SUBSTITUTION OF ELECTRICAL DRYERS FOR NATURAL GAS DRYERS
Aditya Chintalapati, University of Michigan
Nicholas E Myers, University of Michigan
Abstract
In the U.S., there are numerous small and medium size manufacturing plants, where automated
drying processes are utilized. Electric heaters are often used to preheat the air flowing with high
velocities before it is blown onto a product in the drying process. One facility that uses such a
process is the MIWI washers manufacturing plant in Jackson, Michigan. Our team looked at
replacing the electric heaters with cheaper and potentially faster-heating natural gas burners. We
determined how to control temperature, flame stability, and air quality changes in the dryer air
stream due to the burning of natural gas. We also investigated the potential for cost savings,
improvement in the production speed, and possible contamination from the products of
combustion in the warm air stream due to the burning of natural gas.
Keywords: Industrial Drying, Natural Gas Heater, Efficiency, Manufacturing Process
Outline
1. Introduction
1. Overview of MIWI plant
2. Potential for cost savings
3. Plant Specifications
4. Technical Considerations
2. Fuel and Air Combustion
1. Stoichiometry
2. Flame Temperature
3. Mixing
4. Mass Flow Rates
3. Emissions
1. Soot
2. CO, NOX, and N2O
3. CO2 from energy use
4. Heat Transfer and Drying Process
1. Nozzle Jet velocity
2. Rate of transfer to plate and manufacturing process speed
3. Heat loss in pipe
5. Financial Analysis
6. Recommendations and Conclusions
1 1. Introduction
In the U.S., there are numerous small and medium size manufacturing plants, where automated
drying processes are utilized. Electric heaters are often used to preheat the air flowing with high
velocities before it is blown onto a product in the drying process. In an automated production
line, the speed at which a product can be manufactured is dependent on the speed at which the
slowest process can be accomplished and in this project we are focusing on the drying process
after a wash of the production items before a final surface treatment. This project builds off an
initial assessment performed by the Industrial Assessment Center [1]. The purpose of this project
was to investigate the potential for the MIWI facility in Jackson Michigan to switch their
electrical dryers into natural gas dryers for the systems they manufacture.
1.1 Overview of the MIWI manufactured drying equipment
The MIWI manufacturing plant is located in Jackson, MI. The plant designs and produces
systems for drying of plastic and metallic components after a wash. Besides producing the drying
systems for sale they also offer in house washing and drying services for external clients. In such
a system (Fig 1), the electric heater heats the air after it is propelled by a blower, which is
funneled into nozzles and is used to quickly dry the parts after the washing process is completed.
The use of electricity to heat air is expensive and slow but easier to control than natural gas
heaters.
Figure 1: Schematic of the the MIWI manufacturing plant’s dryer
1.2 Potential for cost savings
The primary cost saving for the plant will come from switching the power source from electricity
to burning of natural gas. Comparing the electricity used by the dryer with the energy equivalent
cost of natural gas, we were able to determine the following cost savings potential (Fig 2).
2 Tout = 150 C Tout = 120 C Tout = 90 C Tout = 70 C Tout = 50 C Figure 2: Potential for cost saving with respect to current flow rates and temperatures
At the current level of output temperature of 90 C and output volume of 11 m3/min, we could
potentially save up to $3,000 annually per dryer by switching to natural gas.
1.3 Plant Specifications
There were certain specifications that our system had to meet and specific conditions under
which the system had to operate. These specifications (Table 1) were obtained from the
Industrial Assessment Survey that was conducted prior to this project.
