'
!
"
#
$
%
&
!
%
,
&(
)
*
*
*
+
Q = h. A.(TQ − TF )
h-
-WK-1m-2)
0
&
)
QFQ = QFF
dQ
=Q=
dt
Q = k . A.
.+
TQ − TF
%
Material
k (Wm-1K-1)
Prata
420
Cobre
420
Vidro
0.8
Água
0.59
Madeira
0.08
Ar
0.024
-
Js -1m -1 K −1 = Wm −1 K −1 /
1
-
/)
→ Q ( x, t )
Q
TQ − TF
Q = k . A.
TQ − TF
→
− dT
→
dx
∂T ( x, t )
→ Q( x, t ) = − k . A.
∂x
(
[
]
q ( x, t ) = Q ( x, t ) − Q ( x + dx, t ) .dt
∂T ( x + dx, t ) ∂T ( x, t )
q ( x, t ) = kA.
−
.dt
∂x
∂x
6
(
∂ 2T ( x, t )
q ( x, t ) = k . A
dx.dt
2
∂x
(
2
dm = ρ.dV = ρ. A.dx
3
"
)
∂T ( x, t )
q ( x, t ) = c.ρ. A.dx.dT = c.ρ. A.dx
.dt
∂t
4
)
∂T
∂ 2T
=κ 2
∂t
∂x
κ≡ k
c.ρ
&*
+5
+
%
9
&(
')
7
3
∂T
=0
∂t
∂ 2T
=0
2
∂x
T ( x ) = A.x + B
&*
8
!
x= :
x = 0:
T (0) = B = TQ
T ( ) = A +TQ = TF
$
)
T ( x ) = TQ −
TQ − TF
⋅x
Q = k . A.
&(
<
TQ − TF
,)
7
)
.' .,
;
∆
'
∆
'
Q = k1. A.
:
.
∆
,
,
∆T1
= k 2 . A.
∆T2
1
Q
Q
= R1
;
k1 A
A
∆T2 =
Q
Q
= R2
;
k2 A
A
R2 =
Q
Q
= Rn
;
kn A
A
Rn =
1
2
= ... = k n . A.
2
∆T1 =
R1 =
n
∆Tn
n
1
k1
2
k2
...
∆Tn =
5
2
k2
=
&(
,-
/)
7
)
TQ − TF = ∆T1 + ∆T2 + ... + ∆Tn
Q
TQ − TF = (R1 + R2 + ... + Rn ).
A
Q=
$
)
(T
Q
− TF ). A
R1 + R2 + ... + Rn
%
R=
+
>
?
+
k
1
R=
h
A
&(
-
0) 7
/)
Q(rA ) = Q(rB ) = Q
TQ − TF
dT
Q = k . A.
→ Q = −k . A(r ).
dr
TB
rB Qdr
Q rB dr
dT = −
TB = TA −
TA
rA k . A(r )
k rA A(r )
B
%
)
A(r ) = 4π .r 2
Q
TB = TA −
k
@
@
dr
rA 4π .r 2
rB
Q
1
TB = TA −
−
4π .k
r
8
8
rB
rA
Q 1 1
TB = TA −
−
4π .k rA rB
'C
&(
-
1) 7
/)
Q(rA ) = Q(rB ) = Q
TQ − TF
dT
Q = k . A.
→ Q = −k . A(r ).
dr
TB
rB Qdr
Q rB dr
dT = −
TB = TA −
TA
rA k . A(r )
k rA A(r )
B
"
)
A(r ) = 2π .r.
@
Q
TB = TA −
k
@
dr
rA 2π .r.
rB
Q
[ln(r )]rrBA
TB = TA −
2π . .k
8
8
Q
rB
TB = TA −
ln
2π . .k
rA
''
$
&
"
Wrad = e.σ. A.T
)
4
σ = 5.67 × 10 −8 Wm -2 K -4
0 ≤ e ≤1
e=0
e =1
&
4
3
',
$
%
λ
"
λ 2 8E
)
4
λ MAX
D
B
=
T
B = 2.898 × 10 −3 m.K
'0
&(
)
*
"
%
T = 6000 K
&
3
F
4
4
WSol = σ. ASolTSol
= 4πRS2 .σ.TSol
&
*
G
F
WSol . πRT2 4πd 2
&
F
WTerra = σ. ATerraT 4 = 4πRT2 .σ.T 4
4
T
TSol
4
1 RS
=
4 d
2
→
T = 290 K
14