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Harvesting Electrical Power from Waste Heat Using
Stirling Engine
Shahed Md. Abu Sufian, Kawsar Ahmed Sagar,
Muhammad Ahsan Ullah
Department of Electrical & Electronic Engineering
Chittagong University of Engineering & Technology
Chittagong-4349, Bangladesh
[email protected], [email protected]
Abstract— Different processes that use energy and machines
that do work do not have perfect efficiency. So energy is wasted
from these processes in the form of heat. Power generating
stations, industrial processes, rice mills, brick fields and other
human activities are major sources of waste heat. Mud stoves
used in rural areas for cooking purpose produce above 85% of
waste heat. This wasted heat can be used to generate electrical
power using Stirling engine (SE). Stirling engine is a heat engine
that is operated at different temperature levels by cyclic
operation of compression and expansion of working gas. A DC
generator is coupled with the SE to generate electrical energy. In
this research amount of waste heat from significant sources has
been presented and theoretical analysis has been made to harvest
electrical power using a displacer type SE. Utilizing helium as
working fluid and a DC generator having 90% efficiency a SE
with displacer swept volume of 7.37 ×10-4 m3 can generate 80 watt
of electrical power at 115 rpm engine frequency. In this
mathematical approach the phase angle is 90o and the
temperature difference is about 150 0K. The setup discussed is
working as a personal power plant for each rural household.
Keywords—waste heat; Stirling
personal power plant; mud stove;

engine;

harvest

power;

I. INTRODUCTION
Energy that is not used for a system’s purpose is wasted as
heat and escapes the system. Energy of billion dollars is thrown
away every year as waste heat. Of the 100 quadrillion British
thermal units (BTUs) of energy that United States consumes
every year, 50-60% is lost as waste heat [1]. Energy intensive
industrial processes occur at steel mills, cement kilns, furnaces,
refineries and at other industries. All these sources produce
waste heat that is emitted by heated exhaust gas and waste
steam. This waste heat creates a temperature difference
between the heat source and the environment. Using a wellestablished technology power can be generated from this
temperature difference.
Stirling engine (SE) is a closed cycle regenerative heat
engine operating on cyclic compression and expansion of
permanently gaseous working fluid at different temperature
levels [2][3]. Working on Stirling cycle, it converts heat energy
to mechanical energy. In 1816, Robert Stirling and his brother
James first invented and patented this engine [4]. In 20th
century Philips used the engine as a low power portable

978-1-4799-6062-0/14/$31.00©2014 IEEE

Durjoy Baidya
Department of Petroleum & Mining Engineering
Chittagong University of Engineering & Technology
Chittagong-4349, Bangladesh
[email protected]

generator for his radio [5]. William Beale is another forerunner
SE researcher who invented the free piston SE. This engine had
few moving parts and no crank shaft. In 1978 a SE was
designed to power a submarine. In 1985 McDonnell Douglas
designed a large solar parabolic mirror setup having capability
to track the sun and focus its energy on a SE that is centrally
mounted. Now 850 MW power is generated using this setup
[4]. NASA has considered a nuclear decay heated SE for
missions to the outer solar system [6]. In 2006 Kongtragool
and Wongwises designed a twin power piston SE with
maximum shaft power of 11.8 W and maximum break thermal
efficiency of 0.494% [7].
This paper presents a displacer type SE suitable to install in
the mud stoves used in rural areas of Bangladesh. Mud stove is
a very low efficient cooking instrument which can only use
about 15% of energy it consumes. So, there is a considerable
amount of waste heat from which electrical power can be
harvested using SE. Working on a temperature difference of
150 0K the SE simulated in this paper can generate mechanical
power from waste heat with an efficiency of 3.56%.
Calculation and analysis presented in this paper show that
using a 90% efficient DC generator, 80 W of electrical power
is generated at 7.37 ×10-4 m3 of displacer swept volume and 90o
of phase angle.
This paper is arranged as follows. Section two presents an
analysis on remarkable waste heat sources from where
electrical power can be cultivated. Stirling cycle on which SE
works is discussed in section three. System specifications and
theoretically calculated results are presented in section four.
Prototype that can be installed on mud stove to generate 80 W
of electrical power is shown in section five. Section six depicts
other two prototypes those can be used to harvest electrical
power in kilo watt range.
II. WASTE HEAT SOURCES
Primary metal manufacturing processes deal with a great
amount of waste heat sources e.g. coke ovens, blast furnaces,
basic oxygen furnaces and electrical arc furnaces. Metal
foundries possess waste heat sources such as core baking,
pouring, shot-blasting, heat treating, ladle pre-heating, castings
cooling and quenching. Non-metallic mineral product (cement,
gypsum, alumina, soda ash, lime and kaolin clay)
manufacturing industries use Calcininig in rotary kilns which

are high temperature processes and make a great amount of
waste heat. Raw material melting furnaces, tempering furnaces
and annealing ovens are the source of waste heat in the glass
industry. Distillation (fractional), catalytic cracking, thermal
cracking and various sort of treatment processes make a bunch
of waste heat in petroleum refineries. Several major segments
of a chemical industry such as petrochemicals, industrial gases,
plastic materials, and synthetic organic fibers processing
release high temperature of exhaust gases which are large
sources of waste heat. There are also a large number of flared
energy sources in oil and gas production [8].

