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1 1P 94P
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4 Ra : : g : C : : Pr : : Nu : : h : B :
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7 ( )
8 DC (Bau [1])
9 : u = u(t) (1) 1 : u& = Raρ T cos( θ) dθ Pu (2) π 2 T T : T & = u + β + [ T (, t) T ] 2 W θ θ θ (3) -
10 T W 0 ( t) + Wn ( t)sin( nθ) n= 1 ( θ, t) = W (4) T ( θ, t) = n= 1 S n ( t)sin( nθ) + Cn ( t) + C ( t) cos( nθ) n (5) (4),(5) (1),(3) u& = c u p (6) c& = us c (7) s& uc s Ra[ 1+ εf ( t)] (8) =0 (6) (8) (Lorenz [3]) (Lorenz [3])
11 (Lorenz [3]) ( ) Lorenz equations : x& =σ( y x) (9) y& = rx y xz (10) z & = bz + xy (11)
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17 780mm
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19 3 l/min 15 l/min
20 TakadaRiken TR DIGITAL MULUTIMETER ADVANTEST R6511 DIGITAL MULTIMETER TakadaRiken TR UNIVERSAL SCANNER
21 YEW TYPE3056 PEN RECORDER
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23 RIKO SLIDE TRANS TYPE RSD-10A CAP 1KVA INPUT 100V
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27 1. 25mm 20mm
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30 760m 10mm 10mm left bottom right
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39 5W 20 temperature( ) right bottom left time(sec) 4000 Fig4.2
40 20W 22 temperature( ) 20 left bottom right time(sec) Fig4.3
41 21 30W bottom temperature( ) left right time(sec) Fig4.4
42 30W 2 22 right temperature( ) bottom left time(sec) Fig4.5
43 40W 22 left temperature( ) bottom 19 right time(sec) 4000 Fig4.6
44 23 40W 22 left temperature( ) bottom 19 right time(sec) Fig4.7
45 50W 22 right temperature( ) 20 bottom left time(sec) 3000 Fig4.8
46 55W left 22 temperature( ) 20 bottom 18 right time(sec) Fig4.9
47 60W left 22 temperature( ) 20 bottom 18 right time(sec) Fig4.10
48 65W 24 right temperature( ) bottom left time(sec) 2000 Fig4.11
49 65W 24 right temperature( ) bottom left time(sec) 2000 Fig4.11
50 75W 24 temperature( ) right bottom left time(sec) 3000 Fig4.12
51 75W 24 temperature( ) right bottom left time(sec) Fig4.13
52 100W 26 right temperature( ) bottom left time(sec) Fig4.14
53 100W 26 right temperature( ) bottom left time(sec) Fig4.16
54 200W 30 right temperature( ) left bottom time(sec) Fig4.17
55 30 200W right temperature( ) 25 bottom left time(sec) Fig4.18
56 300W 35 right temperature( ) left bottom time(sec) Fig4.19
57 W right temperature( ) bottom left time(sec) Fig4.20
58 40 500W right temperature( ) 30 bottom left time(sec) Fig4.21
59 500W temperature( ) right bottom 26 left time(sec) Fig4.22
60 45 800W right 40 temperature( ) 35 bottom 30 left time(sec) Fig4.23
61 45 800W right 40 temperature( ) 35 bottom 30 left time(sec) Fig4.24
62 50 right 1000W 45 temperature( ) bottom 30 left time(sec) Fig4.25
63 W 45 right temperature( ) bottom left time(sec) Fig4.26
64 23 40W temperature( ) time(sec) Fig4.27
65 W temperature( ) time(sec) Fig4.28
66 24 60W 1 temperature( ) time(sec) Fig4.29
67 24 60W 1 temperature( ) time(sec) Fig4.30
68 70W temperature( ) time(sec) Fig4.31
69 100W temperature( ) time(sec) 680 Fig4.32
70 25 200W 3 temperature( ) time(sec) Fig4.33
71 400W temperature( ) time(sec) Fig4.34
72 50W frequency(hz) Fig4.35
73 50W 80 l 60 b r frequency(hz) Fig4.36
74 200 60W frequency(hz) Fig4.37
75 200 60W frequency(hz) Fig4.38
76 200 60W b 100 r l frequency(hz) Fig4.39
77 75W 60 r 40 b 20 l frequency(hz) Fig4.40
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80 [1]Haim H.Bau and YuZou Wang, Chaos: A Heat Transfer Perspective, Annual Review of Heat Transfer [2]P.Wealander, On the Oscillatory Instability of Differentially Heated Fluid loops, J.Fluid Mech.,vol29,pp.17-30,1967. [3]Edward N Lorenz, Deterministic Nonperiodic Flow, J Atmospheric Sci.,vol.20,pp ,1963. [4],,
81 Eq: %0i*X^i (i=0-9) %00 = e+00 %01 = e+01 %02 = e+01 %03 = e+01 %04 = e+01 %05 = e+01 %06 = e+00 %07 = e+00 %08 = e-01 %09 = e-03 points = 16 <DY^2> = e-01 r or R = e-01
82 Eq: %0i*X^i (i=0-9) %00 = e+00 %01 = e+01 %02 = e+01 %03 = e+01 %04 = e+01 %05 = e+01 %06 = e+00 %07 = e+00 %08 = e-01 %09 = e-03 points = 16 <DY^2> = e-01 r or R = e-01
83 Eq: %0i*X^i (i=0-9) %00 = e+00 %01 = e+01 %02 = e+01 %03 = e+01 %04 = e+01 %05 = e+01 %06 = e+00 %07 = e+00 %08 = e-01 %09 = e-03 points = 16 <DY^2> = e-01 r or R = e-01
84 Eq: %0i*X^i (i=0-9) %00 = e+00 %01 = e+01 %02 = e+01 %03 = e+01 %04 = e+01 %05 = e+01 %06 = e+00 %07 = e+00 %08 = e-01 %09 = e-03 points = 16 <DY^2> = e-01 r or R = e-01
85 Eq: %0i*X^i (i=0-9) %00 = e+00 %01 = e+01 %02 = e+01 %03 = e+01 %04 = e+01 %05 = e+01 %06 = e+00 %07 = e+00 %08 = e-01 %09 = e-03 points = 16 <DY^2> = e-01 r or R = e-01
86 Eq: %0i*X^i (i=0-9) %00 = e+00 %01 = e+01 %02 = e+01 %03 = e+01 %04 = e+01 %05 = e+01 %06 = e+00 %07 = e+00 %08 = e-01 %09 = e-03 points = 16 <DY^2> = e-01 r or R = e-01
87
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66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI
65 8. K 8 8 7 8 K 6 7 8 K 6 M Q σ (6.4) M O ρ dθ D N d N 1 P Q B C (1 + ε)d M N N h 2 h 1 ( ) B (+) M 8.1: σ = E ρ (E, 1/ρ ) (8.1) 66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3)
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