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A fluid enters a heated pipe of 5 cm diameter at 285 K with a mass flow rate of 0.25 kg/s. Because of fully-developed turbulent condition, the convection coefficient between the fluid and the pipe surface is found to be approximately 1200 W/m-K, irrespective of the distance from the entrance or the thermal condition of the surface. Assume that the specific heat of the fluid remains constant at 4180 J/kgK during the flow.
Find out the mean temperature of the fluid after it has traveled 5 m in the pipe when
(a) the pipe is heated uniformly via a heating wire at a rate of 5600 W/m2
(b) the pipe surface is maintained at a temperature of 320 K.

Respuesta :

Answer:

A)  Mean Temperature = 287.80K

B)  Mean Temperature = 300.78K

Explanation:

D = 0.05m

T = 285K

M = 0.25kg/s

h =   [tex]1200 W/m^{2} k[/tex] K

CP = 4180 j/kg k

Part A) Pipe Heated Uniformly

Ф = [tex]5000 w/m^{2}[/tex]

L = 5m

Ф = m cp [T2 - T1]/A

AФ = 0.25 * 4180 [T2 - 285]

5600 * π * dL = 0.25 * 4180 [T2 - 285]

5600 * π * 0.05 * 5 = 0.25 * 4180 [T2 - 285]

T2 = 289.20

TM = [tex]\frac{T2+T1}{2}[/tex]

TM = [tex]\frac{289.20 + 285}{2}[/tex]

TM = 287.1 K

Part B) Pipe Maintained at 320K

Ф = hA [Ts - T1]

Ф = 1200 * π * 0.05* 5 [320 -285]

Ф = 32986.72 watt'

Ф = mcp [T2 - T1]

32986.72 = 0.25 * 4180 [T2 - 285]

T2 = 316.56K

TM = [tex]\frac{T2+T1}{2}[/tex]

TM = [tex]\frac{316.56 + 285}{2}[/tex]

TM = 300.78 K

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