification, it is assumed thatthe type of heat exchanger and its size may be characterizedand selected on the basis of UA product. UA product rep-resents the output of a heat exchanger for a unit logarith-mic temperature difference (LMTD). Design procedureproposed here uses UA product as a heat exchanger sizingparameter. A mathematical model of the system is devel-oped in the following section.

3.2. Mathematical model of the system

Energy balance of a well mixed storage tank can beexpressed as

ðqCpV stÞdT st

dt¼ qs � qLs � qstl ð7Þ

where the storage losses (qstl) are estimated to be

qstl ¼ U stAstðT st � T aÞ ð8Þ

Solar useful heat gain rate (Duffie and Beckman, 1991) isestimated using the following equation:

qs ¼ Ac½ITF RðgoÞ � F RU LðT st � T aÞ�þ ð9Þ

where + sign indicates, hot water from the collectorenters the tank only when solar useful heat gain becomespositive. It may be noted that Eq. (9) represents a linear

mc

Cold stream pump

Tci

Tco

Loadpump

Thi

Tho

HX Load

mstAUX

rial process heat configuration.

691

characteristic equation for a solar collector. For high tem-perature applications and for concentrating collectors, thismay not always be suitable. For such systems, a second orhigher order characteristic equation may be more suitable.For more accurate results, a non-linear characteristic equa-tion should be used instead of (9). The proposed methodol-ogy is independent of the nature of the characteristicequation. However, for the system, for which the method-ology is demonstrated, it has been observed that an accu-rate non-linear characteristic equation does not improvethe system sizing significantly (Kulkarni, 2008).

Solar flux incident on the aperture of a tracking concen-trator is calculated as

IT ¼ Ibn cos h ð10Þ

Combining Eqs. (8) and (9) with Eq. (7), energy balance ofthe tank can be expressed as

ðqCpV stÞdT st

dt¼ Ac½ITF RðgoÞ � F RU LðT st � T aÞ�þ

� qLs � U stAstðT st � T aÞ ð11Þ

Load met by solar energy is given by

qLs ¼ mstCphðT st � T hoÞ ð12Þ

To determine the solar contribution of load (qLs), hotstream outlet temperature (Tho) and storage mass flow rate(mst) must be known. For calculating Tho,heat exchangerparameters such as number of transfer units (N), heatcapacity flow rate ratio (R) and cold or hot fluid tempera-ture effectiveness (P), have to be considered. In this case,hot stream flow rate mh is the storage flow rate mst andhot stream temperature Thi is the storage temperature Tst.Number of transfer units (N), heat capacity flow rate ratio(R) and cold or hot fluid temperature effectiveness (P) aredefined as follows:

N ¼ UAmstCph

ð13Þ

R ¼ mstCph

mcCpc

ð14Þ

P ¼ ðT st � T hoÞðT st � T ciÞ

ð15Þ

Computation begins with the assumption of initial storagetemperature (Tsti), storage flow rate (mst) and heat exchan-ger sizing parameter (UA). With these parameters known,values of N and R can be calculated using Eqs. (13) and(14). For simplicity, a counter flow heat exchanger is as-sumed. The relation between N, R, and P on the basis ofhot stream is used (Shenoy, 1995):

P ¼ expð�NðR� 1ÞÞ � 1

expð�NðR� 1ÞÞ � Rfor R 6¼ 1 ð16aÞ

P ¼ NN þ 1

for R ¼ 1 ð16bÞ

With hot stream effectiveness P known, hot stream outlettemperature Tho can be calculated:

T ho ¼ T st � PðT st � T ciÞ ð17Þ

With known P and R, the cold process stream outlet tem-perature can also be determined:

T co ¼ T ci þ PRðT st � T ciÞ ð18Þ

The minimum cold process stream outlet temperature(Tco,min) needed to fulfill the complete demand can bedetermined as