III. STIRLING CYCLE
Stirling engine converts waste heat to mechanical energy
working on Stirling cycle (SC). It comprises of four processes
that are described below using p-V and T-s diagram of ideal
SC. These diagrams are shown in Fig. 2 and Fig. 3
respectively.

A research work [9] investigated several industrial
processes to estimate waste recovery opportunities and found
that among 8400 Tera Btu / year of waste heat about 1500 Tera
Btu/ year is lost in the form of exhaust gases on the basis of a
reference enthalpy of 298 0K. Fig. 1 represents the graphical
view of the work potential and amount of waste heat losses
from various industrial stages.
Some common machines such as coke oven (gas), coke
oven (waste gas), blast furnace, stalk melter, iron cupola (with
recovery), conventional fuel boilers have efficiency of 76%,
37%, 19%, 24%, 38% and 30% respectively. So, these
machines are huge sources of waste heat and serve good
prospects to harvest electrical power [9].

Fig. 2. Ideal Stirling cycle p-V diagram [3]

Rice mills and brick fields are also very good sources of
waste heat. The thermal efficiency of the rise mills is very low
(15-30%) [10].The amount of heat wasted in brick fields is
about 50-60% [11].
In rural areas, mud stoves are widely used for cooking
purpose. The open fire mud stove has a very low efficiency of
15% [12]. The most efficient cooking system in the rural areas
is the Improved Cooking System (ICS) which is locally known
as ‘Bandhu Chula’, has an efficiency of 27% -29% [13]. Wood
chips, log wood, wood pellets are used as fuel in these stoves.
Log wood has net calorific value of 4.1 KWh/kg [14]. If it is
used as fuel in the improved cook stove, 10.48 MJ of heat
energy will be wasted by burning 1 kg of log wood.

Fig. 3. Ideal Stirling cycle T-s diagram [3]

A. Isothermal Compression
When the power piston travels inwards this stage occurs. In
this stage gas is compressed and volume is reduced which in
turns raises the pressure. The area between points 1 and 2
under the p-V diagram indicates the work done to compress the
gas, Wc. In this process heat is removed to the environment by
the cooled cylinder and the removed heat, Qc is the area
between points 1 and 2 under the T-s diagram.
B. Isochoric Heating
At this stage, the piston remains at its most inwards point
and the volume is kept constant. Heat is added to the gas and
its temperature is raised from cooling temperature, Tc to heated
temperature, Th. Gas pressure reaches maximum point, pmax.
The area between points 2 and 3 under the T-s diagram depicts
the heat added from the regenerator, Qr1.

Fig. 1. Work potential & waste heat losses from specific industrial processes
[9]

C. Isothermal Expansion
The expanding heated gas pushes the power piston
outwards and energy transferred to the piston is We which
equals the area between points 3 and 4 under the p-V diagram.
In this stage heat added from the heat source to the heated
cylinder is Qe and it represents the area between points 3 and 4
under T-s diagram. This stage also increases the overall volume
and lowers the pressure.

D. Isochoric Cooling
At this stage, the piston remains at its outer most point and
the volume is kept constant. Heat is absorbed from the gas and
its temperature is lessened from Th to Tc. Gas pressure gets
down to the minimum point pmin. Heat absorbed by the
regenerator is Qr2 and it equals Qr1.
IV. CALCULATION
Three types of Stirling engines are available. These are
alpha type, beta type and gamma or displacer type. In this
research purpose, displacer type SE is used as it has large heat
transfer area, works on low and medium temperature difference
and it is easy to be constructed. This paper evaluates the
following specifications shown in Table 1.
TABLE I.

