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Heat Transfer To a Fluid in a CSTR University Of Illinois

Heat Transfer to a Fluid in a CSTR

Lab Prep ReportUnit Operations Lab 1

January 25, 2011Group 3

Russel CabralJay Gulotta

Scott MorganBrian MottelMrunal PatelFrank Perez

Sukhjinder Singh

Unit Operations CHE-381 Group No. 3 Spring 2011 01/25/2011Cabral, Gulotta, Morgan, Mottel, Patel, Perez, Singh

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1. Introduction

Stirred tanks are used for many different processes in the chemical industry, which can

include mixing of solutions, leaching, and chemical reactions. An impeller will be used

to continuously stir the tank and perfect mixing can be assumed. Baffles are also in

place to enhance the mixing. This particular lab will allow one to study a range of heat

transfer processes. The focus will the measurement of the heat transfer coefficient

between the fluid and the inside vessel wall.

The values of the heat transfer coefficients are functions of the fluid flow field

and the molecular transport properties of the fluid [1]. Analyzing the parameters will

include the dependence of the heat transfer coefficient on fluid properties, impeller

speed, and the use of the baffles. Once these values are obtained, they can be

compared to results from other labs or investigators. Theoretical analysis has shown

that the heat transfer coefficient between a fluid and a surface can be related in terms

of dimensionless groups. Convective flow can be used as an example, which only needs

Reynolds number, Prandtl number, and geometric factors to correlate heat transfer data

over a broad range of conditions.


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2. Literature Review/ Theory

In this experiment, three heat transfer cases can be considered;

1) Heat transfer condensing steam to the tank wall2) Heat transfer across the internal fluid to the wall of the stirred tank3) Heat transfer across the tank wall

In all three cases the heat transfer operation may be written as:

Q=U i A∆T Q=UA ∆T (1)

where

Q – heat transferred [=] J / sec Ui – overall heat transfer [=]

Wm2 K

A - area available for the flow of heat [=] m2

∆T - difference in temperature [=] K

From equation (1) it can be seen that the relationship between Q and ∆T is linear and U

is constant, (Wikipedia). However in practice, U is not a constant and is influenced by

both the temperature difference and the absolute value of the temperatures. Therefore,

determination of the overall heat transfer coefficient a requirement in any heat transfer

operation.

Thusly, U will depend on the mechanism by which heat is transferred, (Perrys,

section 8). This can be due to the properties of the material and the geometry of the fluid

paths. In case 1, heat from steam is transferred solely by convection. In case 2, heat is

transferred through the metal by conduction and in case 3; the liquid also transmits heat


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readily by conduction, although convection transfer is considerably greater than the

transfer by conduction.

The flow of heat by conduction in a solid is a result of the transfer of vibrational

energy from one molecule to another and in fluids it occurs as a result of the transfer of

kinetic energy. Heat transfer by convection arises from the mixing of elements of fluid. It

is important to note that convection requires mixing of fluid elements and is not governed

by temperature alone is in the case of conduction.

Consider the simplest case where a solid wall is separating two fluids at two

different temperatures.

Figure (1). Direction of heat flow as a function of time.

At steady state Q, the heat transferred, is the same for any point in the dQ’s direction or

there will be a heat accumulation will result which implies steady state has not been

reached. Therefore dQ is zero and the heat capacity on the solid wall is assumed to be

constant.

A temperature profile at steady state for the above situation is shown below;


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Figure (2). Temperature profile at S.S.

From equation (1), Q is then;

Q=hi A (T ❑2−T 3 )=ho A (T 1−T 2 )=U i A (T 1−T 3)(2)

Q – heat transferred [=] J / sec Ui – overall heat transfer [=]

Wm2 K

hi - the wall heat transfer coefficient at the inner surface [=] W

m2 K

ho - the wall heat transfer coefficient at the outer surface [=] W

m2 KT1 - temperature of the hot fluid [=] KT2 - temperature of the outer and inner wall [=] KT3 - temperature of the cold fluid [=] K

When the solid wall is covered with scale the equation above will change to take

into account scaling of the wall. In this experiment, the apparatus is assumed to be free

of scale.

