Using household items, the authors designed an experiment to cool a can of beer from room temperature to 3°C. They hypothesized that adding salt to an ice bath would lower the freezing point and cool the can faster than a pure ice bath. Experimental results supported this, as a can cooled over twice as fast in a 10% salt-ice bath compared to a pure ice bath. Theoretical modeling found higher convective heat transfer coefficients in salt baths explain the faster cooling. While adding more salt further lowered temperatures, diminishing returns were observed with increasing salt concentration.
The specific heat (C) is the quantity of heat required to raise the temperature of one gram of a substance by one degree Celsius or Kelvin. A calorimeter constant is a constant that measures the heat capacity of the calorimeter. It is calculated by applying a known amount of the heat and determining the resultant change in temperature in the calorimeter
The specific heat (C) is the quantity of heat required to raise the temperature of one gram of a substance by one degree Celsius or Kelvin. A calorimeter constant is a constant that measures the heat capacity of the calorimeter. It is calculated by applying a known amount of the heat and determining the resultant change in temperature in the calorimeter
Packed Bed Reactor for Catalytic Cracking of Plasma Pyrolyzed Gasijsrd.com
Packed bed reactors play vital role in chemical industries for obtaining valuable product, like steam reforming of natural gas, ammonia synthesis, sulphuric acid production, methanol synthesis, methanol oxidation, butadiene production, styrene production. It is not only used for production but also used in separation process like adsorption, distillation and stripping section. Packed bed reactors are work horse of the chemical and petroleum industries. Its low cost, and simplicity makes it first choice to any chemical processes. In our experimental work vacuum residue is used as a feed which is pyrolyzed in the primary chamber with the help of plasma into hydrogen and hydrocarbon gases which is feed stream to the Ni catalyst containing packed bed reactor called catalytic cracker. Ni loading in the catalyst about 70 % is used to crack or decompose lower molecular hydrocarbon in to hydrogen to maximize the energy content per mass flow of gas steam and also to minimize the carbon dioxide equivalent gases at outlet of the reactor. Since cracking is surface phenomena so the catalyst play important role in designing of reactor shape. Parallel Catalytic packed bed with regeneration and deactivation can be used for commercial production of clean fuel.
Thermal response test and soil geothermal modellingDavid Canosa
Bachelor project consisting in implementing a thermal response test (TRT) in BHE VIA14 placed in the energy park of VIA University College (Horsens), analyzing the results and modeling the BHE in FEFLOW software.
Packed Bed Reactor for Catalytic Cracking of Plasma Pyrolyzed Gasijsrd.com
Packed bed reactors play vital role in chemical industries for obtaining valuable product, like steam reforming of natural gas, ammonia synthesis, sulphuric acid production, methanol synthesis, methanol oxidation, butadiene production, styrene production. It is not only used for production but also used in separation process like adsorption, distillation and stripping section. Packed bed reactors are work horse of the chemical and petroleum industries. Its low cost, and simplicity makes it first choice to any chemical processes. In our experimental work vacuum residue is used as a feed which is pyrolyzed in the primary chamber with the help of plasma into hydrogen and hydrocarbon gases which is feed stream to the Ni catalyst containing packed bed reactor called catalytic cracker. Ni loading in the catalyst about 70 % is used to crack or decompose lower molecular hydrocarbon in to hydrogen to maximize the energy content per mass flow of gas steam and also to minimize the carbon dioxide equivalent gases at outlet of the reactor. Since cracking is surface phenomena so the catalyst play important role in designing of reactor shape. Parallel Catalytic packed bed with regeneration and deactivation can be used for commercial production of clean fuel.
Thermal response test and soil geothermal modellingDavid Canosa
Bachelor project consisting in implementing a thermal response test (TRT) in BHE VIA14 placed in the energy park of VIA University College (Horsens), analyzing the results and modeling the BHE in FEFLOW software.
ASIS International Collaborating on Security Awareness StandardEmblez Longoria
Emblez Longoria is a retired law enforcement officer who is currently a senior security consultant at Verizon Communications. Emblez Longoria obtained his Certified Protection Professional (CPP) from ASIS International.
