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.
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.
Heat Transfer with a Liquid Metal. The liquid metal bismuth at a flow rate of 2.00 kg/s enters a tube having an inside diameter of 35 mm at 425°C and is heated to 430°C in the tube. The tube wall is maintained at a temperature of 25°C above the liquid bulk temperature. Calculate the tube length required. The physical properties are as follows (H1): k = 15.6 W/m K, c,=149 J/kg K, u = 1.34 x 10-3 Pa s.
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