mjh140/ChE 0101 Final Report.docx · Web viewIn industry, fluidized bed reactors are implemented in many ways, from small laboratory-scale devices to large industrial units. Their

FLUIDIZED BED

Solomon Astley, Rebecca Uhlean, Michael Hensler,

Krishna Gnanavel, Celina Celmo, David Forcey

ChE 101, Thursday B-3

Due Date: December 10, 2015

1

Table of Contents

Nomenclature 3 Introduction and Background 4Experimental Methodology 7Results 10Analysis and Discussion of Results 13Summary and Conclusions 15References 16Appendices

A-1, Experimental Data 17A-2, Example Calculations 24A-3, Tabulated Calculations and Results 27

2

Nomenclature

Symbol Term Units

A Surface area of heater m2

Abed Area of the bed m2

Cp Specific heat of air kJ/kg∙°CF Air flow rate L/sΔP Pressure drop in Bed mmH2Omair Mass flow rate or air kg/sρair Density of air kg/m3

Qh Energy input to heater J/sQair Energy input to air stream J/sQloss Heat lost to the environment J/sT1 Temperature of heater surface °CT2A Temperature above alumina material °CT2T Temperature at top of alumina material °CT2M Temperature in middle of alumina material °CT2B Temperature at bottom of alumina material °CT2avg Average bed temperature °CT3 Temperature of inlet air °CUmf Minimum fluidization velocity m/sh Heat transfer coefficient J/m2∙°C∙sξ Efficiency of heat transfer Unitlessk Orifice Equation Constant L/s ∙mmH2O-1/2

V Voltage VoltsI Current Amps

3

1.0 Introduction and Background

Fluidized beds are widely used by chemical and petroleum engineers. A typical fluid bed

is a cylindrical column that contains solid particles and an upward flowing gas. Fluidization is

the process by which these particles are transformed into a fluid-like state. There are many

advantages to using a fluidized bed for industrial purposes. First, they allow for uniform particle

mixing. Since solid particles behave as a fluid, there is sufficient mixing unlike poor mixing that

occurs in a packed bed. Another advantage is they create a uniform temperature gradient. In

other words, heat does not have to be added or removed at any step in the process. Fluid bed

reactors establish an environment where reactants and products can be continuously added or

withdrawn. A continuous state process results in efficient product production and yield. The use

of fluidized beds in industrial processes also has several disadvantages, including the need for a

large reaction vessel and a large input of high velocity gas. Furthermore, it is difficult to

comprehend how fluidized beds behave in large, scaled-up processes [1].

In industry, fluidized bed reactors are implemented in many ways, from small laboratory-

scale devices to large industrial units. Their main purposes include separations, rapid mass or

heat transfer operations, and catalytic reactions. One of the very first applications was

industrialized in 1920 when Fritz Winkler used a fluid bed reactor for a coal gasification process.

Additionally, in 1942, the first circulating fluid bed was developed for fluid catalytic cracking,

converting heavy crude oil to gasoline. Another application, named the Sohio Process, produces

acrylonitrile by reacting propane, air, and ammonia over a catalyst in a fluid bed reactor [1].

Although these are just a few applications of fluid bed technology, its usefulness is evident in

chemical processing, and especially in petroleum industries.

It is important to examine the concepts relevant to this process in order to draw

conclusions from the technical objectives. As previously mentioned, fluidization is the process

by which solid particles are transformed into a fluid-like state via a high velocity gas stream in

the bed. Due to this high gas velocity stream, there is a pressure drop over the bed of solid

particles equal to the weight of the particles, putting them in a fluid-like state. When the air flow

is increased, the pressure drop in the bed also increases. The bed is fluidized when this change in

4

pressure remains constant even when the flow rate is increased. The pressure drop across the bed

is equal to the effective weight of the bed per unit area. The relationship is shown in Equation 1,

ΔP = mp(ρp-ρ)g/ρpA, (1)

where g is the acceleration of gravity, mp is the mass of the bed, ρp is the density of the particles,

and ρ is the density of the fluid (air). When fluidization begins, the velocity of the air is called

the minimum fluidization velocity, Umf [1]. At these conditions, the particles in the bed begin to

bubble and mix with the flowing air.

