Energy- and exergy-based thermal analyses of a solar bakery unit

Iqra Ayub1 • Anjum Munir1 • Waseem Amjad1 • Abdul Ghafoor2 • Muhammad Salman Nasir3

Received: 27 March 2017 / Accepted: 4 March 2018� Akademiai Kiado, Budapest, Hungary 2018

AbstractThe use of solar concentrating technique for cooking purpose has beenwidely reported rather than for the baking processwhich

is rigidly precise and requires process controlled conditions. Secondly, the energy and exergy analyses are rarely made for the

baking process. In this paper, an energy- and exergy-based thermal analysis of an innovative solar bakery unit powered by

Scheffler reflector has been presented. The system comprised of primary reflector (Scheffler reflector), secondary reflector,

receiver and baking chamber. The baking experiments were conducted using four product samples (cakes) at 180 �C. Theentire bakery unit was divided into two main parts, i.e. fan–receiver and baking chamber to find out the inefficiencies of

bakery unit and its components. It was found that fan–receiver component handled major portion of solar energy and showed

energy losses. It possessed high improvement potential (IP) rate (0.153 kW), high exergetic factor (f) value (59.26%) and

low exergy efficiency (15%). Thermal analysis of baking process in the baking chamber showed variations in rate of

energy utilization, energy utilization ratio, exergy losses and exergy efficiency in range of 0.01–0.07 kW, 25–75%, 0.19–1.08

kW and 6.62–56.46%, respectively. The overall exergy efficiency of system was found to be 59.26%. The study provides a

detailed and sequential procedure to perform the thermal analysis of a solar concentrated technology-based bakery unit.

Keywords Solar baking � Thermal analysis � Scheffler reflector � Exergy

List of symbolsW Rate of energy utilization/kJ s-1

Qnet Net available energy/kJ s-1

T Temperature/�Cgr Receiver efficiency/%

ma Air flow rate/kg s-1

x Specific humidity/g of water kg of dry air-1

h Enthalpy/kJ kg-1

/ Relative humidity/%

v Air velocity/m s-1

Cp Specific heat/kJ kg-1 k-1

Qd Heat given by receiver to air as output/kW

QR Heat received by zigzag receiver/kW

Ib Beam radiations/W m-2

Ap Aperture area of Scheffler reflector/m2

Ac Surface area of Scheffler reflector/m2

d Solar declination

EUR Energy utilization ratio/%

Ex Exergy/kJ kg-1

Exr Exergy rate/kJ s-1

gEX Exergetic efficiency/%

f Exergetic factor/%

IP Improvement potential/kJ s-1

Introduction

Adaptation of new ways for thermal applications of

renewable energy resources has become important. Cook-

ing is one of the main energy application processes, and its

share of energy consumption is more in developing coun-

tries [1]. There is need to develop environment-friendly

new cooking and heating technologies due to rising envi-

ronmental issues with the use of fossil fuels and distur-

bance of ecological balance due to forest cutting. Being

freely and abundantly available, solar energy is a better

substitute all around the world. Various types of solar

collectors such as parabolic dish collector, parabolic trough

& Anjum Munir

anjum.munir@uaf.edu.pk

1 Department of Energy Systems Engineering, University of

Agriculture Faisalabad, Faisalabad, Punjab, Pakistan

2 Department of Farm Machinery and Power, University of

Agriculture Faisalabad, Faisalabad, Punjab, Pakistan

3 Department of Structures and Environmental Engineering,

University of Agriculture Faisalabad, Faisalabad, Punjab,

Pakistan

123

Journal of Thermal Analysis and Calorimetryhttps://doi.org/10.1007/s10973-018-7165-3(0123456789().,-volV)(0123456789().,-volV)

collector and evacuated tube collector are designed and

used for cooking and heating purposes [2–6].

In case of baking, more heat is required than cooking to

complete the process effectively. The parabolic-type solar

concentrator is able to provide the required high operating

temperatures which are feasible for the process of baking,

but it requires two-dimensional solar tracking [7]. The

performance of a solar-based heating system depends on

the pattern of energy distribution. The design optimization

of a solar baking unit based on modelling of heat energy

distribution is always a challenging task due to complex

nature of baking process involving water evaporation, start

gelatinization, crust formation and browning reactions.

Therefore, a comprehensive thermal analysis of a system

becomes more important to perform. Presently, combina-

tion of energy and exergy analyses is getting importance

for the determination of systems performance in more

meaningful way [8]. In this regard, exergy analysis gives

more accurate information about the potential of a system

to extract heat from its surroundings [7]. Exergy-based

thermal analysis help to determine the factors for improv-

ing a thermal process and provides a much accurate

information about the effect of thermal process [9].

