Further Maths and Simulation (SC2153)
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
Assignment submission date: 28th February 2018
Assignment feedback: 21st March 2018
You must attempt all questions and show all working.
Please state if you are rounding numbers, and include units where applicable.
1: The admittance, π, in a circuit is given by
π =
1
π
where π is the impedance of the circuit. If Z = 150 β j22, find π.
5 marks
2: By applying Kirchoffβs laws on a circuit, the following mesh equations were obtained:
18πΌ1 + π12πΌ1 β π25πΌ2 = 200
20πΌ2 + π40πΌ2 + 15πΌ2 β π25πΌ1 = 0
Determine, in polar form, the primary and secondary currents, πΌ1and πΌ2 respectively,
through the circuit.
12 marks
3: If 6π₯
2 + 3π¦
2 + π§ = 1, find the rate at which π§ is changing with respect to π¦ at the
point (3, 5, 2)
4 marks
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
4: The stream function, π (π₯, π¦),has a circular
function shape as shown, and is related to the
velocity components π’ and π£ of the fluid flow by
π’ =
ππ
ππ₯ and π£ =
ππ
ππ¦
a) If π = ππβπ₯
2 + π¦
2, find π’ and π£.
b) The flow is irrotational if π satisfies Laplaceβs equation,
πΏ
2 π
πΏπ₯2 +
πΏ
2π
πΏπ¦2 = 0
Determine if the flow is irrotational.
15 marks
5: Determine the force, F, which has a magnitude of 64kN in the direction of the vector
π΄π΅ where A = (2, 4, 6) and B = (6, 3, 4).
8 marks
6: An object is dropped and its position vector, r, is given by
π = (π‘
5 β 2π‘
2
)π + (7π‘
3 β 6π‘
2
)π
a) Find the velocity, π£, and the acceleration, π.
b) What is the angle between π£ and π when π‘ = 2?
12 marks
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
7: If π· = π₯π§
2 + 3π₯π¦
2 + π¦π§
2
a) Determine grad π· at the point (3, 5, 1).
b) Find the direction from the point (1, 1, 0) which gives the greatest rate of
increase of the function of π.
9 marks
8: Consider a two-storey building subject to earthquake oscillations as shown:
Oscillations
The period, T, of natural vibrations is given by π =
2π
β(βπ)
where π is the eigenvalue of the matrix A.
Find the period(s) if A = (
β30 10
10 β20)
10 marks
The equations of motion are
expressed as
π₯Μ= π΄π₯
π€βπππ π₯ = (
π₯1
π₯2
)
π₯1
π₯2
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
9: Below is a screenshot of a mathematical function written in MATLAB, along with its
corresponding vector diagram.
What does this code do? Explain with respect to each line in the code and the figure
shown.
10 marks
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
10:
a) Model Q6 using MATLAB. Include a screenshot of the code and explain what
each line of code is doing.
b) Give two advantages of MATLAB over manual calculations and support your
answers with examples
15 marks
Total available marks – 100
EE 221 β Introduction to Electrical Engineering
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Page 1 of 1
Tuesday, January 23
EE 221 β Introduction to Electrical Engineering
Due β 5
th February 2018 (beginning of the class)
Problem 1: Innovation is the number one driver of US economy. Computer, internet, smart
phones, smart watches, self-driving cars, Amazon Alexa, Google home, military technologies
such as Drones, are some of the examples of innovation and many of these innovative
technologies are utilized by the millions of citizens all around the world.
In this spirit, if all the funds and resources are available to you to do the innovation, what would
you innovate related to your discipline?
To shape up your writing for the innovation topic, please try to incorporate the best answers
(based on your ability) to following questions in your write up:
What is the strong rationale for the topic of innovation?
What are the two goals that will be needed for realizing the innovation?
What are the two objectives of each goal described earlier?
Find and discuss at least one technique or algorithm without which your innovation is not be
possible.
Please submit your paper in PDF format in ECampus β> Homework Assignment 3 link. Use single
spacing, 10 pts Times New Roman font with 1 inch page margin all sides format. Page limit β1
page. Write the title of the innovation in the header space of the page. Use page 2 for graphs,
tables and references. Do not write your name on the document.