Displacer

Working Gas

Helium

Displacer: Swept volume, VSE

7.370 × 10 m3

Displacer: Dead volume, VDE

4.127 × 10-4 m3

Power piston: Swept volume, VSC

2.830 × 10-3 m3

Power piston: Dead volume, VDC

1.459 × 10-3 m3

Expansion volume, VE

60.699 × 10-3 m3

Compression volume, VC
Heated temperature , TE

4.909 × 10-4 m3
463 0K

Cooled temperature , TC

313 0K

c= B/S = 0.3767

(10)

Indicated power,
W= {pmax× VSE × 3.1416 × c × (1-t) × sina ×{ (1 – c) /(1+c)}0.5
/ { 1+ (1– 0.160772)0.5}= 88.89 W
(11)
The frequency of the rotor is calculated from Beale formula
[16],
W= B ×n × pmean ×f ×V
Here, mean pressure,
pmean= pmax / {(1+c)/ (1– c)} 0.5 = 676.9037×103 Pa (13)
Rotor frequency,
(14)

Q=m× s× ΔT = 0.0032x5188x150 = 2490.24 J (15)
-4

Here, m= mass of helium, kg
s= specific heat of helium, JKg-1K-1
ΔT= Temperature difference, 0K
So, the mechanical efficiency of the concerned Stirling engine
is = 88.89x100/2490.24 = 3.56 %
To convert this mechanical power into electrical power a
DC generator with 90% efficiency is used. Flywheel of the
Stirling engine is coupled with the rotor of DC generator using
conveyor belt. The electrical power output then will be
88.89x0.9= 80 W.

0

Phase angle , dx

90

Mole Number of Helium , n

0.8

Gas constant, R

8.314 J mol-1K-1

Cooling method

Water cooling

Using above parameters, from Schmidt formula [15]
mechanical power output of the displacer type Stirling engine
is calculated.
Total momental volume,
V= VE + VC= 3.0595× 10-3 m3

(1)

Maximum pressure, pmax is calculated using the equation,
p× V= n× R× T

(2)
6

pmax= n× R× T/ V=1.006×10 Pa

V. IMPLEMENTATION
From practical data it is found that temperature inside the
mud stove is about 463 0K. Using water cooling system,
temperature of the top plate is maintained at 313 0K. According
to the theoretical calculation presented in this paper using this
150 0K temperature difference 80 W of electrical power can be
harvested from the waste heat of mud stoves. So, Stirling
engine is working as a personal power plant for each house it’s
implemented and people can use this electricity for household
purposes. Fig. 4 depicts a SolidWorks designed prototype that
can be implemented on mud stove.

The temperature ratio t, swept volume ratio v, expansion
and compression dead volume ratios, XDE and XDC respectively
and other constants are found using the following equations.
t= TC / TE = 0.67602

(3)

v = VSC / VSE =3.84

(4)

XDE = VDE / VSE = 0.56

(5)

XDC = VDC / VSE = 1.9793

(6)

-1

(12)

Heat input to the Stirling engine can be calculated from the
equation,

Specifications

Engine Type

(9)

f= W/ (B × n × pmean ×V) = 115 rpm

DESIGN SPECIFICATIONS OF STIRLING ENGINE

Design Parameters

B= (t2 + 2 (t-1) v× cosdx+ v2 – 2t +1)0.5 = 3.85

a= tan (v× sindx)/ (t+cosdx+1) = 66.4204

(7)

S= t + 2t×XDE + 4t× VR/ (1+t) + v + 2×XDC + 1 = 10.23 (8)
Fig. 4. Prototype to implement on mud stove

VI. FUTURE DEVELOPMENT
In this research, specific design of every components of the
displacer type Stirling engine (SE) is under progress. With
these designs a feasible and portable SE will be manufactured
that can be set up on the mud stoves to harvest electrical power.
Increasing the output power is also under consideration. Fig. 5
shows a prototype prepared in SolidWorks that can be
implemented on mud stoves to generate 200 W of electrical
power. Another drafted prototype shown in Fig. 6 can produce
2.5 kW of electrical power using it on brick fields and rice
mills.

temperature difference between the mud stove and outside
environment, so the people of rural areas don’t need any other
gasoline fuel for power generation. Again there is no internal
combustion in this engine. So, SE produces no harmful gas that
can pollute environment. The working fluid used is an inert
gas. Hence, there is minimal risk of explosion. Considering the
advantages and power producing capability from waste heat,
efficient implementation of SE can ensure green energy
production and fulfill the ambition of delivering power to all.
ACKNOWLEDGMENT
The authors would like to convey gratitude to Dr.
Mohammad Mosharraf Hossain, Associate Professor, Institute
of Forestry and Environmental Science, University of
Chittagong, Bangladesh for his continuous support supplying
study materials.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]

Fig. 5. Prototype to implement on mud stove to generate 200 W power

[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]

Fig. 6. Prototype to implement on brick field and rice mill

VII. CONCLUSION
In this work, comprehensive research has been made on
potential waste heat sources. Using suitable method, energy
can be harvested from this waste heat. In this paper a prototype
has been simulated that can produce 80 W of electrical power.
So the energy wasted before in now meeting the electricity
demand of rural household. Stirling engine (SE) works on

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