Various studies have been reported on the thermal

analysis of cooking processes, mainly focusing on energy

analysis. Nahar [10] developed a box-type solar cooker and

conducted its thermal performance using solar radiation

from the top surface and compared its performance with

simple solar oven and hot box solar cooker. The overall

efficiency of improved solar cooker was found to be 24.6%

[10]. In further study, he also performed energy analysis of

a solar cooker using different cover thicknesses of trans-

parent insulation material (TIM). The temperature obtained

was 158 �C using 40 mm TIM compare to 117 �C without

using TIM [11]. Algifri and Al-Towaie [12] reported

thermal analysis of a double glazed solar oven, taking

radiation from the top of its surface only. Maximum

improvement in efficiency was obtained by the addition of

a plane reflector and with proper orientation of cooker [12].

Nouni et al. [13] conducted energy analysis of three dif-

ferent box-type solar cookers to estimate energy output,

energy yield ratio, energy payback period and net energy

yield for possible their implications.

Energy and exergy analyses of solar cooker and baking

units based on vacuum tube collector have been presented

by many researchers. Sharma et al. [14] performed thermal

analysis of an evacuated tube collector-based solar cooker

using PCM as storage unit and obtained high temperature

of 130 �C, sufficient for 2-h cooking in the evening.

Singh et al. [15] investigated a solar cooker based on

parabolic trough collector using thermal oil. The amount of

heat stored was found to be increased by 19.45–30.38%

using PCM comparative to water [15]. Stumpf et al. [16]

integrated single- and double-stage heat pipe in flat plate

and vacuum tube collectors to meet cooking, baking, and

sterilization demand at small institutions. It was concluded

through thermal analysis that heat pipes are efficient means

of heat transport [16]. Kumar et al. [17] presented thermal

performance of evacuated tube collector-based solar pres-

sure cooker and developed a performance predictive model

under varying conditions. Harmim et al. [18] investigated a

box solar cooker with finned absorber and found it 7%

more efficient resulting in 12% decrease in time needed to

heat water comparative to conventional box-type solar

cooker. Richard [19] presented energy and exergy analyses

of a solar cooker, and distribution of energy, exergy and

respective efficiencies was calculated.

In order to get more heat energy for baking process,

solar concentrators are used in various forms and research

continues to make them more efficient. Thermal analyses

of solar cooker and baking systems based on concentrator

have also been reported by various researchers. Shukla

and Gupta [20] performed thermal analysis of a concen-

trating solar cooker and found an average efficiency,

optical losses, geometrical losses and thermal losses to be

14, 16, 30 and 35%, respectively. Panwar et al. [21] con-

ducted energy and exergy analysis of a parabolic solar

cooker, and variations in energy and exergy output were in

the range of 46.67–653.33 W and 7.37–46.46 W, respec-

tively. Pandey et al. [22] conducted an exergy analysis of

paraboloidal- and box-type solar cookers and found that

exergy efficiency of paraboloidal-type solar cooker was

higher than that of the box-type solar cooker. It was also

found that the exergy efficiency is directly proportional to

the volume of water increases [22]. Park et al. [23] pre-

sented an extensive review of energy and exergy analyses

of renewable energy systems like solar thermal, solar

photovoltaic and biomass cookstove. It was concluded that

energy analysis for the renewable energy systems has been

reported more than that of exergy analysis [23].

Zamani et al. [24] conducted a study on exergy analysis of

a double-exposure solar cooker using two similar solar

cookers with variable parabolic mirror position. After

experimentation, an innovative system with a variable

mirror on a parabolic curve was established, having aver-

age exergy efficiency of 30% [24]. Mbodji and Hajji [25]

presented a thermodynamic model of a parabolic solar

cooking system (PSCS) and conducted a comparison of the

model solution using two geometrical configurations

(dia. 9 depth 0.80 m 9 0.08 m and 1.40 m 9 0.16 m) of

a parabolic concentrator. Synthetic oil is used as a heat

storage fluid. The results showed that a 50 W m-2 increase

in the daily maximum solar radiation increases the storage

temperature by 4 �C and a 5% increase in the receiver

reflectance improves the maximum storage temperature by

3.6 and 3.9 �C, respectively [25]. Hassen et al. [26]

I. Ayub et al.

123

developed a baking system powered by solar energy using

thermal oil. Solar parabolic trough concentrator delivers

the heat to the oil which is then transferred to the baking

glass by convection and to baking pan (Injera stove) by

conduction lead to surface temperatures of 191 �C. A

system operated using thermal oil encounters with problem

of maintenances (leakages issues). Injera baking requires

high temperature, and it will become a more efficient stove

if it is attached with auto-trackers and heat storage mech-

anism [26]. Tesfay et al. [27] developed a new technology

of indirect solar stove for baking purpose comprising of a

parabolic dish having aperture area of 2.54 m2. It was

found that the heat losses at stagnation temperature of

system show that maximum loss of about 304.4 W be

encountered from receiver. The losses from stove and

pipeline were about 269.95 and 94.8 W, respectively. In

order to reduce these losses, system optimization is

required to improve the overall baking time for which

thermal analysis especially exergy aspect is important to

determine [27]. Sansaniwal et al. [28] presented the

research to summarize the previous findings on energy and

exergy analyses of different solar energy systems (solar

drying, solar air conditioning and refrigeration, solar water

heating, solar cooking and solar power generation through

solar photovoltaic and concentrated solar power techniques

used for various heat and power generation applications).