Domenica i cow boy a diano raduno "amici del cavallo"LiForYou
Per la tua “ vacanza su misura” a Diano Marina prenota con Liforyou.it: il portale specializzato per la Liguria. www.liforyou.itPer info: 329.8580990 – oppure info@liforyou.it. Troviamo la migliore sistemazione per Te , con il tuo budget. Riceverai gratuitamente la LIFORYOU CARD per avere sconti per la vacanza e una guida ristoranti e non solo.
Basic Study on Solid-Liquid Phase Change Problem of Ice around Heat Transfer ...IJERDJOURNAL
Abstract:- Phase change heat transfer around heat transfer tubes is one of the basic problem of an ice heat storage exchanger. It can lead to decrease of thermal storage efficiency and damage of heat transfer tubes if continued freezing further after the ice has bridged because of the generated ice thermal resistance and volume expansion. In this study, we focused on freezing phenomena of phase change material (PCM) between two heat transfer tubes, which can simulate an inside structure of ice heat storage exchangers. Bridging time between two heat transfer tubes was studied numerically. We used water as the PCM, which is filled in the water container. Two horizontal elliptical tubes were used as heat transfer tubes in order to observe the influence of natural convection. Single-domain calculation model was used to calculate arbitrary shape of the two tubes during the ice freezing process. We changed arranged angle and relative position of the tubes to investigate impact of the tube arrangement on freezing phenomenon. In order to confirm the accuracy of our analysis, analytical results were compared with experimental results at the same conditions. Results show that the bridging time was not simply in proportional to the initial temperature of water when considered the natural convection influenced by such as density inversion of water. Moreover, we found that when we set the temperature of tube wall and initial temperature of water as the parameters, bridging time has a similar trend with distance between the axes. Therefore, it is possible to predict the bridging time for elliptical heat transfer tube.
SUMMARYThis report represents the outcome of heat exchang.docxpicklesvalery
SUMMARY:
This report represents the outcome of heat exchange via 4 tubes that are fitted within the shell with four thermocouples to determine the temperature for every pass, two passes for the hot water (in/out) and two for the cold water (in/out). The experiment was commencing according to the amount of hot and cold water that was supplied to the inputs of the heat exchange. The supply was managed by the use of taps that would restrain or allow the gush of water. The temperature for the inputs was constant in the most of the 5 runs while the outputs had been changed due to heat exchange occurring within the shell. Hot water had lost temperature while cold water had gained temperature.
An experiment was set up to resolve the energy losses that affect the hot and cold water, by using thermodynamic laws. During the experiment the water gush rates were measured carefully and the data had been collected and entered to allow the calculations of the energy losses that came out. Finally, it was discovered the heat had been exchanged from the hot into the cold to maintain the temperature inside the shell.
Contents:
SUMMARY:i
1.0INTRODUCTION:1
2.0AIM:1
3.0EXPERIMENTAL METHOD:1
4.0EXPERIMENTAL DATA:2
5.0DATA ANALYSIS:2
6.0DISCUSSION:4
7.0CONCLUSION4
ii
INTRODUCTION:
The exchanger consists of a number of tubes that sit inside a shell that allows cold water to flow through them. Hot water flow through the bordering shell and the two fluids exchange heat. Heat exchanger can come in various forms and as such can have many different motives. A radiator in a car and a boiler in a steam engine are both heat exchanger with the radiator cooling the engine, and the boiler exchanging raw materials into steam that can be used for power generation. The heat exchanger that has been used in this experiment was a basic shell and tube style as shown in figure 1. A Jenco digital thermometer and Jenco thermocouple switches are used in the heat exchanger set up to allow to calculate the measurements for the experiment. Flow meters fitted on the inlet of hot and cold water taps are used to change volume flow rates.
AIM:
The aim of the report is to evaluate the heat losses that came out for the hot water. The experiment will carry of recording temperatures and flow rates and then calculating other possible factors that may cause heat loss.EXPERIMENTAL METHOD:
1) Be familiar with the different part of the experimental.
2) Turn on the cold and hot water taps.
3) Turn valves for the cold water at an initial flow rate (approximate 15 L/min for cold water) Make sure that all the water passes through the flow meters (turn off one of the valves in each water supply line)
4) Water for couple of minutes before reading the data.
5) Take the temperature reading for the thermocouples 1 to 5 by press the Jenco thermocouple buttons.