T co;min ¼ T ci þQL

nLtðmcCpcÞð19Þ

By knowing the hot stream outlet temperature, solar con-tribution to the load during a time step may be determined.In Eq. (19), desired load (QL) over a time horizon (a day)and duration of load in nL time steps (number of hours)is specified. The load is assumed to be uniformly distrib-uted over the time steps. Cold stream mass flow rate (mc)and inlet temperature (Tci) are assumed to be constant inthis analysis. No auxiliary energy will be required ifTco P Tco,min. In all the cases, hot stream flow rate is con-trolled in such away that cold stream outlet temperaturedoes not exceed Tco,min. This ensures effective utilizationof the solar energy. Auxiliary energy is required if Tco <Tco,min and the same is determined as

qaux ¼ mcCpcðT co;min � T coÞ ð20Þ

System parameters are evaluated on the basis of initial stor-age temperature (Tsti). Final storage temperature at the endof a time step t is obtained by solving Eq. (11) numerically:

T stf ¼ T sti þt

qCpV st

ðAcITF RðgoÞ � AcF RU LðT sti � T aÞÞþ�

�mhCphðT sti � T hoÞ � U stðT sti � T aÞ�

ð21Þ

The final storage temperature at the end of a time step willbe the initial temperature for the next time step. Storagetemperature profile over a day is thus, obtained. The max-imum storage temperature (Tst,max) observed in a day isidentified. In this model, the maximum storage operatingpressure is the saturation pressure of water correspondingto the maximum storage temperature. The correlation pro-posed by Chopey (2004) is used to determine the saturationpressure of water corresponding to the maximum storagetemperature.

In the industrial practice, the design pressure pd for thepressure vessel is usually taken to be 1.5 times the maxi-mum operating pressure Ps. Storage tank thickness is cal-culated using the hoop stress equation (Brownell andYoung, 1959).

tt ¼pdDst

4rd

þ tca ð22Þ

With the known storage temperature profile, solar fractionover the time horizon can be calculated as

F ¼QL �

Ptimehorizon

qaux:t

QL

ð23Þ

06 8

100

200

300

400

500

600

700

800

10 12 14 16 18Time of the day in hour

Nor

mal

bea

m ra

diat

ion

(W/m

2 )

Fig. 5. Average daily direct normal radiation used for the illustrativeexample.

692

It is assumed that there is no change in the internal energyof the storage over the time horizon (a day, a month or ayear). The assumption can be mathematically expressed as:

Xtimehorizon

Z t

0

qCpV st

dT st

dt

� �dt ¼ 0 ð24Þ

The average collector efficiency is one of the importantparameters that determine the system performance. Aver-age collector efficiency is defined as follows:

gc ¼PR t

0½ITF RðgoÞ � F RULðT st � T aÞ�þdtPR t

0ITdt

ð25Þ

Equations described above are utilized to study the effect ofdifferent variables on the system design and performance.

3.3. Effect of different design variables

In this section, effects of various design variables on theoverall system design and operations are investigated.Effects of the maximum storage mass flow rate, heatexchanger size and the limiting storage temperature onthe system design are studied. In each case, the design spacefor unity solar fraction is generated and it is illustrated withan example of milk pasteurizing process. The load has adaily demand of 45000 l of hot water for pasteurizing30000 l of milk per day. Load details and other input dataare given in Table 2. The configuration uses concentratingcollector that operates on the beam solar radiation. In themajor part of India, July, August and September are mon-soon months. During monsoon months almost no beamsolar radiation is available. Considering this fact, monthlyaverage of hourly normal beam radiation data (Mani,1981) neglecting these three months is considered. A ninemonth average is calculated to represent a single day.Fig. 5 shows the variation of a nine month hourly averagenormal beam radiation over time. Analysis presented in thefollowing sections makes use of a nine month average ofbeam solar radiation intensity. Ambient data is adopted

Table 2Input data for pressurized hot water storage system example

Location A dairy plant at Pune, India

Load Pasteurization load, QL = 1.88Duration: Four hours (nL), 10 aCold stream: mass flow rate mc

Collectors Paraboloid collector with two aFR (sa) = 0.6 and FRUL = 1.2 WWorking fluid: Water

Storage Storage fluid: Water, pressurizeTank Material: Carbon steel C2Cylindrical, well mixed, alwaysTensile stress for tank material,Factor of safety for pressure veDesign stress = 10 MPaInsulation thickness, ti = 152.4Insulation: Glass wool (k = 0.0

Heat exchanger Counter flow typeCph = Cpc = 4180 J/kg K

on the similar lines. Time step in all the foregoing analysisis 3600 s while time horizon is single day. It may be notedthat the proposed methodology is not restricted to theseassumptions.