For this experiment, calculations for the overall heat transfer coefficients will be

based on the scenario shown below:


Ui

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Figure (3). Cstr Heat transfer arrangement

Assumptions are as follows;

1) No scale 2) Negligible resistance to heat transfer by the solid wall. 3) The wall thickness is small compare to the tank diameter. 4) The fluid inside the vessel is well mixed and thus at a uniform temperature. 5) There is no heat loss from the system to the surrounding.

here

T1 - steam temperature in the jacket [=] KelvinT2 - temperature of vessel wall [=] KelvinT3 - bulk average temperature of the fluid inside the tank [=] KelvinT4 - cooling water (tap water) temperature [=] KelvinAi and Ao - heat transfer area of inner and outer vessel wall respectively [=] m2

h o,wall ,h i,wall , h o,coil - heat transferred coefficients [=] W

m2 K

Uwall - overall heat transfer coefficient of the vessel wall [=] W

m2 K

Q13, Q34 - heat transferred [=] J

sec

At steady state, the heat transferred through the vessel follows from equation (2).

Rearrangement of the equations to a form of T a−T b=Qh A

(T 1−T 2 )=Q13

ho Ao(3)


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(T 2−T 3 )=Q13

hi A i(4)

and t adding equations (3) and (4) produces

(T 1−T 3 )=Q13

{ho Ao+hi A i }(5)

When Ao = Ai = A this equation becomes:

Q13=1

1hi

+ 1ho

A(T 1−T 3) (6)

By comparing with equation (1), the overall wall heat transfer coefficient Uwall is

therefore defined as

Uwall=1

1hi

+ 1ho

(7)

Uwall depends on the material of the vessel and is also listed in many literature sources,

(Perry, section8).

The reasons why the above equations, (3) through (7), are only concerned with

the heat transferred, Q, across the vessel wall is because Q is the same everywhere in the

x direction and heat transfer by conduction has less input variables. Heat transfer by

conduction only depends on the temperature, which is much easier to model than the heat

transfer taking place in the vessel.

To measure the heat transferred to the vessel from the steam, Q13, can be

determined from an energy balance around the agitated vessel. Here the heat in is Q13

while the heat out is Qcoil, Qhx, and Qsurrounding.

The Qcoil , heat transferred to the cooling coil, can be calculated by the following:


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Qcoil=mcw C p (T out−T ¿ )(8)

where

Qcoil - heat transferred to the cooling coil [=] J / sec

mcw - mass flow rate of the cooling water [=] kgsec

Cp - heat capacity of the cooling water [=] J

kg K Tout - outlet temperature of the cooling water [=] Kelvin Tin - inlet temperature of the cooling water [=] Kelvin

A countercurrent heat exchanger is used to cool the re-circulating fluid inside the vessel.

The heat exchanger can be modeled as follow:

Figure (4). Counter-current Heat Exchanger

The apparatus does not measure T3 and T4; however an energy balance can be obtained

by the equation (9) below.

Qh x=mhxC p(T t−T r) (9)

where;

Qhx - heat transfer in the heat exchanger [=] J

sec

Cp - heat capacity of the cooling water [=] J

kg K


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mhx - mass flow rate of the recycle water [=] kgsec

Tt - water temperature inside the vessel [=] Kelvin Tr - recycle water temperature leaving the heat exchanger [=] Kelvin

An overall energy balance around the vessel is defined as:

Q13=Q=Qhx+Qcoil+Qsurrounding(10)

Setting Qsurrounding to zero and substituting equations (8) and (9) into equation (10) to give:

Uwall A (T 1−T3 )=mhx Cp (T t−T r )+mcw C p (T out−T¿ )(11)

For an unsteady case where the recirculation pump and the cooling coil are not used, the

accumulation of heat causes the temperature of the fluid in the vessel to increase.