For research use following website from WVU computers:
http://ieeexplore.ieee.org
https://scholar.google.com/
https://www.engineeringvillage.com/search/quick.url
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CEE 213βDeformable Solids The Mechanics Project: http://customwritings-us.com/orders.php
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CEE 213βDeformable Solids The Mechanics Project
Arizona State University CP 3βProperties of Areas
1
Computing Project 3
Properties of Areas
The computing project Properties of Areas concerns the computation of various properties
of cross sectional areas. In each of our theories (i.e., axial bar, torsion, and beams) we arrive
at a point where we need certain properties of the cross section to advance the analysis. For
the axial bar we needed only the area; for torsion we needed the polar moment of inertia;
for the beam we will need moment of inertia of the cross section about the centroid of the
cross section.
We can develop an algorithm that allows the computation of all of the properties of a cross
section if the cross section can be described as a polygon. The algorithm is built on formulas
for the properties of a triangle. What that program will do is create a triangle from the
origin and the two vertex nodes associated with a side of the polygon. Whether this polygon
adds or subtracts from the accumulating properties will be determined from the vectors
defining the sides of the polygon (see the CP Notes for further clarification). If you loop
over all of the sides, the end result will be the properties of the entire cross section.
The general steps are as follows:
1. Develop a routine that allows you to describe the cross section with a sequence of
points numbered in a counterclockwise fashion starting with 1. The last point
should be a repeat of the first one in order to close the polygon. Some suggestions:
a. Store the (x,y) coordinates of each point in a single array x(N,2), where N
is the number of points required to describe the cross section (including
the repeat of the first point as the last point) and the first column contains
the x values of the coordinate and the second column contains the values
of the coordinate and the second column contains the y value.
b. It will eventually be a good idea to put the input into a MATLAB function
and call the function from your main program. That way you can build up
a library of cross sectional shapes without changing your main program.
c. If you need a negative area region (for a cutout section like in an open
tube) then number the points in that region in a counter-clockwise fashion.
Just keep numbering the vertices in order (no need to start over for the
negative areas).
2. Develop a routine to loop over all of the edges of the polygon and compute (and
accumulate) the contributions of the triangle defined by the vectors from the origin
to the two vertices of the current side of the triangle (that gives two sides) and the
CEE 213βDeformable Solids The Mechanics Project
Arizona State University CP 3βProperties of Areas
2
vector that points from the first to the second vertex (in numerical order). Calculate
the area, centroid, and outer-product contributions to the properties (see the CP
Notes for clarification of this issue).
3. Compute the orientation of the principal axes of the cross section using the eigenvalue
solver in MATLAB (eig) on the moment of inertia matrix J. See the CP
Notes for more information on this task.
4. Create an output table (print into the Command Window) giving the relevant cross
sectional properties. Develop a routine to plot the cross section. Include the location
of the centroid of the cross section in the graphic (along with lines defining
the principal axes if you can figure out how to do that).
5. Generate a library of cross sections, including some simple ones (e.g., a rectangular
cross sections) to verify the code. Include in your library as many of the following
cross sections as you can get done:
a. Solid rectangle with width b and height h.
b. Solid circle of radius R.
c. Rectangular tube with different wall thickness on top and bottom.
d. I-beam with flange width b, web depth d, flange thickness tf, and web
thickness tw.
e. Angle section with different leg lengths and leg thicknesses.
f. Circular tube with outside radius R and wall thickness t.
g. T-beam.
6. Use the program to explore aspects of the problem. For example,
a. Why is it more efficient to use an open circular tube for torsion rather than
a solid cylinder?
b. For beam bending we can control deflections and reduce stresses with a
large moment of inertia about the axis of bending. Show the trade-offs
available in an I-beam when you can select different web and flange depths
and thicknesses. What is the ideal allocation of material? Why would we
never actually do that in practice?
c. Demonstrate that the principal axes of a symmetric cross section lie along
the lines of symmetry. You can do this by showing that the off-diagonal
elements of J are zero for symmetric sections with axes so chosen.
d. Explore any other feature of the problem that you find interesting.
