prepared by: miguel perez joel shepherd. build a java program to represent the finite- difference...
TRANSCRIPT
Prepared By:Miguel PerezJoel Shepherd
Build a Java Program to represent the Finite-Difference Method numerically and graphically for easy visualization of temperature distribution on a hot plate.
Temperature Distribution on a Hot Plate 2
This method is used to solve temperaturedistribution across a square plate.
3Temperature Distribution on a Hot Plate
We built a Java Program to calculate numerical solutions in increments to show visual representation of the temperature distribution. (See additional Resources on CD for Java code)
4Temperature Distribution on a Hot Plate
Example 1 (Output from Java program specifications)
5Temperature Distribution on a Hot
Plate
25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00
50.00 37.52 32.60 30.29 29.03 28.25 27.72 27.33 27.01 26.74 26.49 26.25 26.00 25.73 25.43 25.08 24.61 23.94 22.73 20.00
50.00 42.49 37.60 34.56 32.62 31.30 30.35 29.62 29.03 28.51 28.02 27.55 27.06 26.54 25.96 25.29 24.47 23.41 21.97 20.00
50.00 44.87 40.78 37.80 35.64 34.05 32.84 31.87 31.05 30.32 29.63 28.94 28.23 27.47 26.63 25.68 24.59 23.29 21.76 20.00
50.00 46.22 42.93 40.26 38.17 36.52 35.19 34.07 33.10 32.21 31.34 30.46 29.55 28.56 27.48 26.28 24.95 23.44 21.78 20.00
50.00 47.12 44.50 42.24 40.35 38.77 37.44 36.27 35.21 34.20 33.19 32.15 31.05 29.85 28.54 27.10 25.52 23.79 21.94 20.00
50.00 47.81 45.77 43.94 42.33 40.92 39.67 38.52 37.43 36.35 35.23 34.05 32.77 31.37 29.83 28.14 26.29 24.29 22.18 20.00
50.00 48.42 46.91 45.51 44.23 43.06 41.96 40.89 39.82 38.70 37.51 36.21 34.77 33.17 31.39 29.42 27.27 24.95 22.51 20.00
50.00 48.99 48.01 47.08 46.17 45.28 44.38 43.44 42.43 41.32 40.08 38.68 37.08 35.28 33.25 30.98 28.48 25.78 22.94 20.00
50.00 49.59 49.17 48.72 48.23 47.67 47.01 46.24 45.33 44.26 42.99 41.51 39.78 37.77 35.46 32.86 29.96 26.81 23.46 20.00
50.00 50.24 50.43 50.54 50.50 50.31 49.94 49.37 48.59 47.58 46.32 44.77 42.90 40.69 38.10 35.13 31.77 28.07 24.11 20.0050.00 50.98 51.88 52.59 53.07 53.29 53.24 52.90 52.27 51.35 50.11 48.52 46.54 44.13 41.25 37.87 33.99 29.64 24.92 20.00
50.00 51.87 53.57 54.99 56.04 56.70 56.98 56.89 56.43 55.62 54.42 52.82 50.76 48.18 45.01 41.21 36.73 31.61 25.96 20.00
50.00 52.96 55.64 57.85 59.51 60.63 61.24 61.39 61.11 60.42 59.30 57.73 55.63 52.93 49.52 45.30 40.18 34.15 27.32 20.00
50.00 54.37 58.23 61.34 63.63 65.19 66.10 66.47 66.36 65.80 64.79 63.29 61.23 58.49 54.93 50.36 44.59 37.51 29.17 20.00
50.00 56.31 61.65 65.71 68.59 70.49 71.62 72.15 72.18 71.75 70.88 69.53 67.61 64.98 61.43 56.68 50.37 42.15 31.86 20.00
50.00 59.24 66.39 71.33 74.59 76.63 77.84 78.43 78.54 78.24 77.55 76.42 74.78 72.45 69.19 64.61 58.11 48.88 36.13 20.00