3.3.1. Effect of maximum storage mass flow rate

Effect of storage mass flow rate on the system design isinvestigated. Storage mass flow rates are varied from2 kg/s to 10 kg/s. Other system parameters such as heatexchanger UA value and limiting storage temperature,etc. are kept constant. Results are shown in Table 3. Aver-age collector efficiency and average heat exchanger effec-tiveness are calculated using Eqs. (25) and (16),respectively. From Table 3 it may be observed that theaverage storage temperature during the load period, thecollector efficiency and the solar fraction changes onlyslightly. However, the average heat exchanger effectivenessreduces with increasing storage mass flow rate. Designspaces for unity solar fraction at different storage mass flowrates are shown in Fig. 6. The characteristics are drawn at aconstant heat exchanger UA value of 6000 W/�C and thelimiting storage temperature of 160 �C. Designs with theminimum collector area as well as the minimum storage

GJ/day (30000 LPD of milk).m. to 02.00 p.m., uniform

: 3.125 kg/s, inlet temperature Tci: 85 �C, outlet temperatureTco,min: 95 �Cxis tracking (h = 0)/m2 K (Kedare, 2006)

d5, density 7800 kg/m3

full, with (h/d) = 2.6rd = 50 MPa (PSG, 1993)

ssel design, 5 (Brownell and Young, 1959)

mm4 W/m K)

Table 3Effect of maximum storage mass flow rate on the system performance at a fixed system size of Ac = 180 m2, Vst = 4 m3, UA = 6000 W/�C, Tst,max = 160 �C

Maximum storage massflow rate, kg/s

Average storage temperatureduring load period, �C

Average collectorefficiency

Average HX effectivenessduring load period

Solarfraction

2 114.18 39.72 63.09 0.88593 112.62 40.01 56.14 0.8934 111.9 40.14 52.35 0.89635 111.61 40.2 50.63 0.89786 111.41 40.25 49.44 0.89887 111.27 40.28 48.58 0.89958 111.16 40.3 47.91 0.910 111.02 40.33 46.97 0.9008

1

10

100

1000

200 203 206 209 212 215 218 221 224Collector area,sq.m

Stor

age

volu

me,

cu.m

Unity solar fration curves atUA = 6000 W/°CT st,max = 160°C

Minimum collector area designsMinimum storage volume deasgins

7 kg/s6 kg/s5 kg/s4 kg/s3 kg/s2 kg/s

Fig. 6. Design spaces at unity solar fraction for different maximumstorage mass flow rates.

Table 4Effect of heat exchanger size on system performance at a fixed system sizeof Ac = 180 m2, Vst = 4 m3, mst,max = 3 kg/s and Tst,max = 160 �C

UA, W/�C Average storagetemperature duringload period, �C

Average heat exchangereffectiveness during loadperiod

Solarfraction

2000 136 15.2 0.782600 127.8 23.7 0.823000 123.8 28.1 0.844000 118.7 41.5 0.866000 112.6 56.1 0.898000 110.1 67.6 0.9010000 108.6 74.8 0.91

1

10

100

1000

190 200 210 220 230 240 250Collector area,sq.m

Stor

age

volu

me,

cu.m

Unity solar fration curves atmst = 3 kg/s,T st,max = 160°C

10000 W/°C

8000 W/°C6000 W/°C

4000 W/°C3000 W/°C 2600 W/°C

Limiting storage temperature lines

a1 b1 c1 d1 e1 f1

a

cd

ef

b

693

volume, corresponding to the unity solar fraction for differ-ent storage mass flow rates, are highlighted in Fig. 6. Itmay be noted that the storage mass flow rate does not havea significant impact on the storage volume. However, theminimum collector area requirement decreases significantlywith increasing maximum storage flow rate. Higher valuesof storage mass flow rates are therefore, desired. It may benoted that the higher mass flow rate of the storage waterrequires more electrical power required to pump it throughthe heat exchanger. Appropriate hydraulic analysis may beperformed to select the maximum storage mass flow rate.

Fig. 7. Effect of heat exchanger sizing parameter on the design spaces atunity solar fractions at Tst,max = 160 �C, mst,max = 3 kg/s.