CEE 213βDeformable Solids The Mechanics Project
Arizona State University CP 3βProperties of Areas
3
Write a report documenting your work and the results (in accord with the specification
given in the document Guidelines for Doing Computing Projects). Post it to the Critviz
website prior to the deadline. Note that there is only one submission for this problem (the
final submission).
Please consult the document Evaluation of Computing Projects to see how your project
will be evaluated to make sure that you can get full marks. Note that there is no peer review process for reports in this course.
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- Find the present value, P, for the following cash flows.
i = 12%
- Star Inc. must purchase a small size milling machine. The following is known about the machine and about possible cash flows. The machine is expected to have a useful life of 8 years. The company has a MARR of 7%. Determine the NPW of the machine.
p=.25 | p=.50 | p=.25 | |
First cost | $40,000 | $40,000 | $40,000 |
Annual savings | 2,000 | 5,000 | 8,000 |
Annual costs | 12,000 | 8,000 | 6,000 |
Actual salvage value | 4,000 | 5,000 | 6,500 |
- The company accountant is uncertain which of three depreciation methods the firm should use for welding equipment that costs $150,000, and has a zero salvage value at the end of a 10-year depreciable life. Compute the depreciation schedule for the welding equipment using the methods listed:
- Straight line
- Double declining balance
- Sum-of-yearsβ βdigits
Based on your analysis, which depreciation method is most profitable for the firm?
- A Petroleum company recently completed construction on a large refinery in Louisiana. The final construction cost was $71,000,000. The refinery covers a total of 260 acres. The Expansion and Acquisition Department at the company is currently working on plans for a new refinery in Texas. The anticipated size is approximately 360 acres. If the power-sizing exponent for this type of facility is .70, what is the estimated cost of construction?
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Design of Power system for a Data Center_http://customwritings-us.com/orders.php
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Design of Power system for a Data Center
A data center with the dimension of 40ft Long x 30ft Wide x12ft High is located on the 12^{th} floor of a high rise building in downtown Chicago, IL.Β Β The data center must operate all the time regardless of the availability of power from the utility. The loads can be categorized as high, medium and low critical. Table 1 shows the power rating of each cabinet and the critical level of each load.Β The cabinets are 12-ft wide x 6-ft High x 2-ft deep. Four of these cabinets must be strategically placed in the room to obtain the best heat exchange at minimum cost. The cooling registers are located on the floor and the exhaust registers are placed on the ceiling as shown in Figure 1. The cooling cost per BTU is $0.01. Each cabinet generates 30,000 BTU per hour and heat must be removed to operate properly. The cost of electricity is $0.1 per kilowatt-hour. Exhaust fan can help to remove heat faster.Β A 1000 cfm require a 1 hp motor.
Each highly critical load must be supported by 5 sources of power; such as one utility, 2 UPS and two generators.
Medium critical loads require utility, UPS and two generators.
Low critical loads require utility, UPS and a generator.
Select the sizes for of the two generators to provide power to the racks as well as cooling for High and Medium Critical loads.
The UPS must be able to withstand 20 minutes for Medium and low and 1 hour for High Critical Loads.
Determine the depth of Discharge and battery sizes and type using Table 2 information.
UPS costs $750.00/Kw for 20 minutes operation.
UPS costs $2500/kW for 1 hour operation.
Generator Costs $1000/KW.
Deliverables:
- Provide a drawing to show the location of each load in the cabinet to obtain proper cooling for each load at lowest cost and risk
- Provide a drawing for the cabinet layout
- Determine the size of cooling system (BTU)
- Calculate the size exhaust fans (CFM, hp)
- Provide the UPS size
- Calculate the Battery size and type in the UPS system
- Determine the Generator size
- Calculate the Total power requirement (with 20% safety margin)
- Determine the System Efficiency
- Calculate Total Cost of Cooling, UPS and Generators.
