========== STEADY HEAT TRANSFER ANALYSIS ========== =========== BY BEM USING LINEAR ELEMENT =========== == ALONG WITH STRAIGHT FORMATION OF [A]{X}={RHS} == ==== ELEMENT INFORMATION ==== ELEMENT # NODE(1) NODE(2) B.C. B-VALUE(1) B-VALUE(2) ------------------------------------------------------------------------- 1 1 2 NUEMANN 0.1591549 0.1591549 2 2 3 NUEMANN 0.1591549 0.1591549 3 3 4 NUEMANN 0.1591549 0.1591549 4 4 5 NUEMANN 0.1591549 0.1591549 5 5 6 NUEMANN 0.1591549 0.1591549 6 6 7 NUEMANN 0.1591549 0.1591549 7 7 8 NUEMANN 0.1591549 0.1591549 8 8 9 NUEMANN 0.1591549 0.1591549 9 9 10 NUEMANN 0.1591549 0.1591549 10 10 11 NUEMANN 0.1591549 0.1591549 11 11 12 NUEMANN 0.1591549 0.1591549 12 12 13 NUEMANN 0.1591549 0.1591549 13 13 14 NUEMANN 0.1591549 0.1591549 14 14 15 NUEMANN 0.1591549 0.1591549 15 15 16 NUEMANN 0.1591549 0.1591549 16 16 1 NUEMANN 0.1591549 0.1591549 17 17 18 NUEMANN -0.1591549 -0.1591549 18 18 19 NUEMANN -0.1591549 -0.1591549 19 19 20 NUEMANN -0.1591549 -0.1591549 20 20 21 NUEMANN -0.1591549 -0.1591549 21 21 22 NUEMANN -0.1591549 -0.1591549 22 22 23 NUEMANN -0.1591549 -0.1591549 23 23 24 NUEMANN -0.1591549 -0.1591549 24 24 25 NUEMANN -0.1591549 -0.1591549 25 25 26 NUEMANN -0.1591549 -0.1591549 26 26 27 NUEMANN -0.1591549 -0.1591549 27 27 28 NUEMANN -0.1591549 -0.1591549 28 28 29 NUEMANN -0.1591549 -0.1591549 29 29 30 NUEMANN -0.1591549 -0.1591549 30 30 31 NUEMANN -0.1591549 -0.1591549 31 31 32 NUEMANN -0.1591549 -0.1591549 32 32 17 NUEMANN -0.1591549 -0.1591549 == NODAL INFOMATION AND SOLUTION OF TEMPERATURE == NODAL # X-COORDINATE Y-COORDINATE TEMPERATURE FREE TERM ------------------------------------------------------------------------ 1 0.9238795 2.617316 -0.2723531 0.5625000 2 0.7071068 2.292893 -0.2530663 0.5625000 3 0.3826834 2.076120 -0.2387373 0.5625001 4 -0.4371139E-07 2.000000 -0.2333827 0.5624999 5 -0.3826835 2.076120 -0.2387373 0.5625001 6 -0.7071068 2.292893 -0.2530663 0.5625000 7 -0.9238796 2.617317 -0.2723531 0.5625000 8 -1.000000 3.000000 -0.2924490 0.5625000 9 -0.9238795 3.382684 -0.3102838 0.5625000 10 -0.7071066 3.707107 -0.3239759 0.5625000 11 -0.3826831 3.923880 -0.3325072 0.5625000 12 0.1192488E-07 4.000000 -0.3353972 0.5625000 13 0.3826836 3.923879 -0.3325072 0.5625000 14 0.7071070 3.707107 -0.3239759 0.5625000 15 0.9238796 3.382684 -0.3102837 0.5625000 16 1.000000 3.000000 -0.2924490 0.5625000 17 0.9238795 -3.382684 0.3102838 0.5625000 18 0.7071068 -3.707107 0.3239759 0.5625000 19 0.3826834 -3.923880 0.3325072 0.5625001 20 -0.4371139E-07 -4.000000 0.3353972 0.5624999 21 -0.3826835 -3.923880 0.3325072 0.5625001 22 -0.7071068 -3.707107 0.3239759 0.5625000 23 -0.9238796 -3.382683 0.3102837 0.5625000 24 -1.000000 -3.000000 0.2924490 0.5625000 25 -0.9238795 -2.617316 0.2723531 0.5625000 26 -0.7071066 -2.292893 0.2530663 0.5625000 27 -0.3826831 -2.076120 0.2387373 0.5625000 28 0.1192488E-07 -2.000000 0.2333827 0.5625000 29 0.3826836 -2.076121 0.2387374 0.5625000 30 0.7071070 -2.292893 0.2530663 0.5625000 31 0.9238796 -2.617316 0.2723531 0.5625000 32 1.000000 -3.000000 0.2924490 0.5625000 === SOLUTION OF HEAT FLUX === ELEMENT # HEAT FLUX(1) HEAT FLUX(2) ------------------------------------------- 1 0.1591549 0.1591549 2 0.1591549 0.1591549 3 0.1591549 0.1591549 4 0.1591549 0.1591549 5 0.1591549 0.1591549 6 0.1591549 0.1591549 7 0.1591549 0.1591549 8 0.1591549 0.1591549 9 0.1591549 0.1591549 10 0.1591549 0.1591549 11 0.1591549 0.1591549 12 0.1591549 0.1591549 13 0.1591549 0.1591549 14 0.1591549 0.1591549 15 0.1591549 0.1591549 16 0.1591549 0.1591549 17 -0.1591549 -0.1591549 18 -0.1591549 -0.1591549 19 -0.1591549 -0.1591549 20 -0.1591549 -0.1591549 21 -0.1591549 -0.1591549 22 -0.1591549 -0.1591549 23 -0.1591549 -0.1591549 24 -0.1591549 -0.1591549 25 -0.1591549 -0.1591549 26 -0.1591549 -0.1591549 27 -0.1591549 -0.1591549 28 -0.1591549 -0.1591549 29 -0.1591549 -0.1591549 30 -0.1591549 -0.1591549 31 -0.1591549 -0.1591549 32 -0.1591549 -0.1591549 === TEMPERATURE VALUES AT INTERNAL POINTS === POINT # X-COORDINATE Y-COORDINATE CI*TEMPERATURE FREE TERM -------------------------------------------------------------------------- 1 0.0000000E+00 -63.00000 0.1585578E-01 1.000000 2 0.0000000E+00 -61.00000 0.1637654E-01 1.000000 3 0.0000000E+00 -59.00000 0.1693271E-01 1.000000 4 0.0000000E+00 -57.00000 0.1752802E-01 1.000000 5 0.0000000E+00 -55.00000 0.1816676E-01 1.000000 6 0.0000000E+00 -53.00000 0.1885387E-01 1.000000 7 0.0000000E+00 -51.00000 0.1959507E-01 1.000000 8 0.0000000E+00 -49.00000 0.2039702E-01 1.000000 9 0.0000000E+00 -47.00000 0.2126751E-01 1.000000 10 0.0000000E+00 -45.00000 0.2221573E-01 1.000000 11 0.0000000E+00 -43.00000 0.2325262E-01 1.000000 12 0.0000000E+00 -41.00000 0.2439123E-01 1.000000 13 0.0000000E+00 -39.00000 0.2564734E-01 1.000000 14 0.0000000E+00 -37.00000 0.2704018E-01 1.000000 15 0.0000000E+00 -35.00000 0.2859343E-01 1.000000 16 0.0000000E+00 -33.00000 0.3033656E-01 1.000000 17 0.0000000E+00 -31.00000 0.3230680E-01 1.000000 18 0.0000000E+00 -29.00000 0.3455181E-01 1.000000 19 0.0000000E+00 -27.00000 0.3713364E-01 1.000000 20 0.0000000E+00 -25.00000 0.4013470E-01 1.000000 21 0.0000000E+00 -23.00000 0.4366678E-01 1.000000 22 0.0000000E+00 -21.00000 0.4788567E-01 1.000000 23 0.0000000E+00 -19.00000 0.5301529E-01 1.000000 24 0.0000000E+00 -17.00000 0.5939001E-01 1.000000 25 0.0000000E+00 -15.00000 0.6753337E-01 1.000000 26 0.0000000E+00 -13.00000 0.7831687E-01 1.000000 27 0.0000000E+00 -11.00000 0.9331563E-01 1.000000 28 