Table 1: Showing the current plant specifications and operating conditions
Parameters
Value
Ambient air temperature
TAMB [K]
Relative Humidity of air
RHAMB
Outpute air temperature
TOUT [K]
Mass of exiting air
mAIR [kg/s]
System Power
QEL [kW]
Curent Elecrical Costs
AELC [$/yr]
Outpute Relative Humidity
RHOUT
Current Carbon Emissions
CO2 [ton/yr]
298.15
70%
363.15
0.229
15
3,750
3.16%
64.5
1.4 Technical Considerations
In order to switch use of electricity to natural gas we must meet the previous listed specifications
plus a few other requirements must be addressed. A primary concern is that the emissions in the
natural gas product gas flow should not impact the parts that were being dried, that is we are
trying to use the diluted products from the combustion directly in the drying process. If that is
3 not possible then we must use a heat exchanger to heat air from the hot combustion products and
use that air for the drying. This would introduce one additional step in the process and lower the
overall efficiency of the heating process. There are also other concerns regarding the control of
combustion to ensure that the dryer could be adjusted for different drying settings and that the
temperature in the combustion chamber was at a safe level. We would also have to design a
system such that it can easily interface with the existing air channels and does not require
significant modification of the dryer itself in order to implement it.
2. Fuel and air combustion
The primary purpose of this project was to investigate the feasibility of switching from electrical
dryers to natural gas dryers and the challenges associated with it. In order to tackle these
challenges, we conducted several theoretical and analytical tests to determine the ideal
conditions to operate the system in along with addressing the concerns that the manufacturer
brought up.
The first thing that had to be done was to ensure that natural gas could be used as a viable fuel.
This required our team to ensure that the required mass of natural gas could be safely combusted
while minimizing flame temperatures and that a sufficient amount of secondary air could be
added to cool down the system to the required 90 C output while ensuring that it is fully mixed.
2.1 Fuel Stoichiometry
Natural Gas is made up of several hydrocarbons, however 95% of natural gas is Methane [2].
The combustion equation for natural gas is:
CH4 + 2(O2+3.76N2) → CO2 + 2H2O + 7.52N2
(Eq. 1)
From a stoichiometric analysis of fuel combustion as shown in Appendix A, it was determined
that in order to combust the required 1.08 kg of Natural Gas, we would need to add 18.57 kg of
primary air for stoichiometric combustion.
2.2 Flame Temperature
One of the concerns that was brought up to us by the plant was the temperature in the
combustion chamber itself. In the interest of safety, we had to ensure that the flame temperature
had to be as low as possible. One way to reduce the flame temperature is to ensure that the
combustion happens with excess air. Figure 3 [3] on page 5 shows the change in flame
temperature with respect to the Fuel-Air ratio.
4 Figure 3: Flame Temperature vs. Equivalence ratio for Natural Gas
An Equivalence ratio of 6.0 was determined to be ideal for this application [3]
As shown in Fig 3 above, the minimum fuel to air ratio that still allows for combustion is 0.55
However, in order to stay above this limit and avoid a flame out scenario, the team concluded
that a fuel to air ratio of 0.6 would be ideal. An equivalence ratio of 0.6 would reduce the flame
temperature from 2100K at stoichiometric combustion ratio to a safer 1600K. As discussed in
Section 3, this change also results in decreased emissions from the combustion of natural gas. To
change the equivalence ratio, more primary air would be needed to added required recalculation
of the primary and secondary air flows as shown below.
2.3 Mass Flow Rates
In order to ensure that the air was cooled to 90 C before being blown on to the parts, secondary
air would be mixed with the primary air to reduce the net combustion temperature. Enthalpy of
combustion values for Natural Gas and the products were used to determine the necessary
amount of secondary air required as seen in Appendix B.
The necessary mass flow rates are:
● Fuel Flow Rate = 1.08 kg/hour
● Primary Air Flow = 30.95 kg/hour
● Secondary Air flow = 823.54 kg/hour
2.4 Mixing
An important factor that had to be considered for this project was the mixing of the combustion
product jet and the secondary air in the main pipe. Full mixing is the most desirable situation
because having uniform temperature in the air blown onto the products would ensure that they
would be dried evenly and thoroughly. The problem with this is that the proposed model has
turbulent jet flow (see section 4.3 heat loss in pipes). Research in this area was completed by
Insu Lee recently here at the University of Michigan [4]. In their study, recirculation zones were
found on either side of the primary jet flow when its momentum increased in relation to the coflows (Fig. 4). As the relative momentum of the primary flow decreases, the size of the
5 recirculation zones decrease and they move farther away from the nozzles (very left of the
pictures).
