熱流体システム第1

集中定数系とダイナミクス
(等価回路の考え方)
集中定数系と等価回路
定常伝熱の問題
非定常伝熱の問題
熱通過
Overall heat transfer
固体壁の熱通過伝熱
(定常状態 steady state)
TA
T1
T2
固体壁
TB
強制対流熱伝達
forced convective heat transfer
TA
T1
T2
TB
h: 平均熱伝達率 [Wm-2  K-1]
. .
Q = q A = h1 A (TA-T1)
= h2 A (T2-TB)
熱伝導
heat conduction
TA
T1
x
T2
TB
: 熱伝導率 [W  m-1  K-1]
. .
Q = q A =  A(T1-T2) / x
集中定数による等価回路
equivalent circuit by lumped parameters
TA
T1
x
T2
TA
T1
TB
T2
TB
R1=h1-1A-1 R2= x -1A-1 R3=h2-1A-1
集中定数による等価回路
equivalent circuit by lumped parameters
TA
T1
T2
TB
R1=h1-1A-1 R2= x -1A-1 R3=h2-1A-1
電流:熱流束, 温度:電位, 抵抗:伝熱抵抗
全熱抵抗 RT = R1+ R2 + R3
= h1-1A-1 + x -1A-1 + h2-1A-1
Q=(TA-TB)/RT
非定常熱伝達
unsteady heat transfer
hA(T - T∞ )
=
T0
- cV dT
dt
T∞
非定常熱伝達
unsteady heat transfer
- cV dT
hA( T - T∞ )
T = T0
dt
T∞
T0
@t=0
T-T∞
hA
=
exp(t)
T0-T∞
cV
非定常熱伝達
unsteady heat transfer
T-T∞
hA
=
exp(t)
T0 -T∞
cV
T0
T∞
t
非定常熱伝達
unsteady heat transfer
等価回路
RT = h-1A-1, C =  c V
T0
T∞
時定数
time constant
等価回路
RT = h-1A-1, C=  cV
 = RT C =
 cV
hA
初期温度の1/e (36.8 %) になるまでの時間