Two long concentric horizontal aluminum tubes of 0.2 m and 0.25 m diameter are maintained at 300 K and 400 K respectively. The space between the tubes is filled with nitrogen. If the surfaces of the tubes are polished to prevent radiation, estimate the rate of heat transfer for gas pressure of (a) 1 MPa and (b) 10 kPa in the annulus.

Question

? Two concentric horizontal aluminum tubes with nitrogen between them

? Diameters ? Di = 0.2 m

? Do = 0.25 m

? Temperatures ? Ti = 300 K

? To = 400 K

? Surface of tubes is polished

FIND

The rate of heat transfer for

(a) Pressure (pa) = 1 MPa

(b) Pressure (pb) = 10 kPa

ASSUMPTIONS

? Steady state conditions

? Radiative heat transfer is negligible

? Only the density of the nitrogen is affected by the pressure

PROPERTIES AND CONSTANTS

From Appendix 2, Table 33, for Nitrogen at one atmosphere and the mean temperature of 350 K



Correcting the density for Pressure

Answer 1

The gap between the cylinders (b) = (Do – Di)/2 = 0.025 m

The Grashof and Rayleigh numbers based on the gap between the cylinders (b) are

Case (a)



To use the correlation of Equation (8.33), the following criteria must be met

For case (b)



For case (a): (0.4838)4

(7.93 X 10 6) = 4.35 X 10 5

Therefore, the condition is met for both cases.

The effective thermal conductivity of the gap is given by Equation (8.33)



The rate of heat transfer is given by Equations (2.38) and (2.39)



Case (a) q/L = 681 W/m Case (b): q/L = 68.1 W/m