One of the objectives of the experiment is to determine the effect of the particle size on

Umf. This effect can be determined using the Ergun equation,

(ρs-ρ)g d2ε2 = 150μ(1- ε)Umf (2)

which describes the flow of liquid past a collection of particles [1]. In this equation, ρs is the

density of the solid, μ is the fluid viscosity, and ε is the bed voidage. As most of these values are

constants from scientific literature, it is clear that Umf increases as the particle size increases.

Another objective of the experiment is to study the heat transfer in a fluidized bed. When

the solid particles are mixing with the gas, there is very little variation in the temperature;

however, if a heater is placed in the bed during fluidization, a high rate of heat transfer is

observed. This heat transfer across the bed can be explained using a steady-state energy balance.

5

Figure 1. Energy Balance in a Fluid Bed Reactor [1]

Figure 1 shows the energy balance occurring in the fluid bed chamber. While the calculations are

performed later in the report, it is important to understand the concepts relevant to this process.

The energy input to the heater is calculated using the current and voltage being supplied to the

heater. During heat transfer, some heat is lost through natural convection from the glass. After

calculating the energy input to the air stream and the heat lost to the environment, the overall

heat transfer coefficient between the heater surface and the bed can be calculated [2]. Overall,

the heat transfer across the bed should be higher than the heat transfer through the glass wall of

the chamber.

Three principles that explain the transfer of heat between a heat transfer surface and a

fluidized bed. The first principle is the particle convective mechanism of heat transfer, which

applies to beds of particles with diameters less than about 500 μm and a density less than 400

kg/m3 [1]. The particles, which have a very high heat capacity, transfer heat in the bed through

circulation, generated by the rising bubbles. The second principle deals with heat transfer via

radiation. This mode occurs at high temperatures and when there is a noticeable temperature

difference between the bed and the transfer surface. The last principle, heat transfer by

convection through a gas, is the main mode for heat transfer in the performed experiment. The

high velocity gas stream carries energy, or heat, along with it in a circulating pattern. This is the

explanation as to why the heat transfer coefficients are greater for increasing particle size [1].

6

The fluidized bed project demonstrates these engineering related theories and concepts in

a real-life application. The first technical objective in the experiment was to observe particle

behavior under non-fluidized and fluidized conditions and estimate the minimum fluidization

velocity for both 60-grit and 120-grit alumina particle sizes. Upon completion of this task, it was

necessary to prepare a plot of the pressure drop across the bed versus superficial air velocity for

both grit sizes. This plot was used to identify trend lines and to calculate the minimum

fluidization velocity. The second technical objective was to study the heat transfer behavior and

perform a steady-state energy balance on the system for both grit sizes under both non-fluidized

and fluidized bed conditions. Subsequently, the overall heat transfer coefficient, h, between the

heater surface and the bed was estimated. In addition, the efficiency of energy transfer, ξ, from

the heater to the air stream under both non-fluidized and fluidized bed conditions was estimated

[2].

2.0 Experimental Methodology

2.1 Equipment and Apparatus

A: Fluid Bed Reactor

B: Distribution Chamber

C: Air Flow Meter

D: Heater

E: Thermocouple

F: Pressure Probe

G: Variac

H: Temperature Indicator

I: Bed Manometer

J: Orifice Manometer

7

Figure 2. Fluidized Bed Reactor [3]

Figure 2 is a photo of the equipment utilized during this experiment. The fluid bed reactor

(A) is where the particles are contained and where fluidization takes place. The distribution

chamber (B) is a base to the chamber that allows air to flow through the chamber but does not

allow particles to exit. The air flow meter (C) is used to measure air flow rates of up to 1.7 L/s.

The heater probe (D) provides heat to the system and can be lowered into or out of the bed of

particles. The thermocouple (E) and pressure probe (F) are adjustable probes that are used to

measure the temperature and pressure respectively at various locations in the fluid bed reactor.