The main objective of that article was to bring out valuable

recommendations for wide exploitation of solar energy

systems for different applications, from a thermodynamics

perspective [28]. It has been noted that most of the studies

reported for the thermal analysis are about solar cooker and

mainly presenting only energy analysis as also reported by

Park et al. [23]. There is lack of such studies providing

exergy-based thermal analysis of a solar baking unit, and

no study has been found using fixed focused solar con-

centrator for baking purpose. Solar thermal applications for

cooking purposes have been reported by numerous

researchers but to get baking application through concen-

trating sun radiations has not been widely discussed.

Keeping in view the above-mentioned aspects, energy- and

exergy-based thermodynamic analysis of an innovative

solar bakery unit powered by Scheffler fixed focus con-

centrator has been performed. The available and utilized

solar energy was calculated using principles of energy

conservation. In order to calculate the efficiency of bakery

unit and its components separately, the entire system was

split into parts to conduct exergetic analysis. This study

provides an understanding of the significance of design

configurations on thermal efficiency and help to optimize

the thermal process for a baking unit based on Scheffler

reflector solar technology.

Materials and methods

Solar bakery unit

Figure 1 illustrates the designed solar bakery unit com-

prising of major parts, namely primary reflector, receiver,

secondary reflector, inner and outer chamber of the baking

unit. Solar radiations are concentrated using a primary

reflector (10 m2 Scheffler reflector). The edges of outer

chamber were joined prudently to assure that there is no

direct contact with the insulation material (rock wool),

which would affect the quality of the baking product. The

chamber was made of 0.8-mm-thick sheet of stainless steel

and comprised of an aligned zigzag receiver and pebbled

storage. This receiver was constructed from four pieces of

iron sheet having height and length of 330 and 2000 mm,

respectively, with a space of 30 mm between these two

sheets. The zigzag receiver was protected by a 3.8-mm-

thick tempered glass window, and it was cut into strips to

avoid the breaking of glass due to heat expansion. A DC

motor of 80 W (driven by a solar panel of 160 W) was

installed at the back side of the inner baking chamber

(60 9 60 9 60 cm3) to operate solar fan for the circulation

of air. The backside plate of the inner baking chamber was

made perforated (46%) for uniform airflow distribution

inside the baking chamber. A rectangular passage

(49.5 cm 9 8 cm) at the bottom of the baking chamber

served as an air outlet. Two perforated (17.4%) baking

trays were placed in the inner chamber to place the baking

products.

Concentrated solar radiations from the primary reflector

(Scheffler reflector) are intercepted by secondary reflector

that is further concentrated on the zigzag receiver of solar

bakery unit. The air gets warm while passing through the

receiver and a solar DC fan (80 W) provides draft for the

hot air movement from zigzag receiver to the baking

chamber. After exiting from the baking chamber, the air

partially transfers its remaining heat to the pebble bed

storage to store some thermal energy for 1–2 h of inde-

pendent baking. In case of fully loaded trays, as the process

continue, more vapour will be added to the air passing

through the baking chamber, and at one stage it could be

saturated, except if there is any by-pass for some fresh air.

Therefore, a narrow passage for fresh air is kept which can

be closed with a flap once the humidity does not rise.

A microcontroller (PIC18F252) was used to maintain

the inside temperature of baking chamber by controlling

fan power by employing a temperature sensor (PT-100) and

fan drive relay. Fan automatically turns off and on when

the desired temperature was achieved and below the set

value, respectively.

Energy- and exergy-based thermal analyses of a solar bakery unit

123

Baking experiments

Experiments were conducted to calculate the energy dis-

tribution at various points in the solar bakery unit. Before

to start, primary reflector was washed with water and left

for some time to dry the reflecting surfaces. After that

bakery unit was placed in front of primary reflector such

that the receiver faced the reflector. Pyranometer with

black pipe was installed at Scheffler reflector to record

beam radiation (Ib) in such a way that there would be no

shadow all around the pipe. K-type thermocouples linked

to a data logger were used to measure ambient air tem-

perature, air temperature at baking chamber inlet as well as

at outlet, temperature inside the baking chamber. In order

to measure the temperature distribution within the baking

chamber, the entire baking area was sectioned into three

zones vertically (each of 0.234 m wide and 0.64 m high).

From each section, four temperature measurements were

taken. The Kestrel 5000 Environmental meter (range

0.6–40 m s-1, resolution 0.1, accuracy ± 3%) was used to

measure the air velocity in the baking chamber before

putting the food samples. Its impeller was positioned per-

pendicular to the direction of flow of air coming inside the

chamber and was placed at various positions of inlet per-

forated plate inside the chamber to take an average value.

