MECH 419 Finite Element Methods in Engineering MECH928 Finite Element Techniques in Mechanical Engineering Assignment-2: FE modeling of 2D temperature distribution in a steel plate Project Description: This project aims to solve a 2D steady-state heat transfer in a plate which subjects to different boundary conditions by calculation and ANSYS software. Rules: 2. 1. The assignment may be completed individually or by a group of up to 2 students. The group formation is your own responsibility. Members may be from the same or different tutorial groups. 3. 4. 5. No collaboration between groups is permitted. Any case of plagiarism will be penalized, and students should make themselves aware of the university policies regarding plagiarism. The assignment should be submitted to Moodle. Late submission will incur a penalty as described in the subject outline. If the assignment is completed by the group, a statement indicating the effort or contribution to the assignment by each member and signed by all members must be included at the beginning of the report, or all students agree that they have contributed equally to the report -add a statement at the front of the report, signed by all members. The assignment must be submitted as a formal typed report. You need to include the analysis of the problem, the procedure for the FEM solution, and a discussion of the results. Problem: Consider a steady two-dimensional heat transfer in a thin steel plate whose cross-section is given in the following Figure. There is no heat generation within the plate; the temperature difference through the plate thickness (1 mm) is negligible. The thermal conductivity of the steel plate is 50 W/(m·ºC). The entire top surface ‘4-7-9' is subjected to constant heat flux q" = 2000W/m². The bottom surface ‘1-2-3' is maintained at 120°C. The left side surface ‘1-4' of the body is insulated; the right side surface '3-6-8-9' of the body is under convection with ambient air at Tf= 10 °C with a convection coefficient of h 100 W/(m²ºC). The mesh size is Ax = 0.15m, Ay = 0.2m for the calculation. The nodes are indexed by 1 to 9 in the Figure. Please determine the temperatures at each node. = For ANSYS, you can use any proper mesh type and mesh size to ensure accurate results. But you need to find the temperatures at the positions (1-9) to compare with that from the calculation. dy=0.2m q"=2000W/m² 7 (5) 8 dy=0.2m (3) (4) 4 (1) 5 6 (2) dy=0.2m dx=0.15m dx=0.15m 1 2 120°C 3 120°C 120°C Insulation Air Tf=10°C, h=100W/m².°C Part-1: Calculation, analysis and report (50 marks): (1) Use the finite element method to determine the temperature for each node. You are requested to construct the thermal conductance (stiffness)/load matrices for each element, then assembly them to global thermal conductance(stiffness)/load matrices; (30 marks) In the report, you need to show the procedure to determine the thermal conductance/stiffness and load matrices of each element, and to construct global thermal conductance(stiffness) and load matrices. (Tips: As for solving node temperature by global thermal conductance(stiffness) and load matrices is too difficult by hand, Matlab is recommended. The other program or excel can be used for this purpose. The code/excel file needs to be attached to your report as appendix, and also uploaded the relevant file to the submission link.) (2) You are requested to calculate the heat flux at positions 1, 2 and 3 to maintain the fixed temperatures of 120 °C (10 marks) In the report, you need to show the procedure on how to calculate the heat flux at positions 1, 2 and 3. (3) You are requested to calculate the temperature gradient at center of each element marks) (10 In the report, you need to show the procedure on how to calculate the temperature gradient at the center of each element. Part 2: ANSYS, analysis and report (50 marks): (4) You are requested to construct a 2D model in ANSYS, and use ANSYS to solve the question in Items 1 and 2 and compare them with your calculation; (30marks) In the report, you need to show the geometry of the body, the mesh of the model, boundary conditions, temperature, and heat flux results. You also need to show how to measure the temperature at Positions 1 to 9, and how to measure heat flux at Positions 1, 2 and 3. (Tips: The mesh size and type in ANSYS can be different from the calculation. But you need to determine the temperatures for the exact locations in Item 1, and heat flux in Item 2 for comparison). (5) The thickness of the plate is 1mm. Use ANSYS to determine average reaction heat transfer rate acting on the bottom surface ‘1-2-3', right surface ‘3-6-8-9' and left surface '1-4'. You also need to determine the heat transfer rate at the top surface ‘4-7-9'. Then you are requested to discuss the energy balance of the system. (5 marks) (Tips: In ANSYS, you can use the reaction probe shows the Heat transfer rate). (6) By using ANSYS, plot the temperatures along the line ‘4-5-6' for three convection coefficients acting on the right edge ‘3-6-8-9', 10 W/(m2.ºC), 100 W/(m2.ºC), and 200 W/(m2.ºC), and discuss the results. (5 marks). (Tips: In ANSYS, you can construct the 'path' for this purpose). (7) Use ANSYS to carry out a coupled thermal-stress analysis to determine Von-Mises stresses due to thermal change. Please discuss the results based on the boundary conditions. For this task, you need to change the material to ‘structural steel' from ANSYS Engineering data for steady-state thermal and static structural analysis. Please assume the fixe support on the bottom edge ‘1-2-3', and left edge ‘1-4' (10marks)