Heat in – Heat out = Accumulation of heat in the fluid or

AU (T 1−T3 )−0=mvC p

d T3

dt (12)

Where

mv - mass if fluid in the vessel [=] kgdT 3

dt - the change of the bulk average temperature of the fluid in the vessel with

respect to time [=] Kelvinsec

Cp - heat capacity of the fluid in the vessel [=]J

kg KA - heat transfer area vessel wall [=] m2

U - overall heat transfer coefficient of the vessel wall [=]W

m2 KT1 - temperature of the steam [=] KelvinT3 - bulk average temperature of the fluid in the vessel [=] Kelvin

To obtain theoretical values for this experiment one can use the following equations.


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Experiment data for heating of an unbaffled vessel containing a Newtonian fluid have the

following correlation, (BSL);

hi DT

k=0.36( D I

2 n ρμ )

23 (Cp μ

k )13 (13)

Where

hi – convection heat transfer coefficient at the inner surface of the tank [=] W

m2 KDT – tank diameter [=] meters

μ - viscosity of the fluid [=] kg

m−secDI - impeller diameter [=] meters

Cp - specific heat of the fluid [=] J

kg K

k - thermal conductivity of the fluid [=] WmK

ρ - density of the fluid [=] kgm3

n - speed of rotation of the impeller [=] revolutions

minute

Equation (13) can be simplified further into three dimensionless groups:

N uT=0.36 (Re imp)23 ( Pr )

13 (14 )

where

hi DT

k=N uT = tank Nusselt number [=] dimensionless

DI2n ρμ

=ℜimp = impeller Reynols number [=] dimensionless

Cp μk

= Pr = fluid Prandtl number [=] dimensionless


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In equations (13) and (14), the only unknown variable is hi, wall ; therefore it can

easily be solved. Take caution to verify that each dimensionless group is in fact

dimensionless. Each dimensionless group can be calculated in different measuring

systems (SI or English unit).

The goal of this experiment is to determine the experiment value of hi, wall (UIC)

and compare it with the theoretical value from equations (13) and (14).

3. Experimental

3.1.1 Apparatus

The apparatus used while conducting the “Heat Transfer in a Stirred Tank”

lab procedure consists of constantly stirred tank, which is equipped with a cooling

coil, and lined with a steam jacket. Once the tank is filled with water, a pump

located underneath the tank continuously pumps water out of the tank and through

the shell side of a heat exchanger where heat is removed via cooling water. The

cooled tank water then flows through a rotameter to determine the flow rate and re-

enters the tank. Dial thermometers are located at the inlet and outlet of the heat

exchanger. The cooling coils within the tank are fed cold tap water. The flow rate of

the cooling water is set using a rotameter. The temperature of the cooling water is

displayed on dial thermometers located near the inlet and outlet of the cooling coils.

Steam is fed into the steam jacket of the tank to allow heat transfer into the system.

Steam condensate exits the steam jacket and enters a condenser, which has cooling

water flowing through it. The impeller, which stirs the water in the tank, is


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controlled using a variable power supply. A strabotec is used to measure and

display the speed of the impeller.

Figure (3.1) Upper front of the apparatus


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Figure (3.2) lower half of the apparatus


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Figure(3.3) Side view of the apparatus


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Description of labeled aspects of the apparatus:

LabelNumber

Description Use

1 Strabotec Display rotational speed (RPM) of motor which drives impeller

2 Electric Motor Powers the impeller

3 Variable Power Supply Controls the speed of the electric motor

4 Cooling Coil Inlet Rotameter Displays the flowrate of the cooling coil water

5 Cooling Water Inlet Valve Controls the flowrate of the cooling coil water

6 Recycle Water Rotameter Displays the flowrate of the recycle water

7 Recycle Water Thermometer Displays the temperature of the recycle water

8 Cooling Water Inlet Thermometer

Displays the temperature of the cooling coil water at the inlet

9 Tank Thermometer Displays the temperature of the fluid in the tank

10 Tank Contains the fluids, as well as the impeller and steam jacket

11 Tank Outlet Thermometer Displays the temperature of the condensate exiting the steam jacket before it enters the condenser

12 Condenser Cools the steam condensate

13 Pump Continually re-circulates water through the tank

14 Condenser Thermometer Displays the temperature of the cooling water entering the condenser

15 Recycle thermometer Displays the temperature of the water that exited the tank before it enters the heat exchanger

16 Heat Exchanger Cools the recycled water before it re-enters the tank

17 Pump Power Switch Turns on the pump


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3.2 Materials and Supplies

Item Description

Stir Tank with Impeller Holds water as well as mixes.