3.3.2. Effect of heat exchanger size (UA)

At a fixed system size, Table 4 shows the effect of heatexchanger UA value on the system performance. As heatexchanger UA value increases the heat exchanger effective-ness increases and the average storage temperature duringload decreases. This results in an improvement in the solarfraction and a reduction in the minimum collector arearequirement (Fig. 7). In Fig. 7, the effect of heat exchangersize, on the design space for unity solar fraction is revealed.The limiting storage temperature lines for different heatexchanger sizes are separately drawn. The minimum stor-age volume requirements i.e., the intersections of the con-stant unity solar fraction curves with the limiting storagetemperature lines are depicted by points ‘a’ to ‘f’. The min-imum collector area requirements are represented by points

‘a1’ to ‘f1’. With a decrease in UA value (heat exchangersize), the minimum collector area requirement as well asthe minimum storage volume requirement increases. ThePareto optimal region is the portion of the constant solarfraction curve connecting the minimum collector areaand the minimum storage volume. A suitable economic cri-terion may be applied to obtain an optimum design. With adecrease in heat exchanger UA value, Pareto optimal curvebegins to shrink. For this example, at an UA value of2600 W/�C, the point denoting the minimum collector arearequirement and the point denoting the minimum storagevolume requirement, coincide and the Pareto optimal curveshrinks to a point (point ‘f’ in Fig. 7). For designing a sys-

694

tem with heat exchanger UA values less than 2600 W/�C,economic optimization is not required, as the Pareto opti-mal region is represented by a single point. A larger heatexchanger may be preferred as the minimum collector arearequirement and the minimum storage volume requirementboth decreases simultaneously. However, a large heatexchanger incurs a higher capital cost. Economic optimiza-tion of the overall system may be carried out to choose theappropriate heat exchanger size.

3.3.3. Effect of limiting storage temperature

The limiting temperature of the storage tank (Tst,max)signifies the operating pressure of the system. With anincrease in Tst,max, the operating pressure of the systemincreases and thereby, thickness of the storage tank andassociated piping system increases. This results in anincrease in the capital cost of the overall system. Fig. 8shows design space at unity solar fraction at various limit-ing storage temperatures. The characteristics are drawn ata constant maximum storage mass flow rate of 3 kg/s andheat exchanger UA value of 6000 W/�C. The limiting stor-age temperature lines for different maximum allowablestorage temperature are shown separately in Fig. 8. Theminimum storage volume requirement reduces significantlywith increasing limiting storage temperature. For theexample, required minimum storage volumes correspondto different limiting storage temperatures are highlightedby points ‘a’ to ‘e’ in Fig. 8. It may be noted that the min-imum collector area requirement does not vary significantlyif the maximum storage temperature is beyond a particularvalue. For the example, it has been noted that below 130 �Cof the limiting storage temperature, the sizing curve shrinksin to a point.

From the above study, it may be noted that the maxi-mum storage mass flow rate, heat exchanger size, and thelimiting storage temperature influences the minimum col-lector area requirement as well as the minimum storagevolume requirement. In other words, the design space getsaffected by these variables. To capture the effect of these

1

10

100

1000

200 205 210 215 220 225 230 235 240 245 250Collector area,sq.m

Stor

age

volu

me,

cu.m

Unity solar fration curves atUA = 6000 W/ºCmst,max = 3 kg/s

a160 ºC

140 ºC150 ºC

130 ºC

120ºC

Limiting storage temperature lines

e

d

cb

Constant unity solar fraction curves

Fig. 8. Effect of maximum storage temperature on the design space forunity solar fraction at UA = 6000 W/�C and mst,max = 3 kg/s.

variables simultaneously on the design space, an optimiza-tion based methodology is proposed.

3.4. Design space through system optimization

A methodology to generate the design space of the sys-tem considering simultaneous variation of different designparameters is discussed here. It may be noted that for agiven collector area there exist a maximum and a minimumstorage volume in the design space. Based on this observa-tion, a methodology is followed to generate the designspace where different design variables are varied simulta-neously. The maximum and the minimum allowable stor-age volumes are searched subject to different constraints.These objectives (minimization and maximization of thestorage volume) are optimized separately by varying heatexchanger size and the maximum storage flow rate subjectto a given collector area and solar fraction. For a fixedsolar fraction, by varying the collector area, the loci ofthe maximum and the minimum allowable storage volumesare plotted on the collector area vs. storage volume dia-gram to obtain the design space of the system.