Table-1 Load per Cabinet
20 kW High Critical |
20 kW High Critical |
10 kW Medium Critical |
15 kW Medium Critical |
30 kW Low Critical |
30 kW Low Critical |
Table-2 Battery Information
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Figure-1 Data Center Cabinet Layout for Cooling
EAT223 β THERMOFLUIDS AND ENGINES
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Moderated November 2016
University of Sunderland
Faculty of Applied Sciences
Department of Computing, Engineering and Technology
EAT223 β THERMOFLUIDS AND ENGINES
Assignment 1 of 1
The following learning outcomes will be assessed:
Knowledge
Critical knowledge of the fundamental concepts and analytical methods in the solution of a range of problems related to thermodynamics, fluid mechanics, and heat transfer.
Skills
Design and analyse a variety of air standard cycles and vapour power cycles.
Important Information
You are required to submit your work within the bounds of the University Infringement of Assessment Regulations (see your Programme Guide). Plagiarism, paraphrasing and downloading large amounts of information from external sources, will not be tolerated and will be dealt with severely. Although you should make full use of any source material, which would normally be an occasional sentence and/or paragraph (referenced) followed by your own critical analysis/evaluation. You will receive no marks for work that is not your own. Your work may be subject to checks for originality which can include use of an electronic plagiarism detection service.
Where you are asked to submit an individual piece of work, the work must be entirely your own. The safety of your assessments is your responsibility. You must not permit another student access to your work.
Where referencing is required, unless otherwise stated, the Harvard referencing system must be used (see your Programme Guide).
Please ensure that you retain a duplicate of your assignment. We are required to send samples of student work to the external examiners for moderation purposes. It will also safeguard in the unlikely event of your work going astray.
Submission Date and Time
Before 4pm, Wednesday 22nd March 2017
Submission Location
SunSpace Dropbox
Page 2 of 3
Moderated November 2016
This assignment is set out in two parts, where the first part should help you build the second. You will be allocated one from each of a-e, A-E, and 1-4 (as defined below) to ensure you have an individual set of data for the assignment.
PART 1: IDEAL STANDARD RANKINE CYCLE (50% of marks)
You are required to analyse a standard Rankine cycle by both hand calculation and using the simulation package CyclePad, in order to validate the software. The cycle specifications are as follows:
ο· Boiler pressure: (a) 40; (b) 45; (c) 50; (d) 55 bar; (e) 60 bar (as assigned).
ο· Boiler output temperature: (A) 450; (B) 500; (C) 525; (D) 550ο°C; (E) 575ο°C (as assigned).
ο· Condenser pressure: (1) 0.6; (2) 0.65; (3) 0.7; (4) 0.75 bar (as assigned).
Assume the mass flow rate is 1 kg/s, so that derived work and heat quantities are specific (i.e. per kg of steam). Use a summary table to compare the following:
ο· The specific enthalpy at each point in the cycle, determined both by hand calculation, and by CyclePad.
ο· The net work (Wnet).
ο· The heat in (Qin).
ο· The thermal efficiency (Ξ·th).
PART 2: REHEAT RANKINE CYCLE (50% of marks)
*** You should perform this analysis using CyclePad only. ***
In order to improve the net work output and efficiency of the plant, you are required to investigate the implementation of a two-stage reheat Rankine cycle (as covered in class). Use the same pressures and temperature assigned in Part 1. However, you must choose a pressure for the second stage i.e. the lower pressure turbine and explain how you chose it.
For your chosen design, use another summary table to compare the quantities listed above, obtained from the CyclePad analysis of the reheat Rankine cycle.
More detailed submission requirements are summarised overleaf.
Hints on using CyclePad
(i) You can download a free copy of CyclePad from the following link. If you have any trouble obtaining it, email me and I will send you a copy.
http://www.qrg.northwestern.edu/software/cyclepad/cyclesof.htm
(ii) You will find a Rankine Cycle Solved in the CyclePad library. Use this to help you get started with the first part of the assignment. It comprises four parts: heater, turbine, cooler and pump, corresponding to the boiler, turbine, condenser and feed pump, respectively.