Water Main component at which measurements will be taken from

Condenser Condenses steam.

Heat Exchanger Transfers heat from water.

Graduated Cylinder Used to measure amount of water from the condenser.

Thermometer Measures temperature.

Pump Forces water through apparatus.

Baffles Creates inconsistency in stir tank.

Mop Used to clean up any spillage.

Stop Watch Time the amount of fluid dispelled from condenser.

3.3 Experimental Procedure

Experiment I. Steady State Procedure Using No Baffles

1. Fill the tank (10) with water to a level about two inches from the top of the tank

by opening the yellow water inlet valve (3rd from left). Measure how far down the

water is in the tank to find the volume of the tank. All yellow valves on the back

wall should always open except for the 3rd from the left. That one is only used to

fill the tank and then closed.


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2. Open recycle valve and heat exchanger water valve, which are located right next

to the respective piece of equipment.

3. Turn on the pump (13) by flipping the pump switch (17).

4. Adjust the recycle flowrate to a chosen rate displayed on the recycle rotameter

(6).

5. Open the cooling water valve (5) and adjust the flowrate to a chosen rate

displayed on the cooling water rotameter (4).

6. Open heat exchanger water valve to allow the flow of cooling water.

7. Open condenser water valve to allow cooling water to run through steam

condenser.

8. Open steam inlet valve located behind the tank and not how many turns used

while opening the valve.

9. Turn on the agitator (2) by flipping the mixer switch (3).

10. Adjust the black dial (3) to set the impeller speed to a low rpm value (between

125 and 150 rpm).

11. Record the impeller speed once the system is at steady state.

12. Obtain steady state by adjusting the water heat exchanger and cooling coil

flowrates such that the tank temperature is maintained at 65°C.

13. Allow system to reach steady state by letting system stay for 10-15 minutes.

14. Record steady state temperature readings of all 7 thermometers and flowrates of

cooling water and recycle.


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15. Obtain mass flowrate of steam by measuring the amount of condensate collected

from the steam condenser, located at the bottom of the front of the system, over a

certain time interval.

16. Repeat steps 11-15 for measurements at two additional higher impeller speeds.

17. Repeat steps 11-15 for measurements for two different heat exchanger flowrates

so that two different vessel temperatures are obtained, using the second impeller

speed settings.

18. To safely shut down turn off the impeller, electric pump, and open the valve at the

bottom of the tank, to allow the tank to drain.

Experiment II. Steady State Procedure with Baffles

1. Repeat experiment I, but this time put baffles inside of the tank

2. There is no difference in the procedure between this part of the experiment and

experiment I.

Experiment II. Unsteady State Procedure Without Baffles in the Tank

1. Fill the tank (10) with cold water (< 40°C) to a level about two inches from the

top of the tank by opening the yellow water inlet valve. Measure with a ruler and

record how far down the water level is to obtain the volume of the tank and water

in the tank.

2. Make sure recycle and heat exchanger valves and the cooling water dial are

closed.

3. Turn on cooling water flow to the steam condenser.


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4. Turn on the agitator (2) by flipping the mixer switch (3).

5. Begin steam flow through insulated jacket by slightly opening the steam valve.

Only turn the steam valve a couple turns at most.

6. Carefully record the fluid temperature as a function of time by recording the

temperature from the tank temperature gauge at even time intervals. Record data

until a temperature of about 85°C is reached. The more data points that can be

recorded the more accurate the final data will be.

7. Obtain a second set of measurements.

8. Repeat the experiment using two additional impeller speeds.

9. To safely shut down apparatus, turn off mixer switch and turn impeller speed

knob (3) to zero. Close all valves. Drain tank (10) by opening drain valve to

allow all water to drain from vessel.