The Variac (G) is used to adjust the power provided to the heater. The temperature indicator (H)

displays the temperatures of the heater, outside air, and thermocouple. The bed and orifice

manometers record the pressure drops across the bed of particles and orifice, respectively.

2.2 Experimental Procedures

Before the experiment began, 1.2 kg of the appropriately sized alumina particles (60-grit,

120-grit, and 46-grit on separate occasions) were added to the fluid bed reactor. The air flow rate

was set to 1.7 L/s for ~30-60 seconds in order to loosen the particles.

Technical Objective 1

To begin, the orifice equation constant, k, was calculated by measuring the pressure drop

across the orifice at three air flow rate values (1.4, 1.5, and 1.6 L/s) and substituting this data into

the orifice equation given by

F = k(∆P)½. (3)

Three values for k were calculated and averaged for a final value. Next, the air flow rate was

adjusted to 0.2 L/s using the rotameter, and the pressure drops across the bed and orifice were

recorded. The air flow rate was then increased incrementally by 0.2 L/s until it reached a value of

1.6 L/s. Each time, the pressure drops across the bed and orifice were recorded.

For air flow rates above 1.7 L/s, the pressure drop across the orifice corresponding to the

desired air flow rate was calculated using the derived constant k and the orifice equation. The

rotameter was adjusted to increase the air flow rate until the calculated pressure drop across the

orifice was equal to this calculated value. The pressure drop across the bed was then recorded.

8

This process was repeated until increased air flow rate no longer resulted in a change in the

pressure drop across the bed. Six more incremental increases in the air flow rate were then

performed and the pressure drop across the bed remained constant. This entire process was

performed for alumina particle sizes of 60-grit, 120-grit, and 46-grit.


For this technical objective, the heater was lowered ~2-3 cm into the bed of particles and

turned on by adjusting the Variac to the appropriate setting (24 for 60-grit alumina particles, 20

for 120-grit particles, and 26 for 46-grit). The associated voltage and current were recorded.

First, the air flow rate was adjusted to ~50% of the flow necessary for fluidization. This

system was allowed to run until steady-state was achieved. At this point, the temperatures of the

heater surface and the ambient air were recorded. The thermocouple was positioned above the

bed of particles (in the air space), at the top of the bed, in the middle of the bed, and at the

bottom of the bed. Each time its temperature was recorded.

This process was repeated with an air flow rate significantly greater than the minimum

flow rate required to achieve fluidization. The current, voltage, and various temperatures were

again recorded.

9

3.0 Results


10

Figure 3. Pressure Drop in Bed vs Air Flow, 60 Grit Alumina

Figure 5. Pressure drop in Bed vs Air Flow, 46 Grit Alumina

Particle Size Flow Rate (L/s) Umf (m/s)

60-grit 0.6 0.069

120-grit 0.4 0.046

11

Figure 4. Pressure Drop in Bed vs Air Flow, 120 Grit Alumina

46-grit 1.5 0.173

Table 1. Grit size, flow rate, and estimated Umf

Based on the graphs shown in Figures 3 and Figure 4, the pressure drop across the bed

increases with increasing air flow rate until a critical value (minimum fluidization velocity) has

been achieved. An estimate for these points is tabulated in Table 1. From these estimates, it also

appears that increasing particle grit corresponds to a smaller minimum fluidization velocity.


Flow Rate (L/s) T2A (˚C) T2T (˚C) T2M (˚C) T2B (˚C)

0.75* 33 39 45 27

1.7 38 38 38 38

2.2 37 37 37 37

Table 2. Temperatures of 60-grit bed at non-fluidized* and fluidized conditions


0.4* 29 30 29 29

0.8 32 32 33 33

1.2 33 33 33 33

Table 3. Temperatures of 120-grit at non-fluidized* and fluidized conditions

12


2.2* 32 33 34 32

3.0 31 31 31 31

3.2 31 31 31 31

Table 4. Temperatures of 46-grit at non-fluidized* and fluidized conditions

It is worth noting again that the heater in this system is located about halfway below the surface

of the bed. Table 2 shows that under non-fluidized conditions for the 60-grit alumina, the

temperature of the top, middle, and bottom of the bed are all different. On the other hand, when

the flow rate is increased so that the particles become fluidized, the temperature throughout the

bed is uniform. Both Table 3 and 4 show that using the 120-grit and 46-grit material,

respectively, allows for temperature uniformity even under non-fluidized conditions.