(iii) Note that both heater and cooler are modelled as isobaric (i.e. constant pressure), and both turbine and pump are modelled as adiabatic and isentropic.
(iv) In the second part, you can use the Reheating Vapor Cycle Solved in the library as a template.
Page 3 of 3
Moderated November 2016
Submission requirements
You should keep the material to the minimum necessary to fulfil the following, in the order indicated.
Stage 1 (50%)
ο· A summary table, which includes your manually calculated results (as outlined above) and the CyclePad results.
ο· Detailed cycle hand calculations, including an annotated diagram of the cycle schematic. This can be hand written, but must be neat and legible.
ο· Screenshots of the CyclePad Cycle Properties window, the Assumptions Made window, and the T-s diagram generated by the software.
Stage 2 (50%)
ο· A summary table, showing the CyclePad specific enthalpy results for the reheat Rankine cycle.
ο· An annotated diagram of the cycle schematic.
ο· Screenshots of the CyclePad Cycle Properties window, the Assumptions Made window, and the T-s diagram generated by the software.
Untidy or illegible work will be penalised.
This assignment is worth 30% of the total module mark.
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Assignment help_IE 424
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Assignment help_IE 424
IE 424
Spring 2017
Instructions:Β Answer questions 1 through 4. Please show all work.Β You must not discuss this exam with your classmates or other peopleβall work must be your own.Β Any research must be properly cited.Β This exam is due by 11:59 PM Mountain Time on March 15, 2016. Β Your late submittal will lose points starting at 12:01 am on Thursday 3/16 so plan accordingly.
- Valles Global Industries has a division that operates a fishing fleet that fishes for Alaskan cod. In the table entitled βCod Catchβ in the attached file, you will find the history of the fleetβs catches over 24 months.Β Develop a forecasting model for the fleet that illustrates the forecast for 24 months plus month 25.Β Use a smoothing factor (alpha) of .1.Β Show how you calculated each forecast and the forecast error.Β Discuss the smoothing factorβwill changing this factor improve your forecast?Β How?
- The Sohn Aerospace Division of Sohnco has a demand forecast for the first three months of next year is
JanuaryΒ Β Β Β Β Β Β Β 600 ships
FebruaryΒ Β Β Β Β Β Β 100 ships
MarchΒ Β Β Β Β Β Β Β Β Β Β Β 900 ships
Strangely, they have 100 ships in stock as of December 31.
- a) Plot cumulative demand and a level aggregate production plan with no back orders and no ending inventory.
- b) What production is needed each month to meet part aβs conditions?
- c) Suppose any left-over ships at the end of each month cost $500,000 per month in storage and interest costs. Assume the start-up inventory is not part of the calculation.Β Should we make any changes to our plan?Β Explain your answer.
- Sohn Aerospace is looking at another product line. Their new drone helicopter is popular and they would like to sell what they can with no backorders.Β The CEO does not wish to hire and fire people during the year so he wants you hire a constant number of employees and maintain that size workforce.Β Review the attached file for the table of data and then answer the following questions:
- Β What daily production rate and number of employees will be necessary?
- How many units will be in inventory at the end of each quarter?
- Mullen Magic Shows is evaluating attendance at the shows and planning whether to train more magicians. Β They have the following data:
YearΒ Β Β Β Β Β Β Β Β Β Β Β Β Β Β Total Audience
2013Β Β Β Β Β Β Β Β Β Β Β Β Β Β 97130
2014Β Β Β Β Β Β Β Β Β Β Β Β Β Β 101326
2015Β Β Β Β Β Β Β Β Β Β Β Β Β Β 96956
2016Β Β Β Β Β Β Β Β Β Β Β Β Β Β 99816
2017Β Β Β Β Β Β Β Β Β Β Β Β Β Β 99694
2018Β Β Β Β Β Β Β Β Β Β Β Β Β Β 103762
2019Β Β Β Β Β Β Β Β Β Β Β Β Β Β 104958
2020Β Β Β Β Β Β Β Β Β Β Β Β Β Β 110988
2021Β Β Β Β Β Β Β Β Β Β Β Β Β Β 112157
2022Β Β Β Β Β Β Β Β Β Β Β Β Β Β 110370
- Plot these data, develop a hypothesis of an appropriate model, estimate the modelβs parameters, and forecast passengers for 2023-2025.
