King Fahd University of Petroleum & Minerals Dhahran, Saudi Arabia
ME 315 : HEAT TRANSFER Spring Semester 2005-2006 (052) Homework # 9 Due date: May 15, 2006 Problem # 1 o
A circular pipe of 25-mm outside diameter is placed in an air-stream at 25 C and 1-atm pressure. The air moves in cross flow over the pipe at 15 m/s, while the outer surface of the o pipe is maintained at 100 C. What is the drag force exerted on the pipe per unit length? What is the rate of heat transfer from the pipe per unit length? Assume the following properties for air:
10 υ =19.31×10
−6
2
m s,
ρ = 1.048 k g
/ m 3 , k = 0.0288
W m oC
, Pr = 0.702
Use the following correlation:
Nu D = C Re D Pr
1/ 3
m
where C = 0.193 and m = 0.618.
Problem # 2 o
Consider a sphere with a diameter of 20 mm and a surface temperature of 60 C that is o immersed in water at a temperature of 30 C and a velocity of 2.5 m/s. Calculate the drag force and the heat rate. o
Assume the following properties for water: at 30 C, µ
4 2 7 2 1 0− N .s / m , υ = 8.068×10 10− m / s , k = 0.6172 = 8.034×10 o
At Ts = 60 C, µ s
W m oC
, Pr Pr = 5.45
= 4.674 ×10−4 N .s / m2
Use the correlation recommended by Whitaker. Problem # 3 A tube bank uses an aligned arrangement of 10-mm diameter tubes with S T = SL = 20 mm. There are 10 rows of tubes with 50 tubes in each row. Consider an application for which o cold water flows through the tubes, maintaining the outer surface temperature at 27 C, while o flue gases at 427 C and a velocity velocity of 5 m/s m/s are in cross flow over the tubes. What is the total rate of heat transfer per unit length of the tubes in the bank? Assume the following properties for flue gas: −6
o At 427 C, υ = 68.1 × 10 m / s , k
2
= 0.0524
W o
m C
, Pr = 0.695
ρ =
0.498kg / m 3 , c p = 1.075 kJ / kgK .
At 27C, Pr = 0.707. Use the following correlation: Nu D = 0.26 Re D
0.63
⎛ Pr ⎞ Pr 0.36 ⎜ ⎟ ⎝ Pr s ⎠
0.25
Problem # 4 A tube bank uses an aligned arrangement of 30-mm diameter tubes with ST = SL = 60 mm and a tube length of 1 m. There are 10 tube rows in the flow direction (N L = 10) and 7 tubes o per row (NT = 7). Air with upstream conditions of T∞ = 27 C and V = 15 m/s is in cross flow o over the tubes, while a tube wall temperature of 100 C is maintained by steam condensation inside the tubes. Determine the temperature of air leaving the tube bank, the pressure drop across the bank, and the fan power requirement. Assume the following properties for air; o
A t 27 C ,
ρ = 1.1614
k = 0.0.0263
W o
m C
kg / m , c p = 1.007 kJ / kgK , υ =15.89×10 3
−6
m s
2
,
, Pr = 0.707
At 100oC, Pr = 0.695. Problem # 5 o
Air at 27 C and 1 atm flows at a rate of 5 kg/s over a bank of seventy-five 2.54 cm-diameter o tubes of 1.5-m depth. The tubes are in a five-row staggered array with 4-cm pitch and 77 C wall temperature. Determine the rate of heat transfer, outlet temperature, and pressure drop. Assume the following properties for air: o
At 27 C ,
ρ = 1.18 kg
3
/m ,
µ =1.85×10
c p = 1.01kJ / Kg oC , k = 0.0262
W
0.6
0.36
F c 0.2
⎛ S ⎞ where C = 0.35 ⎜ T ⎟ , Fc = 0.93 ⎝ S L ⎠ h hcp
⎛ T ⎞ = ⎜ s ⎟ ⎝ T b ⎠
−0.5
o
m C
Use the following correlation:
Nu D ,cp =C Re D Pr
−5
kg / m .s ,
, Pr = 0.708