6) Repeat steps from 3) to 5) for 5 different flow rate combinations.EXPERIMENTAL DATA:
Room temperature: 15°C
Run/Quantities
(L/min)
(L/min)
in ...
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Experiment 1: Calorimetry
Post lab
Rawan Douar, Albert Campbell, Riley
Richardson, Christopher Cardenas
02/10/17
Instructor: Meng Chen
CHM2046L
Section: 912
Introduction
We determined the change in enthalpy to be negative, which means energy is sendoff the system and entering the environments in the form of heat.
Calorimetry is the chemical process which is used to measure heat in chemical reaction. The apparatus used is the calorimeter. A coffee cup calorimeter is not technologically advanced but it is effective in stopping heat transfer between the system and the atmosphere. Because the cup is open to the air, this is a constant pressure measurement. Per the first law of thermodynamics, the total energy of an isolated system can neither be created nor destroyed. In other words, energy is preserved in chemical reaction.
Calorimeter will consist of two nested Styrofoam coffee cups and a plastic cover. It will use a temperature sensor armed with a thermocouple probe. There will be a hole in the plastic cover of your calorimeter for insertion of the probe. In this experiment, we are going to study about the redox reactions with coffee cup and calorimeter.
Hypothesis and Objectives
Using a coffee cup calorimeter, the heat of neutralization of HCl and NaOH is measured. From this, the enthalpy change for the neutralization of one mole of HCl can be calculated.
· Introduction to the technique of calorimetry, in which the heat is evolved or absorbed by a chemical reaction is incidental by measuring temperature vicissitudes in an insulated reaction container.
· Reaction involve strong bases and acids will produce more heat.
Methods
Following are the materials that are used in experiment.
· Coffee cup calorimeter thermometer
· Lid or parafilm
· 10 mL graduated cylinder
· HCL
· NaOH
· Water
· 250 mL beaker
Procedure
1. Set up calorimeter apparatus.
2. Measuring solution temperature before mixing.
3. Adding simultaneously HCl and NaOH to the coffee cup.
4. Measure temperature change after mixing.
5. Calculate enthalpy change.
(J. Kotz, P. Treichel, J. Townsend; Chemistry & Chemical Reactivity 7th ed. 2009)
Obtain 10 ml of cold water and get the temperature, and pour it into your calorimeter. Then do the same thing for hot water. After that, measure the final temperature when it reaches equilibrium. Use the initial and the final temperatures to measure Ccal. Now gather two 50 mL beakers, one for NaOH, and one for HCl. Use the 10-mL graduated cylinder and then add the 3 mL of HCl and 7 mL of water, measure the temperature and put it into your unfilled calorimeter. Do the same for NaOH. Then put the thermometer in and measure the exact last temperature of it.
Clean up, and do the same thing aga ...
Aim:
To determine the heat loss in a double pipe heat exchanger counter-current flow
experiment.
Theory:
A double-pipe heat transfer exchanger consists of one or more pipes placed
concentrically inside another pipe of a larger diameter with appropriate fittings to direct
the flow from one section to the next. One fluid flows through the inner pipe (tube side)
in this experiment (hot water), and the other flows through the annular space (annulus)
(cold water).
The double-pipe heat exchanger is one of the basic kinds of exchangers with a very
flexible configuration. There are two types of counterflow or parallel flow for this type
that are the basis of design and calculation for determining pipe size, length, and
number of bends.
Double pipe heat exchanger counter current: heat is exchanged between two flowing
fluids at a different temperature that flows counter current in the heat exchanger double
pipe.
The efficiency is greater in counter-current than in parallel flow because the two fluids
(water) flow separately in counter-current flow when the high different temperatures
meet heat exchange rapidly due to the difference of temperatures, the hot water
becomes warm then cold as heat exchanges, and the cold water becomes warm the heat
exchange occurs till it reaches steady state. As it is explained in Figure 1.
Heat loss can be found by the equation below:
Q=ΔH=mCpΔT
Where: Q=ΔH is the amount of heat transferred to or from the system (J).
m: mass of the system (Kg)
Cp: constant pressure specific heat capacity of the system (J/g°C)
ΔT: difference in temperature of the system °C.
Experiment: Double pipe heat exchanger
4
Figure 1: concurrent and countercurrent respectively.