- Illustrate an exponential smoothing model using an alpha of .1 and then an alpha of .5.
- In doing some analysis, they assume each show has about 500 attendees.Β Each magician they hire can work up to 50 shows a year and is paid $1500 per show up to 50 shows.Β Recently, magicians complained that they are under contract for 50 shows but only paid for shows they work.Β If each magician is paid $500 per show she/he does not work, what does this policy cost per year?
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EAT223 β THERMOFLUIDS AND ENGINES
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University of Sunderland
Faculty of Applied Sciences
Department of Computing, Engineering and Technology
EAT223 β THERMOFLUIDS AND ENGINES
Assignment 1 of 1
The following learning outcomes will be assessed:
Knowledge
Critical knowledge of the fundamental concepts and analytical methods in the solution of a range of problems related to thermodynamics, fluid mechanics, and heat transfer.
Skills
Design and analyse a variety of air standard cycles and vapour power cycles.
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Β
Important Information
You are required to submit your work within the bounds of the University Infringement of Assessment Regulations (see your Programme Guide). Plagiarism, paraphrasing and downloading large amounts of information from external sources, will not be tolerated and will be dealt with severely. Although you should make full use of any source material, which would normally be an occasional sentence and/or paragraph (referenced) followed by your own critical analysis/evaluation. You will receive no marks for work that is not your own. Your work may be subject to checks for originality which can include use of an electronic plagiarism detection service.
Where you are asked to submit an individual piece of work, the work must be entirely your own. The safety of your assessments is your responsibility. You must not permit another student access to your work.
Where referencing is required, unless otherwise stated, the Harvard referencing system must be used (see your Programme Guide).
Please ensure that you retain a duplicate of your assignment. We are required to send samples of student work to the external examiners for moderation purposes. It will also safeguard in the unlikely event of your work going astray. Submission Date and Time | Before 4pm, Wednesday 22nd March 2017 |
Submission Location | SunSpace Dropbox |
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Β
Assignment help-EAT216 β COMPUTER AIDED ENGINEERING
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Moderated October 2016
University of Sunderland
Faculty of Applied Sciences
Department of Computing, Engineering and Technology
EAT216 β COMPUTER AIDED ENGINEERING
Assignment 3 of 3, 2016 – 2017
The following learning outcomes will be assessed:
Knowledge
An understanding of the use of commercial mathematical software packages to assist in solving engineering problems.
Skills
the ability to develop and analyse mathematical models of the behaviour
of a component or system due to external influences and so predict the performance of that component or system.
Important Information
You are required to submit your work within the bounds of the University Infringement of Assessment Regulations (see your Programme Guide). Plagiarism, paraphrasing and downloading large amounts of information from external sources, will not be tolerated and will be dealt with severely. Although you should make full use of any source material, which would normally be an occasional sentence and/or paragraph (referenced) followed by your own critical analysis/evaluation. You will receive no marks for work that is not your own. Your work may be subject to checks for originality which can include use of an electronic plagiarism detection service.
Where you are asked to submit an individual piece of work, the work must be entirely your own. The safety of your assessments is your responsibility. You must not permit another student access to your work.
Where referencing is required, unless otherwise stated, the Harvard referencing system must be used (see your Programme Guide).
Please ensure that you retain a duplicate of your assignment. We are required to send samples of student work to the external examiners for moderation purposes. It will also safeguard in the unlikely event of your work going astray.
Submission Date and Time
Before 4pm, Wednesday 15th March 2017
Submission Location
SunSpace Dropbox
Page 2 of 4
Moderated October 2016
Part 1: Drag coefficient for flow around a sphere
Using the tutorial provided concerning air flow around a sphere as a basis, you are required to
validate the SolidWorks flow simulation software. To do this, derive the drag coefficient CD at the
following Reynolds numbers: 1 10, 100, 10,000, and 100,000.
