(1) Use the finite element method to determine the temperature for each node.

Consider steady two-dimensional heat transfer in an aluminum thin plate whose cross section is given in the following figure. There is no heat generation; the temperature difference through the plate thickness is negligible. The thermal conductivity of the aluminum plate is 170 W/(moC) The entire top surface is subjected to convection with ambient air at Tf = 30oC with a convection coefficient of h = 50 W/(m2oC). The bottom surface is maintained at 100 oC. The left side surface of the body is insulated; the right side surface of the body is under constant heat flux q`` = 1000W/m2. The mesh size is x = 0.015m, y = 0.02m. 
Insulation
q``=1000W/m2
dy=0.02m
dx=0.015m
100oC
Air Tf=30oC, h=50W/m2.oC 
BA
100oC 100oC
dx=0.015m
dy=0.02m
dy=0.02m 
(1) Use the finite element method to determine the temperature for each node. You are requested to manually construct the global stiffness matrix and global load matrix; the solution can be calculated by matlab). (40 marks)  
(2) Use ANSYS to solve the question in Item 1 and compare it with your manual calculation; (40marks)  
(3) Plot the temperatures between points A and B for three convection coefficients (h), 10 W/(m2oC), 50 W/(m2oC) and 100 W/(m2oC), and discuss the results. You can solve the results for h=10 W/(m2oC) and h=100 W/(m2oC) either manually or using ANSYS. (20 marks).      
Dr. Hongtao Zhu May



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