Figure. 6. Efficiency of Heat Transfer ξ vs. Air Flow Rate

13

Figure 6 shows that the heat transfer efficiency is maximized when a large grit size is subjected

to a high air flow rate. Note that the value of ξ corresponding to a flow rate of 2.2 L/s is not

possible; this value was obtained by finding the ratio of Qair to Qh, therefore a value over 1 should

not actually be possible.

14

4.0 Analysis and Discussion of Results

Several variables were highlighted during this experiment, the most important of which

are minimum fluidization air flow (F), the various temperature measurements, the heat transfer

coefficient (h), and the efficiency of heat transfer (ξ). Examination of these variables, as well as

how and why they were calculated, will lead to important conclusions.

The first step in this experiment requires a clear definition of the term “fluidization”. A

relatively constant pressure drop marks this state across the bed of particles, regardless of

increase in air flow. This relationship can be visualized graphically by Figures 3, 4, and 5 of the

results section. The point of interest lies exactly where the pressure drop begins to level off. This

point is called the minimum fluidization air flow (F in L/s). By analyzing the difference between

the two trials, it is clear that a higher grit size requires a lower F. The F values for 60-grit, 120-

grit, and 46-grit are 0.6 L/s, 0.4 L/s, and 1.5 L/s respectively. Consequently, a higher grit size

also corresponds to a lower minimum fluidization velocity. This makes sense because the

particles are more finely ground and therefore easier to move around.

After identifying the point of fluidization, the analysis focuses on the thermodynamic

data of the fluidized state versus the non-fluidized state. The variables examined here will be the

various temperatures measured at different depths of bed (air, top, middle, bottom), the heat

transfer coefficient (h), and the efficiency of heat transfer (ξ). It should be noted that the

temperatures were measured in different depths of the bed as a prerequisite for heat and energy

calculations.

Intuitively, under fluidized conditions, there is a uniform heat distribution throughout the

chamber. This is precisely what has been recorded in Tables 2, 3, and 4 of the results section.

These results illustrate that under fluidized conditions, 60-grit, 120-grit, and 46-grit particles

exhibit uniform heat distribution. The temperatures throughout the chamber measure around

38˚C, 32˚C, and 31˚C, for 60, 120, and 46-grit, respectively. Non-fluidized conditions do not

exhibit such properties, as represented by the difference in temperature measurements (Table 2)

across the non-fluidized flow rate.

The heat transfer coefficient is evaluated through a rearrangement of equation E-7 in

Appendix A-3. It is useful to compare the heat transfer coefficient values as the fluidized

conditions and grit size change in order to gain an understanding of how these two parameters

15

affect heat transfer between the fluid and the glass wall of the chamber. As such, the heat transfer

coefficient can be viewed as the ability to transfer heat from one material to another per unit area

for a specified time. A high h value is expected when using less dense materials since heat is able

to transfer more readily through such materials. This is exactly what is shown in Appendix A-3

when comparing fluidized values with non-fluidized values. In the case of the 60-grit, the h value

of the non-fluidized, dense bed was 175 J/m2∙°C∙s. This is a low value compared to its fluidized h

value of 283 J/m2∙°C∙s. Similarly, in the case of 120-grit, the difference is clearly apparent as the

non-fluidized and fluidized h values are 190 and 273 J/m2∙°C∙s, respectively. Furthermore, the h

value of the non-fluidized, dense bed of the 46-grit was 214 J/m2∙°C∙s, whereas the h value of the

46-grit under fluidized conditions was 249 J/m2∙°C∙s. Thus, for each of the 60, 120, and 46-grit

size materials, the data depicts the heat transfer coefficient of the fluidized condition to be larger

than that of the non-fluidized condition. As mentioned before, under fluidized conditions, heat is

more readily transferred from the heater to the bed, and the comparison of h values shown above

thus demonstrates this correlation.