Figure 4: Recirculation zones in confined flow. Larger Ctnl values indicate lower ratios of
primary jet flow to secondary co-flow [4] (These images are of half the width of the pipes)
For the proposed system, the relative momentum of the primary jet is not very high compared to
that of the secondary co-flow. From this, it can be assumed that recirculation zones would either
not appear, or would be very small and towards the end of the pipe. Because the concentration
only achieves a uniform profile after the center of the recirculation zone, it can be assumed that
not enough mixing to produce a uniform temperature gradient in a one meter pipe. This means
that some sort of mixing apparatus or solution must be implemented in the system.
3. EMISSIONS
One of the main concerns with switching from an electric heater to a natural gas burner is the
production of emissions in the combustion process. These pollutants have the possibility of
contaminating the products being dried, interfering with any coating or future treatment. Three
main forms of emissions from the combustion were taken into consideration in the creation of
the natural gas drying system: soot, CO, and NOx. CO2 emissions were considered as well but
only for the energy usage.
3.1 Soot
Soot is impure carbon particles that are a result of incomplete combustion. Primarily, soot is
produced in diffusion flames where oxygen must diffuse into the flame and mix with the
hydrocarbons. Because this mixing is limited by the rate of diffusion, typically not enough
oxygen is incorporated into the combustion and it is not fully accomplished, resulting in excess
impure carbon. In premixed flames, the oxidizer has been fully mixed with the fuel prior to
combustion. For the premixed flames, the only issue resides in whether or not enough oxygen
has been mixed with the fuel. In the combustion of hydrocarbons, the formation of soot should
theoretically only occur when the C/O ratio exceeds 1[5]. From the stoichiometry mentioned in
equation 1, a complete combustion of premixed flames occurs at an air/CH4 mole ratio of 9.52.
At any mixture above this ratio (more air), it can be assumed that minimal sooting will occur.
Furthermore, the leaner (higher air/fuel ratio) the pre-mixture is, the more of a chance that the
6 oxygen combines with the hydrocarbons to form a complete combustion. Conversely, fuel rich
mixtures will have less complete combustion (Fig. 5). With the proposed ɸ (air/fuel
ratio/stoichiometric air/fuel ratio) of 0.6, it is believed that there will be more than enough air
that sooting can be considered minimal.
Figure 5.: On the left a rich fuel mixture with no premixed oxygen produces a yellow sooty
diffusion flame, and on the right a full oxygen premixed flame produces no soot[6]
3.2 CO, N2O and NOX
Because sooting is not likely with the use of a lean premixed flame, the major concern for
combustion products is the CO that will be produced from the combustion. In an ideal
combustion, all of the carbon in methane will react perfectly with the oxygen from the air and
only the expected product of CO2 that balances the stoichiometric equation will be produced. In
reality, the combustion process is not completely efficient and some of the carbon will not
become fully oxidized. This deviation from theory results in the production of CO. The amount
of carbon monoxide produced is dependent on ɸ [2]. The more air is used, the more likely the
carbon from the methane has sufficient oxygen to from CO2 instead of CO. This effect is very
pronounced, as the amount of CO produced from the combustion can be reduced by almost two
orders of magnitude by using a ɸ of 0.6 instead of a ɸ of 1.0 (Fig. 6.). For ɸ = 0.6, the mole
fraction of CO is just under 1/1000. This fraction of combustion products is almost negligible.
Figure 6: Chemistry of Methane combustion as a function of distance through flame for multiple
values of ɸ [2]
7 Because the oxidizer in the premixed flame is air and not pure oxygen, the nitrogen present in air
must be accounted for. NOX is produced during combustion when nitrogen and oxygen are
present. In this case, because air has a larger amount of nitrogen than oxygen, N2O can also be
produced during the combustion. Unlike CO, this reaction will happen regardless of imperfect
combustion as long as there is air in the mixture. Imperfect combustion does still factor in though
because NO and N2O will be produced even when ɸ is greater than 1 (Fig. 7). A lean mixture is
still the optimal choice when considering NOX and N2O pollution (Fig. 7) Since the N2O only is
produced in small quantities (1 ppm for lean), the primary emission is NO, which is an order of
magnitude smaller for the ɸ = 0.6 mixture than it is for ɸ ≥ 1. For this lean mixture, the total
emission of NO and N2O are even smaller than that of CO and therefore can almost be ignored.