Procedure:
Double pipe heat exchanger: as shown in the figure-2:
1. Power switch: No.1
2. Temperature scale to select a temperature to heat the water in the tank [No.2] in
the figure.
3. Water tank a heating coil is used to heat the water [no.3].
4. Power pump to set a flow rate, the water is pumped through the double pipe heat
exchanger. [No.4]
5. A flow rate measurement is found in no.5
6. [No.6-7-8-9-10] The temperature measurements measure temperature
throughout the process.
7. Then the temperature and flow rate are collected in the temperature screen.
Experiment: Double pipe heat exchanger
5
Figure 2: double pipe heat exchanger.
Experiment: Double pipe heat exchanger
6
observation:
1. Turn on the device with the power switch.
2. The flow rate is set as 157 ml/s.
3. Heat water up to [40-50 Celsius] in this experiment: [44.4 Celsius] by the
heating coil in the water tank, set the desired temperature by the temperature
scale in the water tank.
4. Then water is pumped to the pipes by the power pump.
5. Adjust the valves so that the hot water and cold water flow countercurrent.
6. The hot water flows in the inner pipe in the double pipe through the pipe from
the pump to the heat exchanger
7. the cold water flows in the outer pipe counter current from the tank to the pipes
the valv
Experimental Investigation on Pool Boiling Heat Transfer With Ammonium Dodecy...IJERA Editor
We have so many applications related to Pool Boiling. The Pool Boiling is mostly useful in arid areas to
produce drinking water from impure water like sea water by distillation process. It is very difficult to distill the
only water which having high surface tension. The surface tension is important factor to affect heat transfer
enhancement in pool boiling. By reducing the surface tension we can increase the heat transfer rate in pool
boiling. From so many years we are using surfactants domestically. It is proven previously by experiments that
the addition of little amount of surfactant reduces the surface tension and increase the rate of heat transfer. There
are different groups of surfactants. From those I‟m conducting experimentation with anionic surfactant
Ammonium Dodecyl Sulfate (ADS), which is most human friendly and three times best soluble than Sodium
Dodecyl Sulfate, to test the heat transfer enhancement.
1. Farbo, Jones
1
Determining an Effective Method to Cool Soda Using
Household Items
James Farbo & Ryan Jones
Department of Chemical Engineering, The Pennsylvania State University, University Park, PA, 16802
CH E 350, Section 1, Dr. Costas Maranas
Prompt
Using household items, design a way to cool a can of your favorite carbonated beverage
from room temperature to a suitable drinking temperature of 3°C.
Background/Hypothesis
Our task was to cool an aluminum can of our favorite carbonated beverage, in this case,
light beer, from room temperature to a suitable drinking temperature of 3°C. The general idea
that comes to mind is to cool the can with an ice bath, however this takes far too long.
Consequently, we considered various heat transfer methods to increase the rate at which heat is
transferred from the can to the surroundings. Some brainstormed ideas included putting the can
in an ice bath and creating forced convection by introducing an outside force, creating a packed
and/or fluidized bed tightly surrounding the can, and implementing highly conductive annular
fins on the surface of the can to increase the convective heat transfer coefficient. While
theoretically possible, these ideas weren’t feasible using strictly household items.
Drawing from our knowledge of chemical engineering thermodynamics, we considered
ways in which to drop the temperature of an ice bath by freezing point depression. We
hypothesized that by adding table salt, a common household item, to an ice bath, we could drop
the freezing point of water significantly below its pure liquid value of 0°C at 1 atm, thus cooling
2. Farbo, Jones
2
the can more quickly. In theory, by adding salt (a solute) to an ice bath, the ice-solute mixture
becomes liquid at temperatures where pure water would be a solid.1 On a molecular level, this
phenomenon occurs because the addition of salt disrupts the dynamic equilibrium between water
and ice.2 Salt’s solubility in water prevents some water molecules from freezing; contrarily, the
rate at which ice melts is unaffected. Because melting occurs more rapidly than freezing, it will
continue to occur unless the temperature of the mixture drops low enough to re-establish solid-
liquid equilibrium.