Input parameters include solar radiation data, dailythermal demand, desired solar fraction, collector character-istics, storage parameters, working fluid properties etc.During optimization, to limit the search space and to havea physical significance of the result, suitable range for eachvariable has been incorporated. A limit on the maximumstorage temperature is kept for the safety purpose. Thelimit depends on collector type, nature of demand and stor-age cost. At any instant of time storage temperature shouldnot exceed the limiting specified value. The constraint ismathematically expressed as

T st 6 T st;max ð26Þ

As the storage temperature decreases, the duty of the aux-iliary heater has to be increased to fulfill the demand. Thereis a practical limit on the provision of auxiliary heatercapacity. It is not beneficial to operate the system at verylow storage temperatures. A lower limit on storage temper-ature is therefore, provided. The cold process stream inlettemperature should ideally serve as a lower limit. Due tofinite size of the heat exchanger, a certain temperature dif-ference (dT) is maintained. At any instant of time, storagetemperature should be above the minimum specified limit.The constraint is stated as

T st P T ci þ dT ð27Þ

Similarly, the minimum and the maximum size constraintsare put on the heat exchanger size:

UAmin 6 UA 6 UAmax ð28Þ

On the hot stream side, it is assumed that there is a mini-mum temperature difference between the inlet and the out-let temperature. Corresponding to this minimumtemperature difference, a maximum storage flow rate exists:

Table 5Constraints in the optimization formulation

Description of the constraint Value

Limiting storage temperature constraint, Tst,max 200 �CMinimum cold stream inlet temperature, Tco 85 �CMinimum storage temperature, Tst,min 90 �CMaximum storage flow rate, ms,max 6 kg/sMaximum UA value, UA,max 8000 W/�CMinimum UA value, UA,max 2000 W/�C

695

ms 6 ms;max ð29Þ

The above model is optimized for the minimum and themaximum storage volume. The proposed procedure forgeneration of the design space is demonstrated throughthe previous example. Limiting values of different con-straints are tabulated in Table 5. The design space gener-ated is shown in Fig. 9. Curves in Fig. 9 representconstant solar fractions in the range of 0.6–1. In each case,the minimum collector area and the minimum storage vol-ume points are highlighted. The design space portrays var-iation between the collector area and the storage volume atdifferent solar fractions. The effects of three variables onthe collector area, the storage volume and the solar fractionare accounted.

It may be noted that the design space does not exhibitthe effect of these variables on the economic design onthe overall system. As discussed earlier, it has beenobserved that a larger heat exchanger is desired. However,a larger heat exchanger incurs a higher capital cost. Lowerhalves of the constant solar fraction curves in Fig. 9 areobtained by minimizing the storage volumes. These designsrepresent heat exchanger sizes that designate a minimumstorage volume and not necessarily the minimum systemcost. Heat exchanger size must be optimized on the eco-nomic basis rather than minimum storage volume require-ment. Similarly the effect of maximum storage temperatureon the economic optimization of the overall system is notvisible on the design space. Maximum storage temperaturedecides the maximum storage operating pressure and stor-

1

10

100

1000

10000

100 130 160 190 220 250 280 310 340 370

Collector area,sq.m

Sto

rage

vol

ume,

cu.m

0.6

Constant solar fraction

0.7

m

- Minimum collector area designs- Minimum storage volume designs

0.8 0.9 F=1

a

Fig. 9. Entire design space with optimized storage volume.

age tank thickness. A higher storage temperature indicatesa lower storage volume and associated reduction in thecapital cost. Higher storage temperature also increasestank thickness increasing the capital cost. The design spacetends to demonstrate maximum tank thickness while min-imizing the storage volume. An economic trade off is pos-sible between storage tank volume and tank thickness(weight). The reason being, additional variables influencethe system size, besides collector area and storage volume.To account for the effect of additional variables such asheat exchanger size and maximum storage temperature,economic optimization is carried out. This highlights thedifference between the design space for simple flat platesolar thermal system and that for a concentrator solar ther-mal system with pressurized hot water storage. Because ofadditional variables, the design space does not incorporatethe Pareto optimal region for a solar thermal system withpressurized hot water storage.