Four pans of cakes (each of 1 pound) were placed inside

the baking chamber. Ingredients for cake samples were

white flour, baking powder, sugar, eggs, vanilla essence,

butter and almonds. All these ingredients were mixed well

and then poured into an aluminium baking pan having the

size of six inches (diameter).

Thermal analysis of baking process

The receiver efficiency (ratio of energy output for the

baking unit to the total energy input at receiver) was

measured by using Eq. 1 [29].

gr ¼Qd

QR

ð1Þ

where gr is the receiver efficiency (%), Qd is the heat given

by receiver to air as output (kW) and Eq. 8 used for its

calculation, QR is the heat received by zigzag receiver

(kW) which was calculated using Eq. 2.

QR ¼ Ap:Ib

1000ð2Þ

where Ib is beam radiations (Wm-2) and Ap is the aperture

area of Scheffler Reflector (m2). The aperture area was

calculated using the following equation

Ap ¼ AcCos 43:23� d=2ð Þ ð3Þ

where Ac is the surface area of Scheffler reflector (m2) and

d is the solar declination.

For the baking chamber, a schematic for energy and

mass balance analysis is shown in Fig. 2. The air heating

and moisturizing take place in baking process. The prin-

ciples of conservation of mass and energy can be applied to

model and analyse these processes [29].

Beam radiation

910mm 760mm

Photovoltaic

Latitudeangel ofthe site

tracking systems

Temperaturecontroller

Bakingchamber

Pebbles

680mm

540mm

Fan

Pyranometer

Concentratedradiations

ReceiverStand

B

Secondary reflector

Primary reflector 10m2

Telescopic clampmechanism

(a) (b)

Solar concentrator

Solar bakery unitSolar panel

Fig. 1 Scheffler reflector technology-based solar bakery unit: a CAD of the system, b physically developed system

I. Ayub et al.

123

Conservation of mass for incoming heated air

Mass flow at inlet = Mass flow at outletX

mi ¼X

mo ð4Þ

Subscripts i and o stand for inlet and outlet, respectively.

Mass conservation for moisture from the productX

miw þ mewð Þ ¼X

mow ð5Þ

The warm air entering the baking chamber possesses

some amount of moisture (iw) and moisture added to the

air during the baking process (ew). At the exit, the moisture

present in the air is represented by ow.

The small vent is kept open at the early stages of baking

process to let the exhaust air to go out, and it is recirculated

later on once the amount of moisture added from the pro-

duct is very low. It will happen in case of fully loaded

baking chamber with food items. During recirculation

when air passed through a warm bed of pebbles its tem-

perature and enthalpy increased, while specific and relative

humidity decreased up to some extent.

To express the energy conservation, the following

equation can be used [30].

Qnet �W ¼X

mo ho þV2o

2

� ��X

mi hi þV2i

2

� �ð6Þ

Air conditions in the bakery unit

During the baking process, the drying air conditions change

continuously due to heat and mass transfer mechanism.

Figure 3 shows a schematic of the solar bakery unit for the

thermal analysis of the baking process. The processes of

heating and humidification were defined for the entire

thermal analysis.

Air conditions across the receiver

Starting from point 1, the air properties at the inlet and

outlet of the receiver can be written as

xri [xro; Tri\Tro; hri hro; /rih i /ro ð7Þ

where the receiver inlet and outlet are denoted by ri and ro,

respectively.

The energy obtained by air while passing across the heat

receiver is given as

Q1�2 ¼ mcp T2 � T1ð Þ ð8Þ

Air conditions at the entrance of baking compartment

The air coming out of receiver acts as inlet air for the

baking chamber. The temperature of air at outlet of recei-

ver and inlet of baking chamber remains same so the air

conditions at both points (point 2 and point 3) are equal and

can be written as

xbci ¼ xro; Tbci ¼ Tro; hbci ¼ hro; /bci ¼ /ro ð9Þ

where baking chamber inlet and receiver outlet are repre-

sented by bci and ro, respectively.

During experiments, the measured values of air tem-

perature at inlet and outlet of baking chamber and receiver,

respectively, were found same showing that there was no

energy loss from point 2 to point 3 (due to good insulation

of the unit). The available heat at the inlet of baking

chamber can be calculated as

Baking chamber

Inlet air conditions

mi

ω i

hi

φ i

mo ωo ho φo

Outlet air conditions

Fig. 2 Energy balance of the baking chamber

PV moduleInsulation

Fan

Heated air

Receiver

1

2

5

4

3

Flap

By pass

Concentratedbeams from primary reflectorPebble

bed

Baking chamber

Dcmotor

Fig. 3 Schematic of the solar bakery unit illustrating change in air

conditions during the baking process at different places of the system.

(1) Inlet air for the receiver, (2) warm air from zigzag receiver, (3)

warm air entering the baking chamber, (4) outflow air, (5) recycled air

after passing through pebble bed

Energy- and exergy-based thermal analyses of a solar bakery unit

123

Qheat available ¼ mcp T3 � T1ð Þ ð10Þ

Air conditions at the exit of baking chamber

At the outlet of the bakery (point 4), the air conditions

are associated with the rate of energy used in baking

chamber and can be described as

xbci\xbco; Tbci [ Tbco; hbci [ hbco; /bci\ /bco

ð11Þ

where bci and bco are used to show baking chamber inlet

and outlet, respectively. At outlet, specific and relative

humidity would be more than at inlet while inverse in case

of temperature and enthalpy.