0.0000000E+00 -9.000000 0.1157329 1.000000 29 0.0000000E+00 -8.000000 0.1317931 1.000000 30 0.0000000E+00 -7.000000 0.1534268 1.000000 31 0.0000000E+00 -6.000000 0.1845030 1.000000 32 0.0000000E+00 -5.000000 0.2342072 1.000000 33 0.0000000E+00 -4.250000 0.3000386 1.000000 34 0.0000000E+00 -3.750000 0.1276730E-02 0.6839310E-06 35 0.0000000E+00 -3.250000 0.1150151E-02 0.1256717E-11 36 0.0000000E+00 -2.750000 0.9660174E-03 0.1256755E-11 37 0.0000000E+00 -2.250000 0.7108614E-03 0.6839299E-06 38 0.0000000E+00 -1.500000 0.1619845 1.000000 39 0.0000000E+00 -1.000000 0.1030793 1.000000 40 0.0000000E+00 -0.5000000 0.5023772E-01 1.000000 41 0.0000000E+00 -0.1000000E-03 0.9961606E-05 1.000000 42 0.0000000E+00 0.1000000E-03 -0.9969714E-05 1.000000 43 0.0000000E+00 0.5000000 -0.5023773E-01 1.000000 44 0.0000000E+00 1.000000 -0.1030793 1.000000 45 0.0000000E+00 1.500000 -0.1619845 1.000000 46 0.0000000E+00 2.250000 -0.7108615E-03 0.6839310E-06 47 0.0000000E+00 2.750000 -0.9660174E-03 0.1256925E-11 48 0.0000000E+00 3.250000 -0.1150151E-02 0.1256749E-11 49 0.0000000E+00 3.750000 -0.1276730E-02 0.6839299E-06 50 0.0000000E+00 4.250000 -0.3000386 1.000000 51 0.0000000E+00 5.000000 -0.2342072 1.000000 52 0.0000000E+00 6.000000 -0.1845030 1.000000 53 0.0000000E+00 7.000000 -0.1534268 1.000000 54 0.0000000E+00 8.000000 -0.1317931 1.000000 55 0.0000000E+00 9.000000 -0.1157329 1.000000 56 0.0000000E+00 11.00000 -0.9331563E-01 1.000000 57 0.0000000E+00 13.00000 -0.7831687E-01 1.000000 58 0.0000000E+00 15.00000 -0.6753337E-01 1.000000 59 0.0000000E+00 17.00000 -0.5939001E-01 1.000000 60 0.0000000E+00 19.00000 -0.5301529E-01 1.000000 61 0.0000000E+00 21.00000 -0.4788567E-01 1.000000 62 0.0000000E+00 23.00000 -0.4366678E-01 1.000000 63 0.0000000E+00 25.00000 -0.4013470E-01 1.000000 64 0.0000000E+00 27.00000 -0.3713364E-01 1.000000 65 0.0000000E+00 29.00000 -0.3455181E-01 1.000000 66 0.0000000E+00 31.00000 -0.3230680E-01 1.000000 67 0.0000000E+00 33.00000 -0.3033656E-01 1.000000 68 0.0000000E+00 35.00000 -0.2859343E-01 1.000000 69 0.0000000E+00 37.00000 -0.2704018E-01 1.000000 70 0.0000000E+00 39.00000 -0.2564734E-01 1.000000 71 0.0000000E+00 41.00000 -0.2439123E-01 1.000000 72 0.0000000E+00 43.00000 -0.2325262E-01 1.000000 73 0.0000000E+00 45.00000 -0.2221573E-01 1.000000 74 0.0000000E+00 47.00000 -0.2126751E-01 1.000000 75 0.0000000E+00 49.00000 -0.2039702E-01 1.000000 76 0.0000000E+00 51.00000 -0.1959507E-01 1.000000 77 0.0000000E+00 53.00000 -0.1885387E-01 1.000000 78 0.0000000E+00 55.00000 -0.1816676E-01 1.000000 79 0.0000000E+00 57.00000 -0.1752802E-01 1.000000 80 0.0000000E+00 59.00000 -0.1693271E-01 1.000000 81 0.0000000E+00 61.00000 -0.1637654E-01 1.000000 82 0.0000000E+00 63.00000 -0.1585578E-01 1.000000