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GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper
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© examsnet.com
Question : 36
Total: 65
A small metal bead (radius
0.5
m
m
), initially at
100
∘
C
, when placed in a stream of fluid at
20
∘
C
, attains a temperature of
28
∘
C
in 35 seconds. The density and specific heat of the metal are
8500
k
g
/
m
3
and
400
J
/
k
g
⋅
K
, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in
W
/
m
B
⋅
K
)
" between the metal bead and the fluid stream is
149.9
299.8
449.7
283.3
Validate
Solution:
r
=
0.5
m
m
T
0
=
100
∘
C
T
∞
=
20
∘
C
T
=
28
∘
C
after
t
=
4.35
s
e
c
ρ
=
8500
k
g
/
m
3
C
p
=
400
J
/
k
g
k
h
=
?
As it is lumped system
T
−
T
∞
T
0
−
T
∞
=
e
−
h
A
ρ
V
C
p
×
t
28
−
20
100
−
20
=
e
−
(
h
×
4
π
r
2
ρ
×
4
3
π
r
3
×
c
p
×
t
)
8
80
=
e
−
8500
×
0.5
×
10
−
3
3
×
400
h
=
299.95
w
/
m
2
k
© examsnet.com
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