The temperature and enthalpy of outlet air increased,

while specific and relative humidity decreased up to some

extend when passed through a bed of pebbles (warm

structure due to heat absorbed from receiver via radiations).

These are the air conditions used as inlet for the receiver.

Mass conservation

Heating process

As the air passed though the receiver, its energy increased

and relative humidity decreased. The air mass balance

across a unit volume of receiver can be described as

m1 ¼ m2 ð12Þ

Based on Eq. 8, the air conditions at point 3 (baking

chamber inlet) and point 2 (receiver outlet) are same so the

humidity will also be same as

x2 ¼ x3 ð13Þ

Baking process

During baking process, moisture is added to the drying air

while some negligible amount of moisture was already in

inlet air. So, air exiting the baking chamber will possess

water content as summation of both mentioned above and

can be written as

mbcoxbco ¼ mbcixbci þ mbcinsidexbcinside ð14Þ

The subscript ‘‘bcinside’’ stands for the respective air

condition inside the baking chamber.

The effect of addition of the small amount of moisture

(due to less number of sample products to be baked) to the

air at the beginning of baking process is considered neg-

ligible as it passed through a bed of pebbles (warm struc-

ture due to heat absorbed from receiver via radiations).

Energy balance

Heating process

The bakery component, receiver is responsible for

imparting energy into coming air. The energy balance

equation across the receiver can be written as

Q1�2 or Qnet avaialble ¼ m2h2 � m1h1 or mrohro � mrihri

ð15Þ

The amount of energy transferred to the air while

passing across the receiver can also be calculated as

Q1�2 ¼ mcp T2 � T1ð Þ ð16Þ

This is available heat energy as described before in Eq. 10.

Baking process

During baking process, it is hard to use the full baking

capability of air. So, the unused energy at outlet is normally

guided to recirculate and it is expressed as

Qwasted=recirculated m4h4ð Þ ¼ Qnet available � QEnergy utilized

ð17Þ

The energy at the outlet is stored in pebble bed to store

heat.

The amount of energy utilized in the baking chamber

can be written as

Q3�4 ¼ mcp T3 � T4ð Þ ð18Þ

Based on Eqs. 16 and 18, energy utilization ratio (EUR)

of the baking chamber is given as [31].

EUR ¼ heat utilized

heat supplied¼

CpiTi � CpoTo� �

CpiTi � CpaTa� � ð19Þ

Exergy analysis

In recent years, the exergy concept has been widely used in

thermal processes for system optimization. This analysis

provides a more realistic understanding between energy

losses to the environment and internal irreversibility in the

process. For exergy analysis, a general form equation was

used [32].

Exergy ¼ cpda T � Tað Þ � Ta lnT

Ta

� �ð20Þ

The subscript a stands for ambient condition.

I. Ayub et al.

123

Heating process

Exergy inflow and outflow can be determined by incor-

porating the respective values of temperatures in

Eq. 20. During the heating process exergy inflow at the

inlet of baking chamber can be written as

Exbci ¼ cpda Tbci � Tað Þ � Ta lnTbci

Ta

� �ð21Þ

Baking process

In the baking chamber, exergy losses take place. The

exergy outflow of baking chamber can be written as

Exbco ¼ cpda Tbco � Tað Þ � Ta lnTbco

Ta

� �ð22Þ

Then, exergy loss can be calculated from Eqs. 21 and 22

as

Exergy loss ¼ Exergy inflow � Exergy outflow ð23Þ

Using the calculated values of exergy loss and exergy

inflow, exergy efficiency can be calculated as below [32].

Exergetic efficiency gExð Þ ¼ 1� ExL

Exið24Þ

In order to perform exergy analysis of the solar bakery,

the system is categorized into two major parts, fan–receiver

combination (A) and baking chamber (B) as shown in

Fig. 4.

For each component of the bakery unit, exergy inflow

and outflow were calculated using Eq. 21 by using the

respective temperature values. To determine the compara-

tive inefficiencies of the components based on exergy

analysis, three parameters (exergy efficiency; improvement

potential rate, IP; exergetic factor, f) were selected to cal-

culate. More the value of IP for a component deduces the

possible improvement in that component to increase sys-

tem efficiency. Similarly, higher exergetic factor of a

component means higher amount of energy is used by that

component. The basic equations used for exergy analysis

are tabulated in Table 1.

Error analysis

During an experiment, errors and uncertainties are

inevitable in the measured values depending upon the

accuracy of the instrument used. The instrument selection,

calibration and way to handle the devises are main reasons

of errors. It therefore becomes mandatory to perform a

detailed uncertainty analysis for the experimental measured

and calculated values. Using the concept of the dimen-

sionless relative error in the individual factors denoted by

xn, the errors in the concerned parameters were calculated

as shown in Table 2 using the following equation [33].

