1. Prepared By: Miguel Perez Joel Shepherd

2.  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 Plate2

3. This method is used to solve temperature distribution across a square plate. 3Temperature Distribution on a Hot Plate

4.  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

5. Example 1 (Output from Java program specifications) 5 Temperature Distribution on a Hot Plate 25.00 50.0037.5232.6030.2929.0328.2527.7227.3327.0126.7426.4926.2526.0025.7325.4325.0824.6123.9422.7320.00 50.0042.4937.6034.5632.6231.3030.3529.6229.0328.5128.0227.5527.0626.5425.9625.2924.4723.4121.9720.00 50.0044.8740.7837.8035.6434.0532.8431.8731.0530.3229.6328.9428.2327.4726.6325.6824.5923.2921.7620.00 50.0046.2242.9340.2638.1736.5235.1934.0733.1032.2131.3430.4629.5528.5627.4826.2824.9523.4421.7820.00 50.0047.1244.5042.2440.3538.7737.4436.2735.2134.2033.1932.1531.0529.8528.5427.1025.5223.7921.9420.00 50.0047.8145.7743.9442.3340.9239.6738.5237.4336.3535.2334.0532.7731.3729.8328.1426.2924.2922.1820.00 50.0048.4246.9145.5144.2343.0641.9640.8939.8238.7037.5136.2134.7733.1731.3929.4227.2724.9522.5120.00 50.0048.9948.0147.0846.1745.2844.3843.4442.4341.3240.0838.6837.0835.2833.2530.9828.4825.7822.9420.00 50.0049.5949.1748.7248.2347.6747.0146.2445.3344.2642.9941.5139.7837.7735.4632.8629.9626.8123.4620.00 50.0050.2450.4350.5450.5050.3149.9449.3748.5947.5846.3244.7742.9040.6938.1035.1331.7728.0724.1120.00 50.0050.9851.8852.5953.0753.2953.2452.9052.2751.3550.1148.5246.5444.1341.2537.8733.9929.6424.9220.00 50.0051.8753.5754.9956.0456.7056.9856.8956.4355.6254.4252.8250.7648.1845.0141.2136.7331.6125.9620.00 50.0052.9655.6457.8559.5160.6361.2461.3961.1160.4259.3057.7355.6352.9349.5245.3040.1834.1527.3220.00 50.0054.3758.2361.3463.6365.1966.1066.4766.3665.8064.7963.2961.2358.4954.9350.3644.5937.5129.1720.00 50.0056.3161.6565.7168.5970.4971.6272.1572.1871.7570.8869.5367.6164.9861.4356.6850.3742.1531.8620.00 50.0059.2466.3971.3374.5976.6377.8478.4378.5478.2477.5576.4274.7872.4569.1964.6158.1148.8836.1320.00 50.0064.2973.3578.7081.8483.6984.7485.2685.3985.2184.7283.9182.6880.9178.3374.4968.5859.1543.7720.00 50.0074.5984.0688.2990.4291.5892.2092.5192.6092.5192.2691.8391.1890.2188.7586.4682.6175.3959.7920.00 100.00