4. Anticipated Results

This experiment is divided into three sections; the first of the three sections consists

of three trials and is meant to find the heat transfer coefficient of the wall of the tank

between the steam and the water. The first trial will determine the heat transfer

coefficient of the wall and will have a fixed value. The second trial will determine the

heat transfer coefficient as a function of impeller speed. It is believed that from

equation 3 if the initial conditions are used to find the value for Q13, then equation 4

was then used with the new area since the impeller speed increases the amount of

water in contact with the wall of the tank. Also as equation 4 shows, with a constant

Q13 and the same change in temperature the value for the heat transfer coefficient


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should decrease. The third trial will determine the heat transfer coefficient as a

function of temperature. It is believed that as the change in temperature increases

then the heat transfer coefficient should decrease due to the inverse proportionality

between the two.

The second section of the lab repeats the process of the first with the addition of

baffles in the tank. The baffles will increase the surface area and if we assume the

change in temperature and the heat added are constant the heat transfer coefficient

should decrease going off of equations 3 and 4.

In the last section of the lab a steady state will be reached without the steam then

the steam valve will be opened and the change in temperature will be recorded as a

function of time. By doing so the heat added to the system will increase, thus

increasing the heat transfer coefficient due to the direct relationship between heat

and heat transfer coefficient.


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5. References

1. Bird, R. B., Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena. 2nd ed. New York, NY: Jonh Wiley & Sons, Inc., 2002

2. "Heat Transfer Coefficient." Wikipedia. 19 Jay. 2011

3. Perry, Robert H., and Don W. Green. Perry's Chemical Engineers' Handbook. New York: McGraw-Hill Professional, 2007.

4. University of Illinois at Chicago - UIC. Web. 13 Sept. 2010. <http://www.uic.edu/depts/chme/UnitOps/entry.html>.


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Appendix I: Job Safety Analysis (formerly called WP &C)

What is the purpose of this experiment?

The purpose of this experiment is to study the heat transfer in a constantly stirred

tank, by measuring the heat transfer coefficients associated with the system.

Experiments are carried out under varying conditions; for example steady state,

unsteady state, with and without baffles, different impeller speeds and steam flow

rates.

What are the hazards associated with the experiment?

A hazard associated with this experiment is overfilling the tank and causing it to

spill. Other hazards include accidently burning yourself with the pipe carrying the

incoming steam as well as pressurized components. In addition the impeller motor

is a moving part of machinery and is easily capable of injuring someone.

How will the experiment be conducted in a safe manner?

The tank will be filled with the lid off so that the water level can be easily monitored.

The pump will be turned on after the tank has reached the desired water level to

avoid spilling water. In addition the pump will not be run dry and the impeller will

only be ran at appropriate speeds and monitored via the digital output. Also


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because of moving parts hands will be kept away from the area where injury will

occur.

What safety controls are in place?

The tank drain valve is present and will be used if the water level is too high. In case

of a water spill napkins or a mop will be used, depending on the size of the puddle,

to clean up the spill.

Describe safe and unsafe ranges of operations.

The pump should never be run without having water in the tank. The impeller speed

should be kept at a safe range (100-400 rpm) but higher speeds should be avoided

(above 1000 rpm). In addition the steam flow rate should not go past 50% of the

maximum operating capacity.


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I have read relevant background material for the Unit Operations Laboratory

entitled: “ Heat transfer to a Fluid in a CSTR” and understand the hazards associated

with conducting this experiment. I have planned out my experimental work in

accordance to standards and acceptable safety practices and will conduct all of my

experimental work in a careful and safe manner. I will also be aware of my

surroundings, my group members, and other lab students, and will look out for their

safety as well.

Signatures: First & Last Name 1____electronic_signature___________

Jay Gulotta __ ________________________________________________

Mrunal Patel _ ______________________________________________

Brian Mottel________________________________________________

Frank Perez_________________________________________________

Sukhjinder Singh________________________________

Russell Cabral________________________________________________

Scott Morgan_________________________________________________


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