4. Economic optimization of the overall system

For economic optimization of a solar thermal system,different objective functions such as total annual cost(Kulkarni et al., 2007), annualized life cycle cost (Hawladeret al., 1987), life cycle savings (Gordon and Rabl, 1982),pay back period (Michelson, 1982), internal rate of return(Gordon and Rabl, 1982) etc. have been considered. In thispaper, total annualized cost of the system (TAC) has beenused as an objective function. The total annualized cost ofthe system comprises of the annualized capital cost, annualrepair and maintenance costs of the overall system. Costcoefficients used for this study are reported in Table 6,based on the existing market trends in India. In the designof chosen configuration, storage tank thickness varies withthe maximum storage temperature as well as storage vol-ume. The cost coefficient of storage volume is therefore,mentioned in terms of cost per unit storage volume andunit tank thickness. Total annualized cost of the systemis given as

Table 6Economic parameters adopted for optimization

Discount rate, r% 10.75Life of collectors and storage, n years 15Life of heat exchanger, years 5Life of auxiliary heater, naux years 10Collector cost coefficient, Cc US$/m2 333Storage tank material cost US$/kg 1.1Storage tank cost coefficient per m3 US$/mm

of wall thickness59

Tank insulation price, Cins US$/m2 3 (for a slab thicknessof 25.4 mm)

Heat exchanger cost coefficient, US$/kW/�C 555Cost coefficient of hot water generator, CR,

US$/kW89

Fuel price (LDO), CF US$/kg 0.9Burner efficiency 75%

Exchange rate, 1 US$ = 45.05 Rs (Reserve Bank of India, 2006).

Table 7Economic optimum designs at different solar fractions

Solar fraction 1.00 0.90 0.87 0.80 0.70 0.60 0.50Collector area, m2 207 176 170 156 136 116 97Storage volume, m3 17 12 11 8 5 5 4Heat exchanger UA value, W/�C 8000 6226 5840 5117 4483 3748 3082Maximum storage temperature, �C 119 119 121 123 127 127 127Maximum operating pressure, bar 2 2 2 2 2 2 2Tank thickness, mm 31 28 28 28 27 26 24Total cost, US$/y 14763 14217 14180 14251 14535 14888 15248System capital cost, US$/y 14763 12704 12187 11226 9998 8839 7687Operating (fuel) cost, US$/y 0 1513 1993 3025 4537 6049 7561

14000

14200

14400

14600

14800

15000

15200

15400

0.5 0.6 0.7 0.8 0.9 1

Solar fraction T

otal

cos

t, U

S$

Economic optimum at US$/y 14180F =0.87, A c =170 m2,V st =11 m3

UA=5840 W/˚C, t t =28 mm

Range of solar fractions with 2% increase in total cost

Fig. 10. Variation of total cost with solar fraction.

696

TAC ¼ ðCcollAc þ CstttV2=3st ÞCRFc þ Chx � ðUAÞ

� CRFhx þ COM þ ðCRRaÞCRFaux þð1� F ÞQLCF

ðCVÞFgaux

ð30Þ

Annual repair and maintenance cost of the collector andstorage is taken as 2% of the capital cost while that ofthe heat exchanger is taken as 3% of its capital costs. Forthe case study, the auxiliary heater operates on light dieseloil. Auxiliary heater rating Ra is determined from the per-iod of the maximum auxiliary energy demand.

The mathematical model described in Section 3.2 istransformed into an economic optimization formulation.All the input parameters and constraints remain the sameas in Tables 2 and 5 respectively. The objective functionis minimization of total cost by varying collector area, stor-age volume, heat exchanger UA value and storage massflow rates within a specified range and results are shownin Table 7.

It may be observed from Table 7 that reduction in thesolar fraction reduces the collector area, the storage vol-ume, and the heat exchanger size requirement. There is amarginal increase in the maximum storage temperature(and corresponding operating pressure) with a reductionin solar fraction. It is interesting to note that the tankthickness decreases even if there is an increase in the stor-age temperature. The decrease in tank thickness is attrib-uted to a reduction in the storage volume (22). As thesolar fraction decreases, capital cost decreases while oper-ating cost increases. A trade off between the capital and

Table 8Comparison of global economic optimum with existing design

Optimum design

Solar fraction 0.87Total cost, US$/y 14180Solar system Capital cost, US$/y 8537Auxiliary heater Capital cost, US$/y 3650Operating (fuel)cost 1993Collector area, m2 170Storage volume, m3 11Heat exchanger UA value, W/�C 5840Maximum storage temperature, �C 121Maximum operating pressure, bar 2Tank thickness, mm 28

the operating costs yields a solar fraction with the mini-mum total cost of the system. Fig. 10 shows the variationof total cost with solar fraction. For the given constraints,the global economic optimum is observed at a total cost ofUS$14180/y and at a solar fraction of 0.87. A comparisonof the optimum design with the existing design is shown inTable 8.

