集中定数系とダイナミクス（等価回路の考え方）熱伝導 heat conduction

%&'(23456789
:,-./;<=>?
!01
heat conduction
TA
T/
T2
78*9:;<=>?
TB
!: %(45 [W " m-1 " K-1]
. .
#! A(T2-T/)
Q=qA =
666!x
*+(%$@A
B*+(%$@A
CDEF!0G
forced convective heat transfer
TA
!x
!"#
Overall heat transfer
!"#$%&'(%
)*+,- steady state.
T/
T$
TB
TA
T/
h: QR%(S5 [W"m-2 " K-1]
. .
Q = q A = h1 A (TA-T1)
= h2 A (T2-TB)
q [w/mT2]
$
%01
TB
!"#
%&'()*+,-./
%&'()*+,-./
equivalent circuit by lumped parameters
equivalent circuit by lumped parameters
TA
T/
!x
TA
R1=
/
h1A
TB
T2
T/
!x
R2= ! A
T2
TB
R1=h1-1A-1 R2= !x !-1A-1 R3=h2-1A-1
T2
TA
T/
R3=
TB
/
h2A
C0D%01, EFDCG, HID(%HI
J%HI @K = R1+ R2 + R3
= h1-1A-1 + !x !-1A-1 + h2-1A-1
AL)BMNBO.P@K
J'K!0G
unsteady heat transfer
J'K!0G
unsteady heat transfer
hA( T - T! !
hA(T - TI .
L
- c#V dT
dt
TI
T0
T = T0
<=>?
RT = h-1A-1, C = # c V
@t=0s
H'(
time constant
TUEF$1/e (36.8 %) VWXYZ$[\
T0
C=#cV
T!
T-TI
hA
t
=
exp(t)=exp(")
T0-TI
#cV
J'K!0G
unsteady heat transfer
TI
T0
- c#V dT
dt
RT = h-1A-1
T-TI
t
t
T0 -TI = exp(- RTC ) = exp(- " )
T0
# cV
" = RT C =
hA
TI
t

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