Figure 7.: NO and N2O fractions as a function of distance through flame for multiple values of ɸ
[2]
With the large amount of secondary air that will be added to the combustion products (including
soot), it can be assumed that the minimal amount of emissions that are produced will be so
diluted they will have little to no effect on any further processes the dried parts might go through.
3.3 CO2 from energy usage
Since CO2 is an expected product of methane combustion and remains fairly constant (on the
same order of magnitude) regardless of ɸ, the CO2 emissions were only considered as a part of
determining which fuel source is more environmentally friendly. One of our objectives was also
to reduce the net emissions from the system. It was determined form a life cycle analysis that the
emissions from the system could be reduced by up to 67%, as shown in Appendix C. Reducing
these emissions makes the plant more sustainable while reducing the environmental impact
significantly. This reduction strongly adds value to our proposition since the facility becomes
greener while becoming more profitable.
4 Heat Transfer and Drying Process
The parts will be dried by a combination of blowing the water off the parts as well as through
heat transfer to the part to evaporate the parts itself. Based on a benchmark for a similar drying
system, it was determined that nozzle velocity would need to be 30 m/s [7] with the part being
8 placed 6 cm from the nozzle. There were also analysis done to determine how many parts that
could be dried as well as well as the potential to lose heat through the system.
4.1 Nozzle Jet velocity
To ensure that the parts are dried adequately, high-velocity jets were researched to find the speed
at which a jet will shed a water droplet from a surface. This method adds a second dimension of
drying on tip of the hot air that is being blown onto the products regardless of air speed. This
values was not calculated but instead found to be 30 m/s [7]. After getting this value for the
speed at which the air should hit the product, it had to ensured that the velocity coming out of the
nozzles and the velocity hitting the pieces to be dried did not differ greatly. Equation 2 was used
to find the maximum velocity of a turbulent jet flow as a function of nozzle diameter and
distance from the nozzle [8]. While this does show that the velocity decays rapidly, due to the
small proposed distance from the nozzle to the parts, the velocity decay is not a major concern.
u = 5du0/x (u0 = initial velocity, d = nozzle diameter, x = distance from nozzle)
[Eq. 2]
A second aspect of the nozzle jet velocity that had to be considered was the centerline jet decay.
The effective area of drying had to be considered. It was discovered that the velocity decayed
exponentially as the radial distance from the centerline of the jet increased (Eq. 3). Though this
high level of velocity decay occurs, it was not considered to be a large issue due to the fact that
even if the jet does not shed water droplets that aren’t directly in line with the nozzle, the high
temperature will have sufficient drying in and of itself.
u(x, r) = u0exp(-50r2/x2) (r = radial distance from centerline)
[Eq. 3]
4.2 Rate of heat transfer to plate and speed of manufacturing process
For this analysis, it was assumed that heat would be transferred to the plate via two nozzles that
were to be placed at an interval of 0.25m and would blow hot air on to the conveyer at 30 m/s.
Using heat transfer equations [9] shown below,
[Eq. 4]
[Eq. 5]
We determined that heat could be transferred to a flat Aluminum sheet at a rate of 28.9 KJ/s as
show in Appendix D. If we assume that a flat piece of Aluminum with dimensions
1m*0.5m*0.001m has a mass of 1.35 Kg, it takes 2.5 seconds to heat the part to 90C. Assuming
it takes 10 seconds overall to dry each part, this translates to 900,000 such parts that can be dried
by the plant in the year. For parts of larger mass that have to be dried, the plant would need to
hold them for longer in front of the nozzles in order to transfer a greater amount of heat into
these parts.
