A support rod k = 15 W / m ⋅ K , α = 4.0 × 10 − 6 m 2 / s of diameter D = 15 m m and length L = 100 m m spans a channel whose walls are maintained at a temperature of T b = 300 K . Suddenly, the rod is exposed to a cross flow of hot gases for which T ∞ = 600 K and h = 75 W / m 2 ⋅ K . The channel walls are cooled and remain at 300 K. (a) Using an appropriate numerical technique, determine the thermal response of the rod to the convective heating. Plot the midspan temperature as a function of elapsed time. Using an appropriate analytical model of the rod, determine the steady-state temperature distribution, and compare the result with that obtained numerically for very long elapsed times. (b) After the rod has reached steady-state conditions, the flow of hot gases is suddenly terminated, and the rod cools by free convection to ambient air at T ∞ = 300 K and by radiation exchange with large surroundings at T sur = 300 K . The free convection coefficient can be expressed as h W m 2 ⋅ K = C Δ T n , where C = 4.4 W / m 2 ⋅ K 1.188 and n = 0.188 . The emissivity of the rod is 0.5. Determine the subsequent thermal response of the rod. Plot the midspan temperature as a function of cooling time, and determine the time required for the rod to reach a safe-to-touch temperature of 315 K.
A support rod k = 15 W / m ⋅ K , α = 4.0 × 10 − 6 m 2 / s of diameter D = 15 m m and length L = 100 m m spans a channel whose walls are maintained at a temperature of T b = 300 K . Suddenly, the rod is exposed to a cross flow of hot gases for which T ∞ = 600 K and h = 75 W / m 2 ⋅ K . The channel walls are cooled and remain at 300 K. (a) Using an appropriate numerical technique, determine the thermal response of the rod to the convective heating. Plot the midspan temperature as a function of elapsed time. Using an appropriate analytical model of the rod, determine the steady-state temperature distribution, and compare the result with that obtained numerically for very long elapsed times. (b) After the rod has reached steady-state conditions, the flow of hot gases is suddenly terminated, and the rod cools by free convection to ambient air at T ∞ = 300 K and by radiation exchange with large surroundings at T sur = 300 K . The free convection coefficient can be expressed as h W m 2 ⋅ K = C Δ T n , where C = 4.4 W / m 2 ⋅ K 1.188 and n = 0.188 . The emissivity of the rod is 0.5. Determine the subsequent thermal response of the rod. Plot the midspan temperature as a function of cooling time, and determine the time required for the rod to reach a safe-to-touch temperature of 315 K.
A support rod
k
=
15
W
/
m
⋅
K
,
α
=
4.0
×
10
−
6
m
2
/
s
of diameter
D
=
15
m
m
and length
L
=
100
m
m
spans a channel whose walls are maintained at a temperature of
T
b
=
300
K
. Suddenly, the rod is exposed to a cross flow of hot gases for which
T
∞
=
600
K
and
h
=
75
W
/
m
2
⋅
K
. The channel walls are cooled and remain at 300 K.
(a) Using an appropriate numerical technique, determine the thermal response of the rod to the convective heating. Plot the midspan temperature as a function of elapsed time. Using an appropriate analytical model of the rod, determine the steady-state temperature distribution, and compare the result with that obtained numerically for very long elapsed times.
(b) After the rod has reached steady-state conditions, the flow of hot gases is suddenly terminated, and the rod cools by free convection to ambient air at
T
∞
=
300
K
and by radiation exchange with large surroundings at
T
sur
=
300
K
. The free convection coefficient can be expressed as
h
W
m
2
⋅
K
=
C
Δ
T
n
,
where
C
=
4.4
W
/
m
2
⋅
K
1.188
and
n
=
0.188
. The emissivity of the rod is 0.5. Determine the subsequent thermal response of the rod. Plot the midspan temperature as a function of cooling time, and determine the time required for the rod to reach a safe-to-touch temperature of 315 K.
Q3: An engine produce 750 kW power and uses gaseous C12H26 as a fuel
at 25 C; 200% theoretical air is used and air enters at 500 K. The products
of combustion leave at 800 K. The heat loss from the engine is 175 kW.
Determine the fuel consumption for complete combustion.
Qu 5 Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt% at a position 4 mm into an iron carbon alloy that initially contains 0.10 wt% C. The surface concentration is to be maintained at 0.90 wt% C, and the treatment is to be conducted at 1100°C. Use the data for the diffusion of
carbon into y-iron: Do = 2.3 x10-5 m2/s and Qd = 148,000 J/mol. Express your answer in hours to three significant figures.
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Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning