The cross section of a long circular tube, which is divided mw two semicylindrical ducts by a thin wall, is shown. Sides 1 and 2 are maintained at temperatures of T 1 = 600 K and T 2 = 400 K , respectively, while the mean temperatures of gas flows through ducts 1 and 2 are T g , 1 = 571 K and T g , 2 = 449 K , respectively. The foregoing temperatures are invariant in the axial direction. The gases provide surface convection coefficients of h 1 = h 2 = 5 W/m 2 ⋅ K while all duct surfaces may be approximated as blackbodies ( ε 1 = ε 2 = ε w = 1 ) . What is the duct wall temperature, T w ? By performing an energy balance on the gas in side 1, verify that T g , 1 is, in fact equal to 571 K.
The cross section of a long circular tube, which is divided mw two semicylindrical ducts by a thin wall, is shown. Sides 1 and 2 are maintained at temperatures of T 1 = 600 K and T 2 = 400 K , respectively, while the mean temperatures of gas flows through ducts 1 and 2 are T g , 1 = 571 K and T g , 2 = 449 K , respectively. The foregoing temperatures are invariant in the axial direction. The gases provide surface convection coefficients of h 1 = h 2 = 5 W/m 2 ⋅ K while all duct surfaces may be approximated as blackbodies ( ε 1 = ε 2 = ε w = 1 ) . What is the duct wall temperature, T w ? By performing an energy balance on the gas in side 1, verify that T g , 1 is, in fact equal to 571 K.
Solution Summary: The author explains the energy balance equation for the duct wall temperature and the surface convection of coefficients.
The cross section of a long circular tube, which is divided mw two semicylindrical ducts by a thin wall, is shown.
Sides 1 and 2 are maintained at temperatures of
T
1
=
600
K
and
T
2
=
400
K
, respectively, while the mean temperatures of gas flows through ducts 1 and 2 are
T
g
,
1
=
571
K
and
T
g
,
2
=
449
K
, respectively. The foregoing temperatures are invariant in the axial direction. The gases provide surface convection coefficients of
h
1
=
h
2
=
5
W/m
2
⋅
K
while all duct surfaces may be approximated as blackbodies
(
ε
1
=
ε
2
=
ε
w
=
1
)
. What is the duct wall temperature, Tw? By performing an energy balance on the gas in side 1, verify that Tg,1 is, in fact equal to 571 K.
Fluid is flowing through a 20 mm inside diameter and 25 mm outside diameter brass tube at no leaking with temperature at 65℃ and length of 10 m. Surface conduction of hot fluid is 5.2W/(m^2℃) and thermal conductivity of brass is 12.84W/(m℃). Brass tube is covered by silica of 6 mm thickness with thermal conductivity of 13.84W/(m℃) . Outside of it, is a fluid with 45℃ with surface conductance of 3.2W/(m^2℃). Find the heat transfer from the hot fluid with temperature of 65℃ to fluid with temperature of 45℃.
Problem: Convection related
Water enters a tube at 27°C with a flow rate of 450 kg/h. The rate of heat transfer from the tube wall to the fluid is given as qs′(W/m)=ax, where the coefficient a is 20 W/m^2 and x(m) is the axial distance from the tube entrance.
(a) Beginning with a properly defined differential control volume in the tube, derive an expression for the temperature distribution Tm(x) of the water.
(b) What is the outlet temperature of the water for a heated section 30 m long?
(c) Sketch the mean fluid temperature, Tm(x), and the tube wall temperature, Ts(x), as a function of distance along the tube for fully developed and developing flow conditions.
t = 30 + 0.9563 (62.2- 30) = 60.79°C (Ans.)
Example 4.14. A very thin glass walled 3 mm diameter mercury thermometer is placed in a
stream of air, where heat transfer coefficient is 55 W/m2°C, for measuring the unsteady temperature
of air. Consider cylindrical thermometer bulb to consist of mercury only for which k
and a = 0.0166 m2/h. Calculate the time required for the temperature change to reach half its final
or,
%3D
8.8 W/m C
%3D
value.
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