9 4.3 HEAT LOSS IN PIPES
While the heat loss in the pipes leading from the combustion to the nozzle should theoretically be
the same in both electrical and natural gas systems, it is an important component that needed to
be calculated to be factored into the design of the system. To find the rate of heat transfer, Qu
between the pipe and the air, the local surface-convection resistance Rku had to be calculated[9].
The first step in finding this value was to determine the kind of flow that would happen inside
the system. Equation 6 was used to find the Reynolds number of the flow (where v is the mean
velocity of the fluid, Dh is the hydraulic diameter, and ν is the kinematic viscosity of air). This
value was calculated to be 56,735, which was much larger than the critical Reynolds number of
2,300. This means the proposed flow would be turbulent.
Re = uDh/ν
[Eq. 6]
After the kind of flow was determined, the normalized local surface-convection conductance (or
Nusselt number) Nu had to be calculated for a turbulent flow (Eq. 7).
!
< 𝑁𝑢 ≥ 0.027𝑅!!.! Pr !
(Pr air = 0.7)
[Eq. 7]
The Nusselt number was then used to calculate the number of transfer units NTU (Eq. 8)
!
𝑁𝑇𝑈 = 𝜋𝐿 < 𝑁𝑢 > !!
(𝑀 = mass flow rate, Cp = specific heat)
[Eq. 8]
!
This values was in turn used to calculate Ru (Eq. 9).
!
𝑅𝑢 = !! !!!"# !!"#
!
[Eq. 9]
With Ru, and the local temperatures of the surface and air flow, the heat transfer rate was
calculated to be -1018.82 J/s (assuming a 1m pipe) (Eq. 10).
!
!!!"#
𝑄! = !"#$%&'
[Eq. 10]
!"
The exit temperature of the air after the heat loss was also calculated to be 85.86 Celsius (with
original air temperature of 90 C) (Eq. 11).
𝑇!"#$ = 𝑇!"# − (1 − exp −𝑁𝑇𝑈 )(𝑇!"# − 𝑇!"#$%&' )
[Eq. 11]
This meant that the heat loss in the pipe only dropped the temperature a few degrees. This means
that heat loss in the pipes was not a serious issue as it would be very easy to raise the original
temperature of the air by a few degrees to offset this heat loss. This problem could be easily
fixed by slightly decreasing the amount of secondary air added to the combustion products or by
adding a layer of insulation to the pipe.
5 FINANCIAL ANALYSIS
While the reduction of carbon emissions in the drying process is a great part of switching from
electric to natural gas energy, an industrial drying plant would ultimately make its decision based
on financial motivations. If switching to natural gas could save money, it would be the easy
choice. The financial considerations for this kind of switch are ultimately two-fold. First, how
much can using natural gas instead of electricity save in energy costs, and second, how much
will the switch itself cost.
According to the energy information administration [10], current average industrial retail prices
in Michigan are $0.07 per kW-hr for electricity and $2.60 per MMBTU for natural gas. Working
under the assumption that the MIWI plant runs for 3120 hours per year, the cost for using a 15
kW electrical heater is $3,276 per year for a single machine. For a natural gas burner using our
mass flow rate of 1.08 kg/hr, the price of natural gas for a single burner would be $1,180 per
10 year. This means that for each natural gas burner the plant substitutes for an electrical one, they
would save $2,097 per year. Assuming the plant operates 5 dryers, this saves the plant $10,483
per year. This is easily enough money that switching to natural gas would be a good choice for
the MIWI plant.
Energy savings alone are not the whole story. There would be initial costs in purchasing the
natural gas burners to replace the electrical one. The proposed solution uses a Kromschroder BIC
50 industrial burner as a model (Fig 8) [11]. The BIC 50 burner costs $1,332 each. Average
maintenance and replacement parts for these burners cost ~$544 a year (as quoted from
Combustion 911 customer service representatives). This means that the first year costs for the
burners would be $1,876 each and subsequent year costs would be $544 each ($9,380 and $2,720
for the 5 dryer assumption). Assuming that maintenance is similar for the electrical heaters and
can be ignored, this is still $1,332 per burner, or $6,660 initial cost. While this seems like a large
number, with the saving from the energy cost, the time it would take to cover this would be less
than eight months. Provided the plant has the funds and would be operating for more than a year,
this would be an easy decision to make.
