Question

Problem: A cryogenic fluid is flowing in a 304 SS pipe. The pipe is insulated on its outside surface with 6-mm thick, evacuated, aluminum foil/glass mat insulation. ("Evacuated" means a partial vacuum is drawn on the insulation to remove air that would otherwise fill pores inside the insulation.) The pipe inside diameter is 127 mm; it's outside diameter is 138 mm. The fluid temperature is -173 °C. The air temperature outside the pipe is 27 °C and the temperature of the surrounding room walls is also 27 °C. The thermal conductivity of 304 SS is 9.5 W/m-K at the expected pipe wall temperature; the conductivity of the insulation is 0.00016 W/m-k (yes, 0.00016!) at the expected average temperature of the insulation. The heat transfer coefficient between the cryogenic fluid and inside surface of the pipe is 123 W/m2K, the natural convective heat transfer coefficient between the outside surface of the insulation and outside air is 9.7 W/m 2-K and the radiative heat transfer coefficient between the outside surface of the insulation and room walls is 1.2 W/m2K. Assume thermal contact resistance between the pipe and insulation is negligible. A. Calculate the heat transfer rate per unit length of pipe between the outside of the insulated pipe and cryogenic fluid. B. Determine the temperature of the outside surface of the pipe. C. What 2 design features of the insulation result in its low thermal conductivity (high insulating effectiveness)?

Problem

:

A cryogenic flui

d is flowing in a

304 SS

pipe.

The pipe is insulated

on its outside surface

with

6

-

mm thick,

evacuated,

aluminum foil/glass mat insulation.

(“Evacuated” means a partial vacuum is drawn on the

insulation to

remove air that would otherwise fill

pores inside the insulation.)

The pipe

inside diameter

is 127 mm; it’s outside diameter is 138 mm.

The

fluid temperature is

-

173

o

C

.

T

he

air temperature

outside the pipe is 27

o

C and the temperature of the

surrounding

room

walls

is also 27

o

C.

The thermal

condu

ctivity of

304 SS

is

9.5

W/m

-

K

at the expected pipe wall temperature

;

the conductivity of the

in

sulation is 0.00016 W/m

-

K

(yes, 0.00016!)

at the expected average temperature of the insulation .

The forced convective heat transfer coefficient between the cryogenic fluid and inside surface of the pipe is

123 W/m2-K, the natural convective heat transfer coefficient between the outside surface of the insulation and outside air is 9.7 W/m

2-K and the radiative heat transfer coefficient between the outside surface of the insulation and room walls is 1.2 W/m

2-K. Assume thermal contact resistance between the pipe and insulation is negligible.

A.Calculate the heat transfer rate per unit length of pipe between the outside of the insulated

pipe and cryogenic fluid.

B.Determine the temperature of the outside surface of the pipe.

C.What 2 design features of the insulation result in its low thermal conductivity (high insulating effectiveness)?

Answer 1

Draw the thermal circuit of the given arrangement as shown. Rconv tamamen - Ricony Rcond Rinem Rins Rrad Here, Ti is the fluid temperature Ti is the inner surface temperature of the pipe T, is the pipe outer surface temperature without insulation Tz is the pipe outer surface temperature with insulation To is the temperature of the surroundings. Ri.com is the convection resistance due to the cryogenic fluid flow ing in the pipe, Rcond is the conduction resistance due to the thickness of the pipe Rins is the insulation conduction resistance from outer surface to pipe insulation, Rcom is the convection resistance from insulation to the air temperature Rrad is the radiation resistance from insulation to the surrounding air temperature Now find the convection resistance due to the cryogenic fluid. R.COM 14 hex 2nr 2 123x27x0.127, 0.02037 Find the conduction resistance due to the thickness of the pipe. In Rcond 2īkl 0.138/2 In- =_0.127/2 21x9.52 1.3916X10-3 L Find the radius of insulation. dins = d.+ 2t = 138+12 = 150 mm Find the conduction resistance due to insulation. In 'ins ns2 kins 0.150/2 0.138/2 21x 0.00016L 82.941, L -K/W Find the convection resistance from insulation to the air temperature Rconv=n 1 - h, 2. trinsi 1 9.7x27x(0-150 ) 9.7x27x 0.2187 Find the radiation resistance from insulation to the surrounding temperature. Read hinten h 200rins L 1.2x2x ax 0.150 1.7683 Find the total thermal resistance, 1 1 ER = Ri.com + Rcond + Rins + (Rcon 1 + Ryad 0.02037 1.3916X103 82.941 L + + 0.2187 1.7683 82.962 10 19462 LL 83.156 Find the heat transfer rate per unit length of the pipe between the outside of the pipe and cryogenic fluid. ER 27-(-173) 83.156 = 2.405L = 2.405 W/m (B) Find the temperature of the outside surface of the pipe. L 9 T3-T; R .com + Rcond + Rins Tz-(-173) 2.405 =- 0.02037+1.3916X10* +82.941 199.525=T3 +173 T3 = 26.525°C (C) The two design features are, depends on insulation material and thickness of the insulation.