Heat Transfer To a Fluid in a CSTR University Of Illinois
Heat Transfer to a Fluid in a CSTR
Lab Prep Report
Unit Operations Lab 1
January 25, 2011
Group 3
Russel Cabral
Jay Gulotta
Scott Morgan
Brian Mottel
Mrunal Patel
Frank Perez
Sukhjinder Singh
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.
2. Literature Review/ Theory
In this experiment, three heat transfer cases can be considered;
1) Heat transfer condensing steam to the tank wall
2) Heat transfer across the internal fluid to the wall of the stirred tank
3) Heat transfer across the tank wall
In all three cases the heat transfer operation may be written as:
Q=UiA∆T Q=UA∆T (1)
where
Q – heat transferred [=] J / sec
Ui – overall heat transfer [=] Wm2K
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 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;
Figure (2). Temperature profile at S.S.
From equation (1), Q is then;
Q=hi A T2-T3=ho A T1- T2=Ui A (T1-T3) (2)
Q – heat transferred [=] J / sec
Ui – overall heat transfer [=] Wm2K
hi - the wall heat transfer coefficient at the inner surface [=] W m2K
ho - the wall heat transfer coefficient at the outer surface [=] W m2K
T1 - temperature of the hot fluid [=] K
T2 - temperature of the outer and inner wall [=] K
T3 - 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:
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 [=] Kelvin
T2 - temperature of vessel wall [=] Kelvin
T3 - bulk average temperature of the fluid inside the tank [=] Kelvin
T4 - cooling water (tap water) temperature [=] Kelvin
Ai 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 m2K
Uwall - overall heat transfer coefficient of the vessel wall [=] W m2K
Q13, Q34 - heat transferred [=] Jsec
At steady state, the heat transferred through the vessel follows from equation (2). Rearrangement of the equations to a form of Ta-Tb =Qh A
T1- T2=Q13ho Ao (3)
T2- T3=Q13hi Ai (4)
and t adding equations (3) and (4) produces
T1-T3= Q13ho Ao + hi Ai (5)
When Ao = Ai = A this equation becomes:
Q13 = 11hi+1ho A(T1-T3) (6)
By comparing with equation (1), the overall wall heat transfer coefficient Uwall is therefore defined as
Uwall = 11hi+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:
Qcoil=mcw CpTout- Tin (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 [=] Jkg 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.
Qhx = mhx Cp(Tt-Tr) (9)
where;
Qhx - heat transfer in the heat exchanger [=] Jsec
Cp - heat capacity of the cooling water [=] Jkg K
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 AT1-T3= mhx CpTt-Tr+mcw CpTout- Tin (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
A U T1- T3-0=mv Cp dT3dt (12)
Where
mv - mass if fluid in the vessel [=] kg
dT3dt - 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 [=] Jkg K
A - heat transfer area vessel wall [=] m2
U - overall heat transfer coefficient of the vessel wall [=] W m2K
T1 - temperature of the steam [=] Kelvin
T3 - bulk average temperature of the fluid in the vessel [=] Kelvin
To obtain theoretical values for this experiment one can use the following equations.
Experiment data for heating of an unbaffled vessel containing a Newtonian fluid have the following correlation, (BSL);
hiDTk=0.36 DI2 n ρμ23Cp μk13 (13)
Where
hi – convection heat transfer coefficient at the inner surface of the tank [=] W m2K
DT – tank diameter [=] meters
μ - viscosity of the fluid [=] kgm-sec
DI - impeller diameter [=] meters
Cp - specific heat of the fluid [=] Jkg K
k - thermal conductivity of the fluid [=] Wm K
ρ - density of the fluid [=] kgm3
n - speed of rotation of the impeller [=] revolutionsminute
Equation (13) can be simplified further into three dimensionless groups:
NuT = 0.36 Reimp23Pr13 (14)
where
hi DTk=NuT = tank Nusselt number [=] dimensionless
DI2 n ρμ= Reimp = impeller Reynols number [=] dimensionless
Cp μk = Pr = fluid Prandtl number [=] dimensionless
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 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
Figure (3.2) lower half of the apparatus
Figure(3.3) Side view of the apparatus
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
3.2 Materials and Supplies
Item / DescriptionStir 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