In actual practice, commercial concentrating collectorsare available only in discrete sizes. The type of concentrat-ing collector used for this study is available at a fixed size of160 m2. The entire economic optimization is performed wita fixed collector size of 160 m2. Table 8 also shows an opti-mized design with a fixed collector area of 160 m2. Existingdesign consists of 160 m2 of collector area, 5 m3storage vol-ume, heat exchanger UA value of 3500 W/�C and the stor-age tank thickness of 160 mm. The existing design gives asolar fraction of 0.78 and the annualized system cost of

Existing design Optimized design with fixed collector area

0.78 0.8218956 1421310833 71254740 44273383 2661160 1605 93500 5572200 12216.00 2.1160 27

Table 9Range of system designs encompassing 2% increase in the minimum totalcost

Solar fraction 0.71 0.978Total cost, US$/y 14471 14461System capital cost, US$/y 10085 14126Operating (fuel) cost 4386 334Collector area, m2 138 200Storage volume, m3 6 14Heat exchanger UA value, W/�C 4554 7448Maximum storage temperature, �C 127 121Maximum operating pressure, bar 2 2Tank thickness, mm 27 30

697

US$/y 18956. For the given constraints, the optimumdesign exhibits a better economic benefit and performancethan the existing design with and without a given collectorarea. The global optimum design depicts a 12% gain in thesolar fraction at the cost of 21% increase in the solar capitalcost as compared to the existing design. An overall benefitof 25% is expected in the total annualized cost for the glo-bal optimum design. As compared to the existing design,there is an increase in the collector area of 6%, an increasein storage volume by 120% and an increase in the heatexchanger size by 67%. However, there is a 40% reductionin the maximum storage temperature and it brings downthe maximum operating pressure by 88% and the tankthickness by 83%. Overall capital cost decreases substan-tially with a reduction in the maximum operating pressureof the storage tank. There are also a 23% reduction in aux-iliary heater capital and 41% reduction in operating cost.Designing the system with a lower limiting storage temper-ature thus, improves the economic advantage.

The optimized design with a fixed collector area of160 m2 shows no substantial change from the global opti-mum design. There is a 2% increase in the total annualizedcost of the fixed collector area design. The increase isattributed to a 21% increase in the auxiliary heater capitaland a 33.5% increase in the operating cost. In comparisonof fixed collector area design with the existing design dem-onstrates that there is a 21% saving in the operating cost.

Storage temperature profile with the global optimumsystem design is shown in Fig. 11. Milk pasteurization loadoccurs between 10 a.m. and 2 p.m. In the morning hours,up to 10 a.m. there is insolation but no demand. This raisesthe storage temperature to 120 �C. Withdrawal of heat dur-ing demand decreases the storage temperature to a mini-mum of 103 �C at 2 p.m. Beyond 2 p.m. storagetemperature steadily lifts up till sunshine is available upto 5 p.m.

From Fig. 10, it may be noted that the TAC curve doesnot change significantly near the global optimum. Due touncertainties associated with system parameters, solar inso-lation, cost data, etc. a globally optimum value may notnecessarily provide a meaningful result in actual practice.

00 2 4 6 8

20406080

100120140160180200

10 12 14 16 18 20 22 24Time,h

Tem

pera

ture

, °C

Maximum storage temperature constraint ,200°C Storage temperature profile

Minimum storage temperature ,90 ºC

Fig. 11. Storage temperature profile with optimum system size,Ac = 148 m2, Vst = 7 m3.

