It is proposed to air-cool the cylinders of a combustion chamber by joining an aluminum casing with annular tins ( k = 240 W/m ⋅ K ) to the cylinder wall ( k = 50 W/m ⋅ K ) . The air is at 320 K and the corresponding convection coefficient is 100 W/m 2 ⋅ K . Although heating at the inner surface is periodic. it is reasonable to steady-state conditions with a time-averaged heat flux of q i n = 10 5 W/m 2 . Assuming negligible contact resistance between the wall and the casing, determine the wall inner temperature T i the interface temperature T 1 , and the tin base temperature T b . Determine these temperatures if the interface contact resistance is R t , c n = 10 − 4 m 2 ⋅ K/W .
It is proposed to air-cool the cylinders of a combustion chamber by joining an aluminum casing with annular tins ( k = 240 W/m ⋅ K ) to the cylinder wall ( k = 50 W/m ⋅ K ) . The air is at 320 K and the corresponding convection coefficient is 100 W/m 2 ⋅ K . Although heating at the inner surface is periodic. it is reasonable to steady-state conditions with a time-averaged heat flux of q i n = 10 5 W/m 2 . Assuming negligible contact resistance between the wall and the casing, determine the wall inner temperature T i the interface temperature T 1 , and the tin base temperature T b . Determine these temperatures if the interface contact resistance is R t , c n = 10 − 4 m 2 ⋅ K/W .
Solution Summary: The author calculates the thermal conductivity of the inner wall, fin base temperature, and interface temperature using the following formula.
It is proposed to air-cool the cylinders of a combustion chamber by joining an aluminum casing with annular tins
(
k
=
240
W/m
⋅
K
)
to the cylinder wall
(
k
=
50
W/m
⋅
K
)
.
The air is at 320 K and the corresponding convection coefficient is
100
W/m
2
⋅
K
.
Although heating at the inner surface is periodic. it is reasonable to steady-state conditions with a time-averaged heat flux of
q
i
n
=
10
5
W/m
2
.
Assuming negligible contact resistance between the wall and the casing, determine the wall inner temperature
T
i
the interface temperature
T
1
,
and the tin base temperature
T
b
.
Determine these temperatures if the interface contact resistance is
R
t
,
c
n
=
10
−
4
m
2
⋅
K/W
.
1 - A square chip, with side w = 5 mm, operates under isothermal conditions.The chip is positioned on a substrate so that its side and bottom surfaces are thermally insulated, while its top surface is exposed to theflow of a refrigerant at T∞ = 15°C.
From reliability considerations, the chip temperature cannot exceed T = 85°C. The refrigerant being air, with a convection heat transfer coefficientcorresponding h = 200 W/(m2K), what is the maximum allowable power for the chip?
Since the coolant is a dielectric liquid for which h = 3000 W/(m²K), what is the maximum allowed power?
Consider a heat conductor in the form of a long cylinder, with inner and
outer radii R1 and R2, respectively. Heat is generated within the cylinder,
where the temperature O(r, t) at position r and time t satisfies the modified
heat equation
= DV0 + H,
where D is the thermal diffusivity, and H is proportional to the rate of heat
production. The inner and outer surfaces of the cylinder are cooled by a fluid
maintained at constant temperature Oo.
(a) If the temperature is in a steady state and depends only on the
distance r from the centre of the cylinder, use cylindrical coordinates
(r, 0, 2) to write down an ordinary differential equation for O(r) valid in
the region R1
Determine the time needed to decrease the temperature of a solid cylinder from 40 C to 35 C if the ambient temperature is equal to 31 C.
The cylinder has a length equals to 0.9 m and diameter equals to 100 mm. The heat convective coefficient is equal to 1.3 W/m^2.K. The
cylinder has a conductivity equals to 2 W/m.K, a density equals to 1200 kg/m^3 and its Cp is equal to 4.700 kJ/kgK.
Select one:
a. 83325 s
O b. 10500s
O c. 45360 s
O d. 30050 s
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