After calculating the heat given by the heater and the heat absorbed by the air, the

efficiency of the system can be estimated by the ratio, Qair/Qh. The value of this ratio, ξ,

represents the percentage of heat from the heater that is transferred into the air and particles. The

general trend in this data is expected; under fluidized conditions this value should be high, and

under non-fluidized conditions this value should be low. In Appendix A-3, it is clear that the ξ

values under fluidized conditions supersede that of non-fluidized conditions: 27% and 96% for

60-grit, 15% and 68% for 120-grit size, and 74% and 85% for 46-grit. Appendix A-3 also shows

an anomaly in 60-grit: an efficiency over 100%. This observation is contrary to what is expected:

a higher grit size yields a more efficient heat transfer. An explanation may be rooted in how well

the orifice manometer can represent air flow through the system. Some errors in calibration may

lead to a Qair value higher than Qh, especially when using the high flow rates necessary to fluidize

low grit particles. This could possibly explain the value of ξ over 1, or 100%.

16

5.0 Summary and Conclusions

The purpose of the fluidized bed experiment was to study the effect of fluidization on

physical and thermodynamic properties such as temperature, pressure, and velocity of particles.

Additionally, a second trial was performed to examine the effect of a change in grit size on the

various data and conclusions. After fluidization was achieved, a constant k was calculated for

each grit size and used to relate pressure across the bed to the flow rate of air through the bed.

After the minimum fluidization velocity was found for each grit size, heat was added to

the system and analyzed under fluidized and non-fluidized conditions. This is the core of why the

experiment was performed. By effectively fluidizing the bed, the heat energy from the source, in

this case the heater, is more uniformly distributed throughout the chamber and to the particles.

Upon further analysis, it should be noted that more finely ground particles work well in favor of

this heat transfer.

Generally, in practical applications and industry, fluidized beds are used to create a

uniform distribution within a chamber. Sometimes, the materials may vary; for example, any

fluid can be used instead of air, such as water, or an unreactive ideal gas. Instead of heat transfer,

a chemical reaction may be occurring throughout a batch or semi-batch process chamber; or far

greater or smaller sized particles can be used in the bed. Regardless of how much the calculated

values vary, the core conclusion still holds true; that is, under fluidized conditions uniformity

exists throughout the chamber.

17

7.0 References

[1] M.J. Baird and S Shannon. Fluid Bed Laboratory Manual. University of Pittsburgh, Department of Chemical Engineering, Apr. 2013.

[2] Fluidized Bed - TO’s & Procedures

[3] “Air– Specific Heat at Constant Temperature and Various Pressures,” The Engineering Toolbox. [Online]. Available: http://www.engineeringtoolbox.com/air-specific-heat- various-pressures-d_1535.html. [Accessed Oct. 26, 2015].

[4] “Air Properties Definitions,” National Aeronautics and Space Administration. May 5, 2015. [Online]. Available: https://www.grc.nasa.gov/www/k-12/airplane/airprop.html. [Accessed Oct. 26, 2015].

18

Appendix A-1

Experimental Data


Table A-1.1. Determining Constant, k, Using 60 Grit Alumina

Air Flow Rate (L/s) x (mmH2O) Solving for k using F=k(ΔP0)1/2

1.4 19.4 0.318

1.5 22.0 0.320

1.6 23.9 0.327

Avg ΔP0 = 21.8 Avg k = 0.322

Table A-1.2. Collection of Data Using 60 Grit Alumina

Air Flow Rate (L/s) Pressure Drop Across Orifice (mmH2O)

Pressure Drop in Bed (mmH2O)