Similar observations were reported by Shenoy et al.(1998) in designing and optimizing heat exchanger net-works. A 2% margin is allowed for the minimum totalannualized cost. The lower and the upper limits of solarfractions corresponding to a 2% increase in the minimumtotal annualized cost are shown in Fig. 10. The limits ofsolar fractions are observed to be 0.71 and 0.98 respec-tively. The corresponding costs and system parametersare shown in Table 9. At the lower limit of solar fraction(F = 0.71), the system configuration requires 26% lowercapital investment as compared to the upper limit. Amountof auxiliary energy needed is nearly 12 times higher. On theother hand, the upper limit of solar fraction (F = 0.98)implies a system configuration with higher capital invest-ment and lower operating cost. Based on the available cashflow for investment, an appropriate system configurationmay be chosen for the process heat application.

The design procedure is illustrated using a single dayanalysis. The system can be designed more precisely byincorporating the annual radiation data in a dedicatedoptimizer tool. It may be noted that the nine-month aver-age beam normal radiation data are used for the singleday analysis. The results obtained using a single day anal-ysis matches with the system data obtained from the field(Kulkarni, 2008). The methodology has been successful inapplication to a specific configuration of industrial processheating. However, the same can be effectively applied in thedesign and optimization of a variety of configurations.

5. Conclusions

Optimum component sizing is important in design andintegration of solar systems with industrial process applica-tions. In this paper, a methodology is proposed to designand optimize concentrating solar collector based systemswith pressurized hot water storage. The proposed method-ology is based on the concept of design space. The conceptof design space was introduced by Kulkarni et al. (2007) todesign and optimize flat plate solar collector based system.However, the proposed methodology is restricted as thestorage water temperature is less than 100 �C. For mediumtemperature industrial application, water needs to be pres-surized to avoid boiling inside the receiver and storage

698

tank. In this paper, the original concept of design space isextended to include pressurized hot water storage. It maybe noted that the proposed methodology has been appliedwith the assumption of a well mixed storage tank. In real-ity, there is thermal stratification for large storage tank.Relaxing the assumption of well mixed storage tank andaccounting for storage tank stratification will definitelyimprove the system performance and provide benefit in sys-tem sizing. Present research is directed towards incorporat-ing the effect of thermal stratification on the optimal sizingof the overall system.

Design space is the region bounded by constant solarfraction curves traced on the collector area vs. storage vol-ume diagram and it represents all possible feasible designconfigurations subject to different constraints. Constraintssuch as existing collector area, limitations on availablefloor spacing, existing storage volume, or maximum allow-able storage volume due to structural restriction, etc. caneasily be incorporated in the proposed methodology. Theproposed design space approach may be useful in retrofitcases as well.

The problem of design and optimization of a real systemis usually a multi-objective task. To capture the effects ofdifferent objective function, the Pareto optimal regionshould be identified. The Pareto optimal region signifiesthe portion of the design space where the optimal solutionlies. Depending upon the objective function, an optimalsolution from the Pareto optimal region may be selectedfor sizing the system appropriately. In case of a flat platesolar collector-based system, the Pareto optimal regioncomprises of the region bounded by the loci of the mini-mum collector area requirement and the minimum storagevolume requirement. However, this region does not repre-sent a Pareto optimal region for concentrating collectorbased system. This is because additional variables such asheat exchanger size and the maximum storage temperaturealso influence the system sizing.

Application of the proposed methodology is illustratedthrough a case study of pasteurization of milk. The thermaldemand of the pasteurization process is 1.88 GJ over 4 h aday (45000 l of hot water at 90 �C) to pasteurize 30000 l ofmilk per day. It is observed that the global optimum con-figuration of the system corresponds to a solar fractionof 0.87. When compared with the existing system, the glo-bal optimum design demonstrates a 23% saving in the totalannualized cost. Due to uncertainties associated with sys-tem parameters, solar insolation, cost data, etc. a globallyoptimum value may not necessarily provide a meaningfulresult in actual practice. A range of possible designs withnear-minimum total annualized cost is also identified.Based on the actual cash flow, a designer can appropriatelydesign the system.

The proposed design and optimization tool offers flexi-bility to the designer in choosing a system configurationon the basis of desired performance and economy. Thedesign tool makes an attempt, to contribute towards theglobal endeavor of enhanced and accelerated utilization

of solar energy in industrial processes. The study demon-strates the possibility of application of design space meth-odology to a variety of industrial process heatconfigurations in an effective way.

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