50.00 64.29 73.35 78.70 81.84 83.69 84.74 85.26 85.39 85.21 84.72 83.91 82.68 80.91 78.33 74.49 68.58 59.15 43.77 20.00
50.00 74.59 84.06 88.29 90.42 91.58 92.20 92.51 92.60 92.51 92.26 91.83 91.18 90.21 88.75 86.46 82.61 75.39 59.79 20.00100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
Example 1 (Graph)
Temperature Distribution on a Hot Plate 6
Example 2 (Output from Java program specifications)
7Temperature Distribution on a Hot Plate
25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00
50.00 37.46 32.49 30.16 28.94 28.25 27.89 27.76 27.83 28.08 28.51 29.16 30.08 31.33 33.10 35.68 39.76 47.03 62.17 100.00
50.00 42.35 37.35 34.27 32.37 31.22 30.60 30.39 30.53 31.02 31.87 33.12 34.85 37.21 40.41 44.88 51.37 61.21 76.67 100.00
50.00 44.62 40.33 37.23 35.10 33.73 32.97 32.73 32.97 33.69 34.90 36.67 39.08 42.29 46.52 52.12 59.64 69.79 83.30 100.00
50.00 45.81 42.17 39.29 37.17 35.74 34.93 34.71 35.06 35.98 37.50 39.69 42.62 46.44 51.32 57.51 65.32 75.04 86.77 100.00
50.00 46.49 43.32 40.68 38.64 37.22 36.43 36.26 36.71 37.80 39.58 42.09 45.41 49.64 54.91 61.36 69.14 78.30 88.74 100.00
50.00 46.89 44.01 41.55 39.60 38.23 37.47 37.34 37.88 39.11 41.08 43.83 47.42 51.92 57.42 63.98 71.63 80.33 89.91 100.00
50.00 47.09 44.37 42.01 40.11 38.76 38.02 37.94 38.54 39.87 41.97 44.89 48.66 53.35 58.99 65.59 73.13 81.53 90.58 100.00
50.00 47.14 44.46 42.11 40.21 38.85 38.10 38.02 38.66 40.05 42.24 45.27 49.17 53.98 59.71 66.36 73.86 82.11 90.91 100.00
50.00 47.06 44.31 41.88 39.91 38.48 37.69 37.59 38.22 39.63 41.86 44.95 48.93 53.83 59.65 66.37 73.92 82.18 90.96 100.00
50.00 46.86 43.91 41.31 39.19 37.65 36.77 36.60 37.19 38.58 40.81 43.92 47.94 52.90 58.81 65.65 73.35 81.78 90.75 100.00
50.00 46.51 43.24 40.37 38.03 36.32 35.31 35.04 35.56 36.89 39.08 42.16 46.18 51.18 57.17 64.17 72.11 80.88 90.27 100.00
50.00 45.99 42.25 39.00 36.37 34.44 33.27 32.88 33.29 34.52 36.62 39.63 43.59 48.58 54.65 61.83 70.11 79.40 89.48 100.00
50.00 45.24 40.85 37.10 34.11 31.94 30.60 30.07 30.35 31.46 33.42 36.29 40.13 45.04 51.12 58.47 67.16 77.16 88.26 100.00
50.00 44.16 38.89 34.52 31.15 28.74 27.24 26.59 26.74 27.69 29.46 32.11 35.72 40.43 46.41 53.85 62.96 73.85 86.39 100.00
50.00 42.53 36.08 31.03 27.31 24.74 23.16 22.42 22.46 23.23 24.75 27.08 30.32 34.65 40.31 47.63 57.03 68.93 83.47 100.00
50.00 39.90 31.94 26.25 22.38 19.84 18.31 17.58 17.53 18.11 19.32 21.22 23.92 27.61 32.61 39.38 48.64 61.38 78.58 100.00
50.00 35.14 25.54 19.71 16.16 14.00 12.74 12.13 12.05 12.43 13.28 14.63 16.59 19.33 23.17 28.66 36.80 49.39 69.45 100.00
50.00 25.13 15.40 10.92 8.59 7.28 6.55 6.20 6.14 6.33 6.77 7.47 8.51 9.99 12.12 15.32 20.51 29.94 49.85 100.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Example 2 (Graph)
Temperature Distribution on a Hot Plate 8
