代写Capstone Project in Mathematical Sciences III代写C/C++程序
- 首页 >> C/C++编程Capstone Project in
Mathematical Sciences III
Applied Mathematics Project
Student Project Choices
School of Mathematical Sciences
July 31, 2025
Introduction
Below are four mass and heat exchange processes which are project options for the Applied Project in this course. The first two are mass exchange processes, the second two are energy exchange processes. The references supplied give some further information to assist you with deciding on what problems interest you. As part of your project you will need to do your own research and find additional information. At this stage, please read this document and any other information you wish, and decide on your top two preferences in preparation for working out what each person does.
Note that the links provided were valid at the time these project descriptions were prepared but have not been checked recently. Hence they are not guaranteed to work. However the descriptions provide enough key words to do a Google search.
1 The Heart-Lung Machine
Background
The heart-lung machine was invented by John Heysham Gibbon (1903-1973), to take over the functions of the heart and lungs during open heart surgery. His first machine was build in 1937, but it wasn’t used successfully in such an operation on a human until 1953 [2]. Now heart-lung machines are used routinely in heart surgery. In addition, they are used in “extracorporeal membrane oxygenation” to assist newborns/children/adults with unde- veloped/failing heart and/or lungs [3]. During development of the machine a number of different methods for oxygenating the blood were tried, with the “membrane lung” becoming the method of choice.
Task
You are to develop a mathematical model of membrane-lung oxygenation to determine the concentrations of oxygen and/or carbon dioxide in the blood as it passes through the machine. You might consider whether the heart-lung machine should be operated in a counter-current (gas and blood flowing in opposite directions) or co-current (gas and blood flowing in the same direction) configuration. For a discussion of the same issue in the context of heat exchange see [1]. What use(s) might a model such as yours have?
2 Haemodialysis
Background
In a healthy person, the kidneys cleanse the blood. In cases of severe kidney failure dialysis may be necessary to remove waste products and water from the blood. Two kinds of dialysis are currently available: haemodialysis, for which the blood is removed from the body for cleansing and then returned, and peritoneal dialysis, in which the blood is treated within the body [4]. You are to consider haemodialysis [5, Pstras & Waniewski(2019)].
Task
You are to develop a mathematical model of haemodialysis so as to determine the change in concentrations of waste products in the blood as it passes through the dialysis unit. You might consider whether the dialyser should be operated in a counter-current (dialysate and blood flowing in opposite directions) or co-current (dialysate and blood flowing in the same direction) configuration. For a discussion of the same issue in the context of heat exchange see [1]. What use(s) might a model such as yours have?
3 Lake-Source Cooling
Background
An interesting environmental initiative to use the cold water of Cayuga Lake to provide cooling for Cornell University and Ithaca High School, New York State, USA, was proposed in 1994 and was completed in 2000 [6]. It received numerous awards, including the Association of Energy Engineers Energy Project of the Year (2001) and the New York State Society of Professional Engineers Engineering Achievement of the Year Award (2001), to name just two. The temperature of the water being returned to the lake was an environmental issue that caused some concern.
Task
You are to develop a mathematical model of the heat exchange process to determine the temperature of the water returned to the lake and/or the cooling of the water from the University/High School. A heat exchanger may be used with a counter-current (hot and cold streams flowing in opposite directions) or co-current (hot and cold streams flowing in the same direction) configuration. You might investigate which configuration is best. For a discussion of this issue see [1]. What use(s) might a model such as yours have?
4 Continuous Pasteurization
Background
Pasteurization of milk (and other fluid foods) requires that the milk be heated to a pre- scribed minimum temperature and held at that temperature for a minimum period of time, before being cooled. There are two basic methods for achieving this, a batch method and a continuous method [7]. You are to consider the continuous method [8, Aquiar & Gut(2014].
Task
You are to develop mathematical models of the heat exchange processes in the “regenerator”, “heater” and/or “cooler” sections of a HTST continuous pasteurizer to determine the change in temperature of the milk. You might consider whether heat exchangers should be operated in a counter-current (hot and cold streams flowing in opposite directions) or co-current (hot and cold streams flowing in the same direction) configuration. For a discussion of this issue see [1]. What use(s) might a model such as yours have?
References
[1] R.J. Brogan, Heat exchangers, Thermopedia, https://www.thermopedia.com/ content/832/, viewed 19 August 2022.
[2] Wikipedia, Heart-lung machine, https://en.wikipedia.org/wiki/Cardiopulmonary_ bypass, viewed 19 August 2022.
[3] Wikipedia, Extracorporeal membrane oxygenation, https://en.wikipedia.org/wiki/ Extracorporeal_membrane_oxygenation, viewed 19 August 2022.
[4] National Kidney Foundation, Dialysis, https://www.kidney.org/atoz/content/ dialysisinfo, viewed 19 August 2022.
[5] National Institute of Diabetes and Digestive Kidney Diseases, Hemodial- ysis, https://www.niddk.nih.gov/health-information/kidney-disease/ kidney-failure/hemodialysis, viewed 19 August 2022.
[Pstras & Waniewski(2019)] L. Pstras, J. Waniewski, Mathematical Modelling of Haemodial- ysis: cardiovascular response, body fluid shifts and solute kinetics. Springer Nature
Switzerland AG (2019). https://doi.org/10.1007/978-3-030-21410-4
[6] Cornell University, Lake source cooling, https://medium.com/cornell-university/ lake-source-cooling-d307913dfc47, viewed 19 August 2022.
[7] International Dairy Foods Association, Pasteurization, https://www.idfa.org/ pasteurization, viewed 19 August 2022.
[8] Zwirner Equipment Company, What is HTST pasteurization? https://www .
zwirnerequipment.com/blog/what-is-htst-pasteurization/, viewed 19 August 2022.
[Aquiar & Gut(2014] H.F. Aguiar, J.A.W. Gut (2014) Continuous HTST pasteurization of liquid foods with plate heat exchangers: Mathematical modeling and experimental val- idation using a time-temperature integrator, Journal of Food Engineering 123, 78-86. http://dx.doi.org/10.1016/j.jfoodeng.2013.09.022