This thermodynamic argument prompted us to design an experiment that tested the
effectiveness of cooling a can of light beer a in a salt-ice-water mixture versus a pure ice-water
mixture. Considering the phase map of salt-ice-water, shown below in Figure 1, we chose to cool
the can at 10% and 20% salt concentrations (by weight) and compare results to a pure ice-water
solution.2
Figure 1. Phase map of a salt-ice-water solution.2 Salt becomes saturated in ice-water
solution at 23.3% NaCl (by weight); the lowest possible mixture temperature is -21.1°C.
3. Farbo, Jones
3
These concentrations were selected because they promote significant freezing point
depression, and are close to but not exceeding the solubility limit of 23.3% salt (by weight).
To test the validity of our experimental setup, theoretical proof of concept is essential.
Arguably, the most important factor necessary for correctly modeling our experiment is
determining the value of the convective heat transfer coefficient, h, of the ice water bath. Due to
the absence of an external driving force, the liquid experiences no motion; thus, convection is
assumed to be free. Furthermore, the can is cylindrical and can therefore be modeled as a long
horizontal cylinder. Equations 9.33 and 9.34, shown below, have been empirically derived using
dimensionless variables and can be used to model external free convection for a long horizontal
cylinder at the film temperature.3
(9.33)
(9.34)
In Eqs. 9.33 and 9.34, RaD represents the Rayleigh number, a dimensionless parameter
that characterizes buoyancy-driven flow (i.e. free convection) involving both laminar and
turbulent flow, shown below in Eq. 9.25.3
(9.25)
The properties necessary to calculate the Rayleigh number (i.e. the fluid’s kinematic
viscosity, thermal diffusivity, and thermal expansion coefficient) are often tabulated for easy
4. Farbo, Jones
4
access.3 If they are not tabulated for a specific species, they can often be calculated by utilizing
common correlations (listed below) and linear interpolation. For the saltwater solutions,
obtaining the necessary constants requires referencing the literature for thermal properties
dependent on both temperature and percent salinity4 in addition to both linear interpolation and
extrapolation as necessary. By far the most troublesome constant to calculate is the thermal
expansion coefficient. This can be found by plotting the density of the fluid as a function of
temperature and dividing the negative of the slope of this curve by the density of the fluid
(equation 3) (Figures S2 and S3).
(1)
(2)
(3)
At this point, the Rayleigh number can be used to calculate the averaged Nusselt number
for a large range of Rayleigh numbers in both the laminar and turbulent flow regimes via
equation 9.34, and the average convective heat transfer coefficient can be subsequently found by
equation 9.33.
With the convective heat transfer coefficient of the ice-water bath in hand, the most
logical approach for assessing the temperature distribution inside the aluminum can is to
consider an effective heat transfer coefficient, U, which incorporates the convective loss from the
bath and the conductive heat loss from the aluminum can. Ultimately, the rate of heat loss is
5. Farbo, Jones
5
dependent on the least resistive element of the thermal circuit. Therefore, if the thermal
resistance of the aluminum can is negligible compared to that of the liquid inside the can, it may
be neglected.
𝑅" =
𝑙
𝑘
+
1
ℎ
(4)
𝑈 =
1
𝑅"
(5)
The theoretical cooling time can then be calculated in one of two ways: from the
approximate solutions to the one-dimensional transient conduction temperature distribution for
an infinite cylinder or by numerical integration of the one-dimensional partial differential heat
equation in cylindrical coordinates.
(6)
The latter approach is more user friendly as it doesn’t require the copious calculations
associated with analytically solving transient systems. In short, this method analyzes one radial
slice of the can at a time, ultimately mapping out the temperature distribution within the can at
several different positions; these temperatures can then be averaged so that the liquid can be
treated as having a uniform temperature at all times. Additionally, the time and radius increments
can be adjusted accordingly to increase the accuracies of the local derivatives and provide similar
answers to those that would be obtained analytically.
Experimental
Cooling a can of light beer—pure ice bath
Firstly, we obtained three cans of light Busch beer and allowed them to equilibrate to
6. Farbo, Jones
6
room temperature for 30 minutes. Upon obtaining laboratory access from Professor Wayne
Curtis, we then created an ice bath by adding 4.5 Kg of water and 1.5Kg of ice to a rectangular
container and allowed it to equilibrate for 5 minutes. Using a thermocouple, we measured the
initial temperatures of both the ice bath and the liquid beer. Subsequently, we suspended and
submerged the can of beer into the ice bath using a ring stand and clasp (Figure S1). Upon
complete submersion, we immediately started recording time using a stopwatch while
simultaneously measuring the temperature of the beer until it reached a refreshing drinkable
temperature of 3°C.