You will be required to compare your values with those shown in Fig. 1 (final page). To do this you
may use Fig. 1 and superimpose your values, plotted by hand. You should submit this as part of
your report.
Part 2: Flow over a cone
Develop a flow simulation for a three dimensional cone pointed into the airflow, as represented by
Fig. 2. You should create a three dimensional cone with the value of the half-vertex angle (Ξ΅)
assigned to you. This is the angle measured from the centreline of the cone to one of its walls, also
shown in Fig. 2. You should also derive the value of the drag coefficient CD, for a Reynolds number
anywhere in the range 105 and 106.
Fig. 2: Cone
Note that for both the sphere and the cone, Reynolds number is given by the following equation,
where D is the diameter of the sphere, or the base of the cone as shown in Fig. 2:
ο
ο²UD
Re ο½
You can assume the density and dynamic viscosity of air when using this equation are 1.177 kg/m3
and 1.846ο΄10-5 Pa s, respectively.
Ξ΅ D
Page 3 of 4
Moderated October 2016
Report
Your report should include the following information:
Description
Mark
Part 1
Demonstration of working simulation of flow over a sphere (in class).
10
Derivation of drag coefficient CD at the required values of the Reynolds number (report).
20
Plot of CD versus Re (report).
10
Part 2
Demonstration of working simulation of flow over a cone (in class).
10
A description of how the problem was tackled in SolidWorks. This should include any assumptions made and a tabulated summary of the boundary conditions used. It should also include screenshots of the model and mesh, and vector and contour plots of the resulting flow (report).
30
Derivation of drag coefficient CD, for a Reynolds number between 105 and 106 (the value you have used must be stated).
20
Marks will be deducted for untidy or illegible work.
Reference
Hoerner, S. F., 1965. Fluid-Dynamic Drag. 1st ed. Bricktown New Jersey: Hoerner Fluid Dynamics
K. Burn
October 2016
Page 4 of 4
Moderated October 2016
Fig. 1: CD versus Reynolds number for flow across a sphere (Aerospaceweb.org, 2012)
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CHEG 3300 β Mass Transfer-Mechanistic Engineering Approach to Improve Mass Transfer in Unit Operations
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Project Work (CHEG 3300 β Mass Transfer)
Mechanistic Engineering Approach to Improve
Mass Transfer in Unit Operations
Submission due dates: March 13 and April 21
Project Description
A chemical engineer has a task to enhance the hydrodynamic and mass transfer rate in the fluid by
developing a mechanistic engineering approach to vary the physical properties of the fluid,
intensify the absorption and diffusion process. One of the approaches could be incorporating
nanofluids or nanoparticles to enhance the performance of gas absorption systems. The principal
advantages of using nanoscopic fluids or nanoparticles are: (a) amount of chemical absorbents can
be decreased (b) tower or column height can be reduced, both by achieving larger mass transfer
coefficients with nanoscopic fluids or particles. The major objective of this project work is to
propose a comprehensive mass transfer model to enhance the mass transfer rate either in a packed
bed column or a plate column.
Investigate how to enhance the gas side mass transfer coefficient. Thoroughly investigate various
operating conditions by specifying the characteristic parameters of the system in the first step.
Consider a laminar flow for both the compressible gas and incompressible fluid. The effects of
pressure and concentration on the physical properties of the gas phase must be studied. It is
important in the first step to achieve the equilibrium state for the interacting components.
Investigate the transport properties such as molecular diffusion to achieve the state. Thoroughly
study the thermodynamics in the solution and how to accomplish the equilibrium steady states by
sequentially investigating the properties of the system, variables, parameters to be evaluated and
their corresponding boundary conditions to understand the contributions, limitations of latent heat
and sensible heat combined with hydrodynamic properties to maintain the equilibrium throughout
the column height.