Figure 8: Kromschroder BIC 50 Burner used in the proposed solution [11]
RECOMMENDATIONS AND CONCLUSIONS
Natural Gas can be used to substitute for electrical drying and result in a cheaper, cleaner drying
process for the company. If the plant operates 5 dryers, they can save up to $10,500 per year by
switching. They can recover the initial cost of the dryers in savings in 8 months. The fuel flow
rate in the dryers can be controlled with a maximum flame temperature of 1600K. The emissions
from the burning of natural gas at an equivalence ratio of 0.6 would be very low and these would
be further diluted by the addition of secondary air. It would reduce equivalent CO2 emissions by
67%.
The BIC 50 burner [11] that we chose has adjustable controls that the plant can use to control the
flow of natural gas and primary air to change the temperature and magnitude of exiting air as
required. The dryer is less than 0.5 cubic meters in volume; hence it is reasonable to assume that
it could be used to replace the existing electrical heater without space being a constraint.
11 To have a uniform temperature for the output air, we would place a simple mixing apparatus or
fan somewhere in the main pipe. This would alleviate the problem of recirculation zones. This
would be a cheap and easy way to ensure total mixing.
A recommendation that would help reduce emissions from the combustion would be to
implement an exhaust gas recirculation system. This system would recirculate a portion of the
exhaust gas back into the combustion chamber. This would effectively raise the temperature of
the primary intake air and dilute its nitrogen. This would lower the NOX production of the
system, further reducing overall emissions concerns.
12 REFERENCES
[1] Substitution of Natural Gas for Electric Industrial Drying: A cost Saving Strategy. (2014).
Industrial Assessment Center, University of Michigan.
[2] Chemical Composition of Natural Gas-Union Gas. (n.d.). Retrieved April 24, 2015, from
https://www.uniongas.com/about-us/about-natural-gas/Chemical-Composition-of-NaturalGas
[3] Belcadi, A., Assou, M., Affad, E. H., Chatri, E. H. (2012), CH4/NOX Reduced Mechanisms
Used for Modeling Premixed Combustion. Energy and Power Engineering, 4, 264-273.
[4] Lee, I. A study of mixing in confined turbulent jets: Part I: Co-flowing streams. University
of Michigan at Ann Arbor.
[5] Haynes, B. S., & Wagner, H. G. (1981). Soot Formation. Progress in Energy and
Combustion Science, Volume 7 (Issue 4), pp. 229-273
[6] Premixed flame. (n.d.). Retrieved April 23, 2015, from
http://en.wikipedia.org/wiki/Premixed_flame
[7] Hot-Air Blow-Off Parts Drying. (n.d.). Retrieved April 24, 2015, from
http://www.stingraypartswasher.com/parts-washer-option-hot-air-blow-off-parts-dryer.html
[8] Cushman-Roisin, B. (2014). Turbulent Jets. In Environmental Fluid Mechanics (pp. 153159). New York, NY: John Wiley & Sons
[9] Kaviany, M. (2011). Convection: Bounded Fluid Streams. In Essentials of heat transfer
principles, materials, and applications. New York, NY: Cambridge University Press.
[10] U.S. Energy Information Administration - EIA - Independent Statistics and Analysis. (n.d.).
Retrieved April 23, 2015, from http://www.eia.gov/
[11] Industrial Burner for Gas BIC. (n.d.). Retrieved April 23, 2015, from
https://www.combustion911.com/products/industrial-burners/bic/
Appendix A: Fuel Stoichiometry
!