U ¼ x1ð Þ2 þ x2ð Þ2 þ � � � þ xnð Þ2h i1=2

ð29Þ

Result and discussion

Air temperature at various sections of the baking chamber

was also measured (Sect. 2.2). Figure 5 shows experi-

mental measured temperature distribution pattern within

the baking chamber. A uniform temperature distribution

can be observed because of uniform air flow within the

baking chamber (Fig. 5). The average temperature in the

baking chamber was approximately 180 �C. This unifor-

mity facilitates a uniform baking process and ultimately

produces a product of uniform quality measures.

Energy

Figure 6 shows the rate of energy utilization with respect to

baking time during the baking process. It can be observed

that more energy was consumed at the early stages of the

baking process due to more mixture (loosely bounded

surface moisture) of cake ingredients. After certain period

of time, the rate of energy utilization decreased due to

crusty and hardened layer of baking samples, creating

resistance for the penetration of heat into the product. In a

baking process, product quality to be maintained is always

a challenging task, and it mainly depends upon temperature

inside the baking chamber. Beside the importance of

temperature selection for the baking process, its uniform

B: Baking chamber

A: Fan-receiver

2

3

4

1

Fig. 4 Schematic of the solar bakery components for the exergy

analysis

Energy- and exergy-based thermal analyses of a solar bakery unit

123

distribution significantly affects the rate of energy utiliza-

tion. Non-uniform heating inside the baking chamber

causes variation in colour and moisture contents which can

be reduced with better design and optimum operating

conditions. The warm air was introduced uniformly inside

the baking chamber employing a perforated plate which

resulted in uniform baking rate for all the baking samples

(04 cakes). The heat transferred from air to cake surface

and from surface to inside the cake occurred with con-

vection and conduction modes of heat transfer, respec-

tively. So, the fact of over- and under-baking was also

reduced, important to control the rate of energy utilization.

Similarly, the calculated results for energy utilization

ratio (EUR) are shown in Fig. 7. It can be clearly observed

that EUR is directly proportional to the rate of energy

consumed as shown in Fig. 7. During the entire baking

process, the EUR decreased from 78 to 24%. The EUR

depends upon the sample layer thickness, type of material,

area exposed to warm air and baking conditions. These

factors are important in controlling the internal and exter-

nal resistant to heat and mass transfer in the baking pro-

cess. Internal resistance depends upon the mass diffusion

process, while external resistance depends upon the surface

convective mass transfer. So rate of energy utilization will

also vary depending upon the nature (chemistry) of the

product to be baked.

Figure 8 shows the comparative view of the energy

efficiencies at various phases of energy flow in the systems.

Table 1 Mathematical relations

used for exergy analysisExergetic efficiency gEx ¼ EXr2�EXr1

PFan�Receiver� 100 (Fan–receiver) (25)

gEx ¼ EXr4

EXr3� 100 (Baking chamber) (26)

Improvement potential rate IP ¼ 1� gð Þ EXi � EXoð Þ (27)

Exergetic factor f ¼ EXi;k

EXi;t� 100 (28)

Table 2 Error of uncertainty for

the measured and calculated

parameters

Parameter measured/calculated Unit Value

Baking chamber inlet temperature �C ± 0.07

Baking chamber inside temperature �C ± 0.02

Baking chamber outlet temperature �C ± 0.08

Temperature before the receiver �C ± 0.08

Ambient temperature �C ± 0.15

Total uncertainty for energy at Scheffler reflector kJ s-1 ± 0.52%

Total uncertainty for energy at receiver kJ s-1 ± 1.49%

Total uncertainty for supplied energy kJ s-1 ± 1.92%

Total uncertainty for energy utilization kJ s-1 ± 2.03%

183

182

181

180 179.5179.87 179.75

179

178

177

176

175

1741 2 3

179 181

179

179.5

179

179.87

Section of baking chamber

Tem

pera

ture

/°C

180

178

180

181

179.75

181

180

178

179.5

Point 1

Point 2

Point 3

Point 4

Average

Fig. 5 Temperature distribution

at various sections of the baking

chamber

I. Ayub et al.

123

Based on data recording and calculation, it can be observed

that energy efficiency of receiver (ratio of the energy

available at receiver to the reflector, Eq. 1) increased from

37 to 65% due to increase in temperature at secondary

reflector (glass window of the receiver). As the focus of

Scheffler reflector is set to the secondary reflector, the

temperature of the receiver increased causing increase its

efficiency. After that heat transfer from receiver to air

depends upon the temperature difference of air and recei-

ver. The energy transfer efficiency (ratio of heat given to

air to heat available at receiver) increased for the first half

hour of baking time and then started to decline due to low

heat transfer rate to the already warm recirculated air. The

energy utilization ratio in the baking chamber was

observed higher at the early stages of baking process due to

more heat transfer to the products and decreased later on. It

can be seen that the difference between the receiver energy

transfer efficiency and energy utilization efficiency

increased after point 1 (marked at graph), which shows the

unused amount of heat available in the incoming air and

could be taken as loss of heat. This difference can be

reduced by putting more cake samples into the baking

chamber. Secondly the difference between the receiver

efficiency and receiver energy transfer efficiency increased

after point 2 (marked at graph). This difference can also be

considered as loss of heat.

