It is a heat transfer problem
ME 332 Design Project 1 Due: May 3rd by 10:00 am You will need to upload the assignment to Gradescope by the required day and time. In this project, you will need to analyze heat transfer within a cylinder of an internal combustion engine. Figure 1 provides a schematic of the cylinder. Note that the actual object is three-dimensional and is axisymmetric around the centerline of the figure. There is a constant heat generation (�̇�) inside the cylinder; this heat escapes through the head (shown as the brown walls) and through the piston. The piston is a rigid assembly comprising of a shaft (blue), top and bottom plates (grey), and ring (yellow). The bottom of the piston and the section of shaft outside of the piston are exposed to oil with a given convective coefficient and temperature. You may neglect radiative losses into the oil. Note: Do not assume that T1 and T2 are similar temperatures. You will need to determine: a) Max heat generation (�̇�) such that T10 is less than 500 K. This will avoid overheating the engine. b) How does changing L3 affect the max heat generation which is allowed and why? c) Heat transfer from cylinder (i.e. region with heat generation) to atmosphere through top and walls of head (brown). d) Heat transfer from cylinder to piston. e) All labeled temperatures. Are the temperatures reasonable? Use your engineering judgement and be sure to include your reasoning (e.g., what is the melting point of the material?) f) Plot of temperature in fin as a function of distance from base to tip (T9 to T10). Encouraged Learning (not required): Find the thermal stress in both the shaft and the ring due to the difference in thermal expansion between the two. You will need to use the equations provided. Assumptions: 1. The walls surrounding the piston (i.e., black) have k=0 W/m-K. 2. There is no radiative or convective heat transfer inside the piston (i.e. enclosed within the yellow). Note that there is radiation exchange between the cylinder (i.e., the brown) with the surroundings. 3. All parts of the piston (top and bottom plates, ring, and shaft) are all rigidly bonded, meaning no separation can occur. 4. Use the convective heat transfer condition for the fin tip. 5. Note: You can assume that T1 and T2 are similar temperatures. Deliverables: 1. Report. Including: a. A copy of the completed table (within your report), which is provided. Do not change the format of the table. You will miss points if you do not maintain the format. b. An appendix showing the details of your work (e.g. energy balance, equations used, etc.). This can be handwritten, but should be neat and show clearly what you did. You will lose points if it difficult to understand your work. 2. An electronic copy of your spreadsheet and code which was used for your analysis. Report: Your report will be graded for being professional and complete. It is to be no longer than 2 Pages (not including the appendix). You want to convey the approach that you used, assumptions and constraints. Your report must include these sections for full credit: objective, approach (e.g., what equations or correlations did you use), design constraints, assumptions, solutions to items (a) – (f), and conclusions. Plots are encouraged (in the report of appendix) Spreadsheet: You need to determine the values for the spreadsheet provided. You will need to upload the spreadsheet and any codes that you developed to Gradescope by the required time. Grading Matrix: Correct answer (25%), correct approach (45%), and professional report (30%). Because most of your points are earned by having the correct approach, be sure to articulate clearly and concisely the approach you took to determine a solution. Expectations: You are encouraged to work with one partner in completing this assignment. However, you and partner are to do your work individually (i.e. you cannot copy from other groups or from previous classes). You will submit one set of deliverables for your team. Hints: 1. Start early. 2. Use engineering judgement. You will need to make assumptions to be able to solve the problem. These should be listed and justified (if appropriate). 3. Anticipate referencing multiple chapters from the book. 4. You can see the process I used in the spreadsheet (which you must complete). This may give you hints about an approach. 5. You may need to use solver functions to determine values. 6. It can be solved using Excel – avoid the trap of thinking you will not able to solve the problem because of coding challenges. 7. Do not forget about the contact resistance between piston plates (grey) and the shaft (blue) and ring (yellow). See values labeled at “R” within the spreadsheet. 8. You will need to iterate in order to find correct values for T11 and T12. 9. EES is a tool that may prove useful for this project. Useful Equations for Encouraged Learning: 1. ? = ??? ∗ ?? ∗ ? (free thermal deflection of a column: CTE is coefficient of thermal expansion, ?? is change in temperature from room temp., l is length) 2. ? = ?? ? (stiffness of a column: A is cross sectional area, E is modulus of elasticity, l is length) 3. ????? = ( ??ℎ??? ??ℎ???+????? )∗∆?∗? ????? (normal stress in ring) 4. ??ℎ??? = ( ????? ??ℎ???+????? )∗∆?∗? ????? (normal stress in shaft) 5. ????? = ? + ? (this will be different for the shaft and the ring) 6. ∆? = ????? − ??ℎ??? Schematic: Cross section shown is axisymmetric about the centerline.