0.2 1.5 34.9

0.4 2.5 78.0

0.6 4.0 110.5

0.8 6.5 122.0

1.0 12.5 125.5

1.2 15.5 126.1

1.4 20.5 127.2

1.6 25.5 127.8

1.7 29.2 128.0

1.8 31.3 128.5

2.0 38.6 128.5

19

2.2 46.7 128.7

2.4 55.6 129.0

2.6 65.2 129.0

2.8 75.6 129.0

Figure A-1.1. Pressure Drop in Bed vs Air Flow, 60 Grit Alumina



1.4 20.3 0.311

1.5 22.8 0.314

1.6 25.8 0.315

Avg ΔP0 = 23.0 Avg k = 0.313

20

Table A-1.4: Collection of Data Using 120 Grit Alumina



0.2 0.8 92.0

0.4 1.8 124.5

0.6 2.8 126.0

0.8 6.3 127.5

1.0 9.3 127.5

1.2 14.0 127.5

1.4 18.6 127.5

1.6 24.8 127.5

1.8 31.9 127.5

2.0 39.6 127.5


21



1.4 19.5 0.297

1.5 22.0 0.318

1.6 25.2 0.340

Avg ΔP0 = 22.2 Avg k = 0.318

Table A-1.6: Collection of Data Using 46 Grit Alumina



0.2 3.0 14.0

0.4 3.0 26.0

0.6 4.0 40.0

0.8 7.0 54.0

1.0 10.0 69.0

1.2 14.0 85.0

1.4 20.0 100.0

1.6 26.0 116.0

1.8 32.1 120.0

2.0 39.6 124.0

2.2 47.9 126.0

2.4 57.0 128.0

2.6 66.8 129.0

2.8 77.5 130.0

3.0 88.9 131.0

22

3.2 101.3 132.0

3.4 114.3 133.0

3.6 128.2 133.0

3.8 142.8 133.0


Technical Objective #2

Collection of Data for Non-fluidized Conditions, 60-Grit Alumina

Air Flow Rate = 0.75 L/s

Pressure Drop in Bed = 125 mmH2O

Voltage = 46 volts

Current = 0.66 amps

T1= 144°C

T2A= 33°C, T2T= 39°C, T2M= 45°C, T2B= 27°C

T3= 24°C

Collection of Data for Fluidized Conditions, 60-Grit Alumina23

Air Flow Rate = 1.7 L/s Air Flow Rate = 2.2 L/s

Pressure Drop in Bed = 130 mmH2O Pressure Drop in Bed = 131 mmH2O

Voltage = 46 volts Voltage = 46 volts

Current = 0.66 amps Current = 0.66 amps

T1 = 111°C T1 = 104°C

T2A= 38°C, T2T= 38°C, T2M= 38°C, T2B= 38°C T2A= 37°C, T2T= 37°C, T2M= 37°C, T2B= 37°C

T3= 24°C T3= 24°C



Pressure Drop in Bed = 124.5 mmH2O

Voltage = 39 volts

Current = 0.56 amps

T1= 101°C

T2A= 29°C, T2T= 30°C, T2M= 31°C, T2B= 29°C

T3= 22°C

Collection of Data for Fluidized Conditions, 120-Grit Alumina


Pressure Drop in Bed = 127.5 mmH2O Pressure Drop in Bed = 127.5 mmH2O

Voltage = 39 volts Voltage = 39 volts


T1 = 88°C T1 = 83°C


T3= 23°C T3= 23°C


24


Pressure Drop in Bed = 127.0 mmH2O

Voltage = 50.1 volts

Current = 0.73 amps

T1= 148°C

T2A= 32°C, T2T= 33°C, T2M= 34°C, T2B= 32°C

T3= 22°C

Collection of Data for Fluidized Conditions, 46-Grit Alumina


Pressure Drop in Bed = 131 mmH2O Pressure Drop in Bed = 132 mmH2O

Voltage = 50.1 volts Voltage = 50.1 volts


T1 = 126°C T1 = 124°C


T3= 23°C T3= 23°C

25

Appendix A-2

Example Calculations

1. Determine constant, k

Equation E-1: F=k(∆P)½

Sample Calculation C-1:

F= 1.4 L/s

∆P= 19.4 mmH2O

k= 1.4 / (19.4)½

= 0.318

= 0.32 L/s ∙mmH2O-½

2. Determine Umf

Equation E-2: Umf = F/Abed


Abed= 86.6 cm2= 0.00866 m2

F = 1.4 L/s = 0.0014 m3/s

Umf= 0.0014 / 0.00866

= 0.16166

= 0.16 m/s

3. Determine energy input to heater, Qh

Equation E-3: Qh= V ∙I


V= 46 volts

I= 0.66 Amps

Qh= 46 ∙0.66

= 30.36

= 30. J/s

26

4. Find mass flow rate of air, mair

Equation E-4: ρair= mair/F


ρair= 1.229 kg/m3 [3]