Mass transfer coefficients can be influenced by the forces acting on the Brownian motions of the
nanoparticles. The direction of flow must be towards the interface. Your approach should be
directed towards increasing the mass transfer coefficients in the column resulting in larger
diffusion flux of the gas into the liquid phase. Consider the residence time distribution in the
column. For example, an increase in the gas flow rate reduces the residence time. Mass transfer
rate can be enhanced because of the large reaction rate. Facilitating larger liquid velocity closer to
the gas-liquid interface is another phenomenon that can enhance the mass transfer rate. Overall,
liquid flow rate plays an important role in the column performance.
Natural convection heat transfer of nanofluids can be considered. You should study the
advantages of using nanofluids compared to conventional micro fluids and how the volume
fraction of nanofluids has an advantage over the micro fluids. Study the heat conductivity
coefficient, enthalpy changes that limit the enhancement heat transfer of nano and micro fluids.
For example when compared to water, nanofluids deteriorate the convection heat transfer
(determined by the volume fraction). Also please note that the heat conductivity coefficient cannot
compensate for the increasing viscosity of the nanofluid. A continuity equation combined with
momentum equation (relating the above behavior) can be evaluated in terms of thermal
conductivity, specific heat and temperature of mixed nanofluid. Enhancement heat transfer can be
accomplished at high temperature differences. The driving force initially is derived from the
temperature difference. Adding nanoparticles not only increases the heat conductivity but also
increases the viscosity of the fluid which creates the viscous forces for the natural convection heat
transfer. At low temperatures, viscous forces play a major role for heat conduction. Therefore the
heat transfer performances at lower temperatures will be worse than the higher temperatures. You
also need to study on how to increase the collisions between these nanoparticles to increase
convection heat and mass transfer. Please note: (a) driving forces increase with temperature
difference (b) dynamic equilibrium in an equilibrium process can be at steady state, but a steady
state need not be in equilibrium in the irreversible process.
Assumptions: Assume that the mixed nanofluid is a continuous medium. There is no motion slip
between nanoparticles and fluids. But there should be thermal equilibrium between nanoparticles
and the mixed fluid. Neglect the effects of column shape, type of material and any presence of
rotating magnetic fields. Assume that the liquid phase composed of nanofluids is a homogeneous
continuous medium. Use fluid mechanics and hydraulic concepts to explain the hydrodynamic
behavior of the column. The liquid and gas flow counter currently in the column. The same
approach can be generalized for the entire column. In its standard state, the enthalpy change of
formation of any element has to be zero. (Note: Enthalpy is proportional to temperature change
or temperature gradient, only in an adiabatic process. An isothermal process will have enthalpy
change). The system has to be in dynamic equilibrium to achieve steady state.
Propose a continuity equation which captures the above phenomena mentioned for an
incompressible liquid phase and a compressible gas phase.
1. Assuming laminar flow, propose an equation of motion for the gas phase.
2. What can be the species continuity equations for liquid and gas phases in the column (nonconductive
systems)?
3. How do we derive the driving force for the overall mass diffusion flux? Use Fickβs law
combined with flow factors of the fluid.
4. Propose a gas phase and a liquid phase mass transfer model which explains the overall
phenomenon at the interface.
Target Assessment Dates:
A. By Monday, March 13, submit the outline/proposal (3-4 pages) for 50% grade:
ο A conceptual model of the proposed system β¦β¦β¦β¦β¦.. (15 points).
ο Proposed approach defining β¦β¦β¦β¦β¦β¦.(20 points)
o variables
o parameters and
o boundaries or limitations
ο Conditions leading to interfacial thermal equilibrium (steady state) β¦.(15 points)
B. By Friday, April 21, submit the following full project report (8-10 pages including the
previous proposal of March 13) for 50% grade:
ο Questions 1-4 mentioned above.
Project Write-Up Structure (valid only for the final report of April 21):
β’ Problem Statement β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦..(5 points)
β’ Task Identified (Include the proposal outline of Mar 13 here)….(5 points)
β’ Parameters Selected β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦………(5 points)
β’ Background β¦β¦β¦.β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦………(5 points)
β’ Approach β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦..(10 points)
β’ Description β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦…(10 points)
β’ Conclusion β¦β¦β¦.β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦…(5 points)
β’ References β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦………(5 points)
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