!!"#!$
𝑚 = !"#
= 15 kW / 50 010 kJ/kg fuel = 1.08 kg/hour
!"#$
𝑚(𝑎𝑖𝑟) =
!∗!.!"∗!".!" !".!" ∗ 1.08 = 18.57 kg/hour
We need at least 18.57 Kg air an hour in order to get stoichiometric combustion
Appendix B: Secondary Air
As shown in equation 1, each mole of fuel requires 2 moles of primary air for combustion. For
reducing the flame temperature to 90C, assume x times as much secondary air is added to the
total gas flow which consists of
CO2 + 2H2O + 7.52N2 + x(3.76N2 + O2) per mole of fuel combusted.
Heat generated from combustion of Methane:
Lower heating value = 50 010 kJ/kg fuel
13 Molar Mass * LHV = 16.043 kg/kmol fuel * 50 010 kJ/kg fuel
= 802 310 kJ/kmol fuel
This amount of energy gets transferred to the product gasses. Therefore the energy equation
states,
Energy = LHV*Molar Mass = 802 310 kJ/kmol fuel
= energy in the products
= ∆ℎ!"! + 2∆ℎ!!" + 7.52 ∆ℎ!! + 𝑥(∆ℎ!! + 3.76 ∆ℎ!! ) per kmol fuel
Assuming all the gas components are ideal gases, then at 90 C target we get :
∆ℎ!"! = 2429.4 kJ/kmol ;
∆ℎ!! = 1804.2 kJ/kmol ;
∆ℎ!!" = 2094.8 kJ/kmol
∆ℎ!" = 1837.8 kJ/kmol
Solving the energy equation for x gives:
x = 90.717
Since for every 2 moles of primary air, x moles of secondary air are required:
!
𝑚(𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦, 𝑎𝑖𝑟) = ! ∗ 𝑚(𝑝𝑟𝑖𝑚𝑎𝑟𝑦, 𝑎𝑖𝑟)
𝑚 𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦, 𝑎𝑖𝑟 = 842.1 Kg/hour
If we are operating at an equivalence ratio of 0.6, you would require 30.95 kg/hour of primary
air. Hence the net secondary air that is required would be 842.1 – 18.4 (additional air added in
primary combustion) Kg/hour which results in a net secondary air requirement of 823.5 Kg/hour.
Appendix C: Emissions Comparison
Net energy output of system (run for 1 hour) = 15 kW * 3600 = 54 MJ
Combustion Efficiency: 94%
Electrical Heater : ~100% [energy.gov] [1]
Distribution : 94% [eia.gov] [2]
Generation of electricity from Coal: 40% [highly efficient power plant, World Coal Association]
[3]
Net Energy needed = 54 MJ/(0.94*0.40) = 150 MJ
Energy from 1 kg of coal = 30MJ [Anthracite, maximum energy content, University of
Washington [4]
Mass of coal needed = 150/30 = 5kg
Emissions from 1kg of coal = 2.3 kg CO2/kg Coal [5]
Net Emissions from running the system for 1 hour: 11.5 kg CO2/hour
[1] http://energy.gov/energysaver/articles/electric-resistance-heating
[2] http://www.eia.gov/tools/faqs/faq.cfm?id=105&t=3
[3] http://www.eia.gov/tools/faqs/faq.cfm?id=107&t=3
[4] http://www.ocean.washington.edu/courses/envir215/energynumbers.pdf
[5] http://www.engineeringtoolbox.com/co2-emission-fuels-d_1085.html
14 Appendix D: Heat Transfer
Diameter of Nozzle = 2 * 10-3 m Length between nozzles = 0.25 m
E = 1 – 𝜋D2/(16L2)
E = 0.99
Reynold’s number is calculated in equation…
ReD = Re = uD/ν = 57,464 (Reynolds number)
𝜈 = 21.30 * 10-6 m2/s u = 30 m/s
Pr = 0.69
The Nusselt’s number is given by the equation below:
<Nu>L = 318557*0.986*0.031*0.81 = 7887
Where,
ϵ = 0.99
ReD = uDh/ν = 5.74 * 104
Ts = 300 K (Assumed)
Tf,∞ = 360 K
<Aku>L = 0.5 m2
Hence, we obtain the net heat transfer rate to the Aluminum part as:
<Qku>L = 0.5 * 7887*0.0306/0.25*(60) = 28,961 J/s
15