6. Example 1 (Graph) Temperature Distribution on a Hot Plate6

7. Example 2 (Output from Java program specifications) 7Temperature Distribution on a Hot Plate 25.00 50.0037.4632.4930.1628.9428.2527.8927.7627.8328.0828.5129.1630.0831.3333.1035.6839.7647.0362.17100.00 50.0042.3537.3534.2732.3731.2230.6030.3930.5331.0231.8733.1234.8537.2140.4144.8851.3761.2176.67100.00 50.0044.6240.3337.2335.1033.7332.9732.7332.9733.6934.9036.6739.0842.2946.5252.1259.6469.7983.30100.00 50.0045.8142.1739.2937.1735.7434.9334.7135.0635.9837.5039.6942.6246.4451.3257.5165.3275.0486.77100.00 50.0046.4943.3240.6838.6437.2236.4336.2636.7137.8039.5842.0945.4149.6454.9161.3669.1478.3088.74100.00 50.0046.8944.0141.5539.6038.2337.4737.3437.8839.1141.0843.8347.4251.9257.4263.9871.6380.3389.91100.00 50.0047.0944.3742.0140.1138.7638.0237.9438.5439.8741.9744.8948.6653.3558.9965.5973.1381.5390.58100.00 50.0047.1444.4642.1140.2138.8538.1038.0238.6640.0542.2445.2749.1753.9859.7166.3673.8682.1190.91100.00 50.0047.0644.3141.8839.9138.4837.6937.5938.2239.6341.8644.9548.9353.8359.6566.3773.9282.1890.96100.00 50.0046.8643.9141.3139.1937.6536.7736.6037.1938.5840.8143.9247.9452.9058.8165.6573.3581.7890.75100.00 50.0046.5143.2440.3738.0336.3235.3135.0435.5636.8939.0842.1646.1851.1857.1764.1772.1180.8890.27100.00 50.0045.9942.2539.0036.3734.4433.2732.8833.2934.5236.6239.6343.5948.5854.6561.8370.1179.4089.48100.00 50.0045.2440.8537.1034.1131.9430.6030.0730.3531.4633.4236.2940.1345.0451.1258.4767.1677.1688.26100.00 50.0044.1638.8934.5231.1528.7427.2426.5926.7427.6929.4632.1135.7240.4346.4153.8562.9673.8586.39100.00 50.0042.5336.0831.0327.3124.7423.1622.4222.4623.2324.7527.0830.3234.6540.3147.6357.0368.9383.47100.00 50.0039.9031.9426.2522.3819.8418.3117.5817.5318.1119.3221.2223.9227.6132.6139.3848.6461.3878.58100.00 50.0035.1425.5419.7116.1614.0012.7412.1312.0512.4313.2814.6316.5919.3323.1728.6636.8049.3969.45100.00 50.0025.1315.4010.928.597.286.556.206.146.336.777.478.519.9912.1215.3220.5129.9449.85100.00 0.00

8. Example 2 (Graph) Temperature Distribution on a Hot Plate8

9. Example 3 (Output from Java program specifications) 9Temperature Distribution on a Hot Plate 0.00 100.0049.8830.0220.6615.5712.4910.539.288.528.178.188.559.3110.5812.5515.6220.7130.0649.91100.00 69.5249.5537.0929.1423.9120.4118.1016.6916.0316.0516.7418.1720.5024.0229.2637.1949.6369.57100.00 78.6761.6149.0640.0733.6729.1726.1124.2023.3023.3324.2726.2129.3033.8340.2349.2161.7378.74100.00 83.5969.2057.5448.4841.6236.5933.0630.8329.7629.7930.9233.2036.7641.8248.6857.7369.3583.67100.00 86.5174.1463.5154.7847.8842.6238.8536.4335.2635.2936.5339.0242.8348.1155.0263.7374.3186.61100.00 88.3477.4067.6759.3852.6147.3243.4640.9439.7139.7541.0543.6447.5652.8759.6567.9177.6088.46100.00 89.5179.5370.4762.5856.0050.7646.8844.3343.0843.1244.4547.0851.0256.2862.8870.7479.7589.63100.00 90.2180.8472.2264.6258.1953.0249.1646.6045.3445.3946.7349.3653.2958.4964.9372.5081.0690.34100.00 90.5481.4673.0765.6259.2954.1650.3147.7546.5046.5447.8850.5254.4359.5965.9373.3681.6990.67100.00 90.5581.4873.1065.6559.3254.2050.3547.8046.5446.5947.9350.5654.4759.6265.9673.3881.7090.68100.00 90.2380.8872.2964.7158.3053.1449.2946.7345.4845.5246.8649.4853.4058.5965.0172.5681.1090.36100.00 89.5579.6170.5962.7356.1750.9547.0844.5443.3043.3444.6647.2751.1956.4463.0070.8479.8189.66100.00 88.3977.5067.8159.5652.8247.5643.7241.2139.9940.0341.3243.8847.7853.0759.8168.0377.6888.50100.00 86.5674.2563.6754.9948.1242.9039.1536.7435.5735.6036.8339.2943.0848.3355.2063.8774.4186.65100.00 83.6469.3257.7148.6941.8736.8733.3631.1430.0830.1131.2233.4837.0242.0548.8757.8769.4583.72100.00 78.7361.7149.2140.2633.9029.4226.3824.4923.6023.6224.5526.4729.5434.0340.4049.3461.8178.78100.00 69.5649.6337.2129.3024.0920.6118.3216.9216.2616.2816.9618.3820.6924.1829.3937.3049.7069.60100.00 49.9130.0720.7315.6512.5910.659.408.658.308.318.679.4310.6912.6415.7020.7730.1049.93100.00 0.00

10. Example 3 (Graph) Temperature Distribution on a Hot Plate10

11. 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 Plate11