Cooling a can of light beer—10 and 20 weight % salt solutions in a water/ice bath
Initially, 5 L of pure water and 4L of pure ice were added to a new rectangular container
(8.666 kg of H2O by weight) and allowed to equilibrate for five minutes. Using a balance, 0.962
kg of salt was weighed and added to the ice bath, creating a 10% salt solution. The solution was
then stirred using a spatula by hand for two minutes to promote the dissociation of salt. Next, the
initial temperatures of both the bath and the second room temperature beer were recorded. Note
that we ensured the initial temperatures of the beers were the same for each trial to ensure a
concise comparison. Finally, the beer was submerged and tested similarly to that of the pure ice
bath.
Analogously, mixing 5 L of pure water, 5.5 L of pure ice, and 2.501 kg of salt created a
20% salt-ice-water solution. Subsequently, the procedure was conducted identically to that of the
previous two trials.
Results and Discussion
Completion of the three experimental trials provided data that supported our original
7. Farbo, Jones
7
hypothesis. Cooling the cans of beer to drinkable temperatures occurred much faster in ice water
with increased salt concentrations relative to pure ice water, shown below in Table 1 (All
theoretical times were found using the cylindrical PDE solver depicted in Figure S4).
Pure Ice/Water 10% Salt in Ice/Water 20% Salt in Ice/Water
Ti,can (°C) 25.3 25.3 25.3
Tf,can (°C) 3.0 3.0 3.0
Tbath (°C) 0 -7.7 -13.5
Experimental
Time (s)
1298.51 521.27 411.49
Theoretical
Time (s)
1770 770 530
htheor;bath (W/m2K) 534.02 800.01 768.75
Percent Error (%) 26.6 32.3 22.4
Notice that the time required to cool a can of beer in 10% Salt in Ice/Water was less than
half of the time needed for a can of beer in Pure Ice/Water, despite the bath temperature
difference only being approximately -8°C. This indicates that there must be a strong driving
force, other than the increase in temperature difference, drastically improving the ability for the
bath to absorb heat from the can. Upon completion of theoretical modeling, a couple noteworthy
causes stand out.
Firstly, significant discrepancies appeared when the mean free convective heat transfer
coefficient was calculated from Eq.’s 9.25, 9.33, and 9.34 for each solution, as seen above in
Table 1. The large difference between h for pure ice/water and the two salt solutions helps
account for the significant difference in cooling times--the higher average h in the salt solutions,
Table 1. Experimental and theoretical data for cooling a soda can at various mixtures of
water, ice, and salt
8. Farbo, Jones
8
relative to the pure ice/water, facilitated much quicker heat transfer from the can. From equations
9.33, 9.34, and 9.25, is it evident that h is directly proportional to the temperature difference
between the initial can temperature and the bath temperature. Inherently this makes sense: the
colder the bath temperature the faster it will cool the can. However, it is notable that h decreases
by ~5% when increasing the salt concentration from 10 to 20%. This may seem counterintuitive,
but h as the salt concentration increases, other properties such as the density, viscosity, and
Prandtl number also increase and the thermal conductivity decreases, negatively affecting the
convective heat transfer coefficient. Despite this decrease in h, the drastically lower temperature
of the 20% salt bath dominates and drives the can to cool faster.
The net result of this experiment is that salt depresses the freezing point of water and thus
accordingly cools the room temperature can more quickly than an ice/water bath alone.
However, there is clearly diminishing returns associated with the amount of salt used. The 10%
and 20% salt solutions cooled the fluid in the can in approximately 8.7 minutes and 6.9 minutes,
respectively. Thus, as the saturation concentration of salt in water (23.3 weight %) is approached,
the cooling effects are diminished as the solution becomes denser, more viscous, and less
conductive. Ultimately, the saltwater solution drastically expedited the cooling process compared
to the ice/water bath which took nearly 22 minutes. The large discrepancies between the
experimental times mentioned above and the theoretical calculations (each yielding an
approximate percent error of 25-30%) is indicative of the many assumptions and approximations
mentioned in Table S1.