F= 0.75 L/s = 0.00075 m3/s

mair= ρair∙F

= 1.229 ∙0.00075

= 0.000919

= 0.00092 kg/s

5. Determine energy input to air stream, Qair

Equation E-5: Qair= mair∙Cp ∙∆Tair


Cp= 1006 J/kg∙°C [4]

∆Tair = T2A– T3

= 33°C – 24°C = 9°C

mair = 0.000922 kg/s (from C-4)

Qair= 0.000922 ∙1006 ∙9

= 8.3477

=8.3 J/s

6. Determine heat lost to environment, Qloss

Equation E-6: Qloss= Qh–Qair


Qh= 30.36 J/s (from C-3)

Qair= 8.3477 J/s (from C-5)

Qloss= 30.36 – 8.3477

= 22.0123

27

= 22.01 J/s

7. Calculate overall heat transfer coefficient, h, between heater surface and bed

Equation E-7: Qh= h∙A∙(T1-T2avg)


Qh= 30.36 J/s (from C-3)

A= 0.0016 m2

T1–T2avg= 144°C – [(33°C+39°C+45°C+27°C)/4]

= 108°C

h = Qh/A∙(T1–T2avg)

= 30.36/0.0016∙108

= 175.694

= 180 J/m2∙°C∙s

8. Estimate the efficiency of heat transfer from heater to air

Equation E-8: ξ = Qair/Qh


Qair= 8.3477 J/s (from C-5)

Qh = 30.36 J/s (from C-3)

ξ = 8.3477/30.36

= 0.274957

= 27.50% efficiency

28

Appendix A-3

Tabulated Calculations and Results

Non-fluidized,

60-grit

Fluidized,

60-grit, A

Fluidized,

60-grit, B

Non-fluidized,

120-grit

Fluidized,

120-grit, A

Fluidized,

120-grit, B

Non-fluidized,

46-grit

Fluidized,

46-grit, A

Fluidized,

46-grit, B

F (L/s) 0.75 1.7 2.2 0.40 0.80 1.2 2.2 3.0 3.2

F (m3/s) 0.00075 0.0017 0.0022 0.0004 0.0008 0.0012 0.0022 0.0030 0.0032

∆P (mmH2O) 125.0 130.0 131.0 124.5 127.5 127.5 127 131 132

V (Volts) 46 46 46 39 39 39 50.1 50.1 5.1.

I (Amps) 0.66 0.66 0.66 0.56 0.56 0.56 0.73 0.73 0.73

Qh (J/s) 30 30 30 22 22 22 37 37 37

mair (kg/s) 0.00092 0.00209 0.00270 0.00049 0.00098 0.00147 0.00270 0.00369 0.00393

T2A (°C) 33 38 37 29 32 33 32 31 31

T3 (°C) 24 24 24 22 23 23 22 23 23

Qair (J/S) 8.3 29.4 35.4 3.5 8.9 14.8 27.2 29.7 31.6

T1 (°C) 144 111 104 101 88 83 141 126 124

T2T (°C) 39 38 37 30 32 33 33 31 31

T2M (°C) 45 38 37 29 33 33 34 31 31

T2B (°C) 27 38 37 29 33 33 32 31 31

T2avg (°C) 36 38 37 29.25 32.5 33 32.75 31 31

Qloss (J/s) 22.01 0.93 -5.00 18.38 12.94 7.00 9.8 7.3 5.4

h (J/m2°Cs) 175.69 259.93 283.21 190.24 245.95 273.00 213.63 243.42 248.66

ξ 0.27 0.97 1.16 0.16 0.41 0.68 0.74 0.80 0.85

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mjh140/ChE 0101 Final Report.docx · Web viewIn industry, fluidized bed reactors are implemented in many ways, from small laboratory-scale devices to large industrial units. Their