• Author / Uploaded
• Roem Esmerna

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Sample Problem for Convection Water entering at 10 C is to be heated to 40 C in a tube of 0.02 m inside diameter at a mass flow rate of 0.01 kg/s. The outside of the tube is wrapped with an insulated electric heating element that produces a uniform flux of 15000W/m2 over the surface. Neglecting any entrance effects, determine the ff.

a.) the Reynolds number b.) the heat transfer coefficient c.) the length of pipe needed for a 30 C increased in average temperature d.) the inner tube surface temperature at the outlet e.) the fiction factor f.) the pressure drop in the pipe g.) the pumping power required of the pump is 50% efficient

Given properties from Table 13 Appendix 2     

p= 997.1 kg/m3 cp= 4178 J/kg-K k = 0.606W/m-K µ = 880.6x10-6 N-s/m2 ave. temp. = 25C

Given on the problem:  To = 40 C + 273 = 313 K  Ti = 10 C+ 273 = 283 K  D = 0.02 m  m = 0.01 kg/s  Q = 15,000 W/m2 Solution:

a.) Re =

uDp 𝜇

0.0319m kg )(0.02 m)(997.1 3 ) s m Re = −6 3 880.6 x 10 kg/m

(

Re = 722.343

b.) NuD = 4.364 Hc = 4.364

k 𝐷

Hc = 4.364 (

0.606W/m−K 0.02m

)

Hc= 132.2292 W/m2-K

c.) QπDL = mCp(T2 – T1 ) mCp(T2 – T1 ) L=

QπD (0.01

L=

kg J )(4178 −K)(313 K−283 K) s kg 𝑊 (15,000 2 )(π)(0.02 m) 𝑚

L = 1.33 m

d.) Q =

T1 =

Qc

= Hc (T1 – T2)

A Qc Ah

+T2 W

T1 =

(15,000 2 ) m W

(132.11 2 −K) m

+ 313 K

T1 = 426.44 K – 273 K

T1 = 153.44C

e.) f =

64 Re

f = 64/723

f = 0.089

L ρu2

f.) ΔP = f( ) (

D 2gc

u=

)

4m ρπD2 4(0.01

u=

kg ) s

kg

(997.1 3)(π)(0.02 m)2 m

u = 0.0319 m/s

1.3299 m

ΔP = 0.089 (

0.02 m

) [(997.1kg/m3)(0.0319 m/s)2 / 2(1 kg - m/ N -s2)]

ΔP = 3.00 N/m2

g.) Pp = m (

∆p

ρnp

)

Pp = 0.01kg/s [ (2.9855 N / m2) / (997.1 kg/m3)(0.5)]

Pp = 6.0 x10-6 W