Conclusion
Through both experimental and theoretical verification, a beer can is cooled significantly
9. Farbo, Jones
9
quicker in 10% and 20% salt in ice/water solution compared to a pure ice/water solution (see
Table 1). Furthermore, our theoretical model of each system proved to be fairly accurate,
producing reasonable percent errors, with respect to the experimental times (see Table 1). Given
the large amount of assumptions (Table S1), a large error was expected, however all calculations
proved to be reasonable. In future beer can cooling experiments, we would use a larger scale
ice/water bath to decrease the dependency of T∞ on time. Furthermore, we would insulate the
bath to minimize heat loss and stir the salt solutions more effectively to facilitate the dissociation
of sodium chloride.
Supporting Information
Assumptions Reasonfor
Assumption
Error Associated with Assumption
Can is an infinite cylinder; assume
adiabatic tip (i.e. L>>D) for all
trials. Furthermore, assume that a
vertical cylinder produces the same
h as a horizontal cylinder.
Modeling convective
heat transfer coefficient
for free convection of a
cylinder
L is not that much greater than D; We
felt that a horizontal infinite cylinder
approximation would be more accurate
than a vertical plane wall
approximation. Because the can is
vertical in the experiment (not
horizontal, as requested by the infinite
cylinder approximation formula) and
horizontal in theoretical calculations,
there is a slight error produced.
Beer and water are thermally
equivalent
No strong temperature
dependent thermal
properties of beer (but
the major component is
water)
Slight discrepancies in thermal
conductivity, density, and heat
capacity due to the presence of syrups,
dissolved carbon dioxide and alcohol
Treat water and ice in mixture as
purely water at Tfilm
Majority of ice in bath
had melted by the time
There was some ice remaining and we
couldn’t quantitatively account for its
Table S1. Assumptions made to carry out theoretical calculations
10. Farbo, Jones
10
the can was submerged properties in the bath
T∞ is not a function of time and the
ice-water bath can be treated as
infinite
We couldn’t solve the
PDE if T∞ varied with
time.
In practice, T∞ indeed changed as a
function of time because ice melted in
the bath
Neglect soda can resistance when
calculating h
hcan accounts for less
than .15% of the total
thermal resistance
Negligible
Solubility of salt in ice/water bath is
100% (applies only to salt solutions)
Allows us to assume
100% of salt added is in
solution i.e. it’s a
uniform mixture
Not all of the salt dissolved causing
error in calculations involving density
Can temperature is initially uniform This assumption allows
for the calculation of
the Rayleigh number
(Ts=Ti) and is fairly
accurate for cans that
have been stored at
room temperature.
It is likely that the temperature at the
centerline of the can was slightly less
than the temperature at the surface due
to aluminum’s high conductivity and
radiation effects in the room
Can is 100% aluminum Allows for simple
calculation of resistance
for can and ultimately,
allows us to neglect it.
Negligible
Fluid in can is not moving We can now treat the
fluid as a solid object,
thus simplifying
calculations
At any given time, the fluid is going to
want to move around and equilibrate
due to inherent buoyancy forces
Supplemental Figures
11. Farbo, Jones
11
Figure S1. Experimental setup for cooling soda can in ice/water/salt bath
Figure S3. Plot of density as a function of temperature (20% salt solution)
Figure S2. Plot of density as a function of temperature (10% salt solution)
12. Farbo, Jones
12
Sample Calculations
Provided as supplementary data
References
1.) Matsoukas, T. Fundamentals of Chemical Engineering Thermodynamics, 1st ed.;
Prentice Hall, 2013.
2.) Senese, F. Why Does Salt Melt Ice?
http://antoine.frostburg.edu/chem/senese/101/solutions/faq/why-salt-melts-ice.shtml
(accessed Dec 7, 2016).
3.) Bergman, T. Fundamentals of Heat and Mass Transfer; John Wiley & Sons.
4.) Sharqawy, M. Seawater
http://web.mit.edu/seawater/Seawater_Property_Tables_8March16.pdf (accessed Dec 7,
2016).
Figure S4. Sample numerical integration of the one-dimensional partial differential heat
equation in cylindrical coordinates for the 10% salt solution