Example 3 (Output from Java program specifications)
9Temperature Distribution on a Hot Plate
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
100.00 49.88 30.02 20.66 15.57 12.49 10.53 9.28 8.52 8.17 8.18 8.55 9.31 10.58 12.55 15.62 20.71 30.06 49.91 100.00
100.00 69.52 49.55 37.09 29.14 23.91 20.41 18.10 16.69 16.03 16.05 16.74 18.17 20.50 24.02 29.26 37.19 49.63 69.57 100.00
100.00 78.67 61.61 49.06 40.07 33.67 29.17 26.11 24.20 23.30 23.33 24.27 26.21 29.30 33.83 40.23 49.21 61.73 78.74 100.00
100.00 83.59 69.20 57.54 48.48 41.62 36.59 33.06 30.83 29.76 29.79 30.92 33.20 36.76 41.82 48.68 57.73 69.35 83.67 100.00
100.00 86.51 74.14 63.51 54.78 47.88 42.62 38.85 36.43 35.26 35.29 36.53 39.02 42.83 48.11 55.02 63.73 74.31 86.61 100.00
100.00 88.34 77.40 67.67 59.38 52.61 47.32 43.46 40.94 39.71 39.75 41.05 43.64 47.56 52.87 59.65 67.91 77.60 88.46 100.00
100.00 89.51 79.53 70.47 62.58 56.00 50.76 46.88 44.33 43.08 43.12 44.45 47.08 51.02 56.28 62.88 70.74 79.75 89.63 100.00
100.00 90.21 80.84 72.22 64.62 58.19 53.02 49.16 46.60 45.34 45.39 46.73 49.36 53.29 58.49 64.93 72.50 81.06 90.34 100.00
100.00 90.54 81.46 73.07 65.62 59.29 54.16 50.31 47.75 46.50 46.54 47.88 50.52 54.43 59.59 65.93 73.36 81.69 90.67 100.00
100.00 90.55 81.48 73.10 65.65 59.32 54.20 50.35 47.80 46.54 46.59 47.93 50.56 54.47 59.62 65.96 73.38 81.70 90.68 100.00
100.00 90.23 80.88 72.29 64.71 58.30 53.14 49.29 46.73 45.48 45.52 46.86 49.48 53.40 58.59 65.01 72.56 81.10 90.36 100.00
100.00 89.55 79.61 70.59 62.73 56.17 50.95 47.08 44.54 43.30 43.34 44.66 47.27 51.19 56.44 63.00 70.84 79.81 89.66 100.00
100.00 88.39 77.50 67.81 59.56 52.82 47.56 43.72 41.21 39.99 40.03 41.32 43.88 47.78 53.07 59.81 68.03 77.68 88.50 100.00
100.00 86.56 74.25 63.67 54.99 48.12 42.90 39.15 36.74 35.57 35.60 36.83 39.29 43.08 48.33 55.20 63.87 74.41 86.65 100.00
100.00 83.64 69.32 57.71 48.69 41.87 36.87 33.36 31.14 30.08 30.11 31.22 33.48 37.02 42.05 48.87 57.87 69.45 83.72 100.00
100.00 78.73 61.71 49.21 40.26 33.90 29.42 26.38 24.49 23.60 23.62 24.55 26.47 29.54 34.03 40.40 49.34 61.81 78.78 100.00
100.00 69.56 49.63 37.21 29.30 24.09 20.61 18.32 16.92 16.26 16.28 16.96 18.38 20.69 24.18 29.39 37.30 49.70 69.60 100.00
100.00 49.91 30.07 20.73 15.65 12.59 10.65 9.40 8.65 8.30 8.31 8.67 9.43 10.69 12.64 15.70 20.77 30.10 49.93 100.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Example 3 (Graph)
Temperature Distribution on a Hot Plate 10
This Java program can be very effective in measuring temperature distribution on a hot plate both numerically and visually through graphs. This program can also be used and modified for more difficult problems that are meticulous and timely to numerically equate by hand.
Temperature Distribution on a Hot Plate 11