Furthermore, heat losses across the walls of the baking

chamber (all sides excluding the air inlet perforated side)

were calculated using Fourier’s law of heat conduction.

Insides of the baking chamber were considered isothermal

to obtain a general relation for heat conduction

Q ¼ �kADTL

where k is the thermal conductivity of the material (for

stainless steel: 12–45 W m-1 K-1), DT is the temperature

difference, A is the cross-sectional area of a wall inside of

baking chamber (0.6 m 9 0.6 m), and L is the wall/side

thickness.

There are four walls/sides of the baking chamber (front,

left and right to the air inlet side and top of chamber). The

losses from the bottom side remain inside the system, i.e.

cause addition of heat to pebbles. The thermal conductivity

of a material, in general, varies with temperature. But

sufficiently accurate results can be obtained by using a

constant value for thermal conductivity at the average

temperature. Thickness of each side of wall comprises of

6 mm rockwool sandwiched into 0.8-mm stainless steel

sheets. Due to good insulation property of rockwool, the

calculated losses were found 10–13% of heat available

inside the baking chamber.

0.08

0.06

0.04

0.02

0.000 5 10 15

Baking time/min

Ene

rgy

utili

zatio

n/kW

20 25 30 35

Fig. 6 Rate of energy utilization during the baking process in the

baking chamber

0 5 10 15

Baking time/min

20 25 30 35

80

60

40

20

0

Ene

rgy

utili

zatio

n ra

tio

Fig. 7 Change in EUR with baking time

020

30

40

50

60

701

2

80

5 10

Reflector-receiver (receiver efficiency)Receiver-air (energy transfer efficiency)Heated air-sample products (EUR)

15

Baking time/min

Ene

rgy

effic

ienc

y/%

20 25 30 35 40

Fig. 8 Energy efficiencies at various phases of energy flow in the

systems

Energy- and exergy-based thermal analyses of a solar bakery unit

123

Exergy analysis

Baking chamber

Figure 9 shows the exergy loss (energy destruction) in the

baking chamber which decreased as baking time pro-

ceeded. The potential of a unit mass of warm air to perform

heat and mass transfer mechanisms decreased with baking

time. This can be understood keeping in view the same

reasons as explained for the energy utilization. Hence,

exergy loss is directly proportional to the energy utilization

and both are influenced by baking temperature, product

type and airflow rate. The higher and lower values of

exergy losses were found to be 1.1 and 0.01 kJ kg-1,

respectively.

As baking process proceeded to its completion phase,

the rate of exergy loss decreased which ultimately caused

the rise of exergetic efficiency based on Eq. 24 as shown in

Fig. 10. The calculated values of exergy inflow, outflow

and exergy loss were used to present the variation of the

exergetic efficiency (which is increased with baking time).

It could be explained with the fact that available energy in

the baking chamber increased with time due to less energy

utilization rate. It means that exergy loss would decrease,

while exergy inflow to the baking chamber will be

increased resulting in an increase in exergy efficiency.

Entire baking system

The outcomes of exergetic analysis for solar bakery unit

are tabulated in Table 3. Based on the performance

parameter (Table 1), the fan–receiver component of the

bakery unit was found to handle major part of the energy

than that of the baking chamber. It can be noted that this

component possessed higher values of exergetic factor and

improvement potential rate while lower value of exergetic

efficiency than that of the baking chamber. Therefore, there

should be some improvement in this component (fan–re-

ceiver) of the bakery unit. From the combination of fan–

receiver, the receiver’s lower efficiency caused loss of

energy. The receiver remained unable to harvest all the

incident energy from the primary reflector. The modifica-

tions in the receiver area and secondary reflector are need

to be done. During the baking experiments under the dif-

ferent baking temperatures, no significant change in the

values of improvement potential was found indicating the

goodness of insulation of bakery unit [34].

Table 4 presents some of the most relevant studies

about energy and exergy analyses of solar-based cookers

to make a comparative assessment of the results.

Although there are many parameters affecting the out-

comes of each system under consideration like design

configuration, products to be processed, capacity of the

unit, airflow rate, the current study showed quite satis-

factory outcomes based on the parameters listed in

Table 4. As the bakery is powered with Scheffler solar

reflector technology, it is better to compare its results with

that system operated through the same technology. In this

regard, Kumar et al. [36] reported a Scheffler community-

type cooker (8.21 m2) for heating of 20 kg water, and

maximum exergy obtained was reported of 0.055 kW. To

make a comparative statement, there is about 50% more

exergy (1.08 kW) obtained with the current study using a

Scheffler reflector of an area of 10 m2.

Experimental and predicted results

The energetic (energy utilization and EUR) and exergetic

(exergy loss and exergy efficiency) parameters based on

experimental data were modelled with respect to baking

time. All the parameters were found best fitted in

00.0

0.2

0.4

0.6

0.8

1.0

1.2

5 10 15

Baking time/min

Exe

rgy

loss

/kJ

kg–1

20 25 30 35 40

Fig. 9 Loss of exergy (energy destruction) during the baking process

00

10

20

30

40

50

60

5 10 15

Baking time/min

Exe

rget

ic e

ffici

ency

/%

20 25 30 35 40

Fig. 10 Exergetic efficiency of baking process

I. Ayub et al.

123

polynomial cubic models using sigma plot 12. The values

for all the constants of a basic polynomial Eq. 29 are

tabulated in Table 5.

y ¼ yo þ axþ bx2 þ cx3 ð30Þ

Figure 11 shows the comparative trend of energy

(Fig. 11a: energy utilization, Fig. 11b: energy utilization

ratio) and exergy (Fig. 11c: exergy loss, Fig. 11d: exergy

efficiency) parameters, and it can be observed that a good

agreement was found between model predicted and

experimental measured parameters. These developed rela-

tionships can be used for the optimal design of bakery unit

to make it more energy efficient.

Conclusions

Energy- and exergy-based thermodynamic analysis of an

innovative baking system powered by Scheffler fixed focus

solar concentrator was performed. The energy and exergy

efficiencies of solar bakery were calculated based on

energy distributions at its components. The receiver energy

efficiency increased with baking time (37–65%). Four

samples of cakes each of 1 pound consumed energy at the

rate of 0.01–0.07 kW with an energy efficiency of 25–75%

in the baking chamber. The rate of energy utilization and

exergy loss (energy destruction) decreased with baking

time. Based on the performance parameters in exergy

analysis, it was found that system component fan–receiver

dealt with major part of solar energy coming from primary

reflector as that component possessed high improvement

potential (IP) rate (0.153 kW), high exergetic factor

(f) value (59.26%) and low exergy efficiency (15%). The

receiver remained unable to harvest and transmit that

energy to air at full extent (Fig. 8). Therefore, energy

efficiency of system could be increased by improving

design configuration of that part. The overall exergy effi-

ciency of system was found to be 59.26%. As the baking

process discontinued, the exergy losses were minimized

while the exergy efficiency became higher at that point.

Table 3 Outcomes from exergetic analysis of bakery unit

Component Exergy

inflow/kJ s-1Exergy

outflow/kJ s-1Exergy

loss/kJ s-1Exergetic

efficiency/%

Improvement

potential/kJ s-1Exergetic

factor/%

Fan–receiver (A) 0.48 0.30 0.18 15.00 0.153 59.26

Baking chamber (B) 0.33 0.18 0.15 54.55 0.068 40.74

Overall system (A–B) 0.81 0.48 1.29 59.26 0.134 100.0

Table 4 Comparison of solar cookers with respect to energy and exergy analysis

Cooker type Energy

efficiency/%

Exergy

efficiency/%

Energy out of

system/utilized/kW

Exergy out/loss/

kW

References

Domestic size parabolic

solar cooker

46.82 32.97 0.046–0.653 0.00–0.046.46 Panwar et al. [21]

Box-type solar cookers 3.05–35.2 2.79–15.65 0.0082–0.061 0.0014–0.0061 Ozturk [35]

Parabolic-type solar cooker 0.58–3.52 0.4–1.25 0.021–0.73 0.0029–0.0066

Solar bakery unit 25–75 6.62–56.46 0.01–0.07 0.19–1.08 Present study

Forced convection solar air

heater (FCSAH)

0.09–0.75 0.08–0.31 Kumar et al. [6]

0.07–0.42 0.06–0.17

Table 5 Values for all the

constants of a basic polynomial

equation

Parameter yo a b c R2

Energy utilization/kJ s-1 0.078 - 0.0019 - 0.0001 2.776E-6 0.9945

Energy utilization ratio/EUR 81.96 - 0.952 - 0.0989 0.0023 0.9976

Exergy loss/kJ kg-1 1.593 - 0.1095 0.0021 - 7.270E-6 0.9983

Exergy efficiency/% 8.773 - 1.3272 0.2057 - 0.0037 0.9961

Energy- and exergy-based thermal analyses of a solar bakery unit

123

Overall, the system gave quite good results in terms of

baking process time, baking quality (good appearance) and

energy utilization rate, and this could be increased further

by optimization and controlling of baking conditions.

Consequently, it is suggested that receiver size, airflow

rate, number of food samples and moisture content should

be taken into consideration for the efficient use of energy to

minimize the energy losses.

Acknowledgements The authors wish to acknowledge the Depart-

ment of Energy Systems Engineering, University of Agriculture

Faisalabad, Pakistan, and International Centre for Development and

Decent Work (ICDD), Germany, for the financial support.

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