The surfaces of two concentric spheres having radii of 75 and 100 mm are maintained at 325 K and 275 K, respectively.

Question

(a) If the space between the spheres is filled with nitrogen at 500 kPa, estimate the

convection heat transfer rate.

(b) If both sphere surfaces are black, estimate the total rate of heat transfer between them.

(c) Suggest ways to reduce the heat transfer.

GIVEN

? Concentric spheres with nitrogen between them

? Nitrogen pressure (p) = 500 kPa

? Sphere radii

? Inner sphere (ri) = 75 mm = 0.075 m

? Outer sphere (ro) = 100 mm = 0.1 m

? Sphere temperatures

? Inner sphere (Ti) = 325 K

? Outer sphere (To) = 275 K

? Both spheres are black

FIND

(a) Convective heat transfer (qc)

(b) Total heat transfer (qtotal)

(c) Suggest ways to reduce the heat transfer

ASSUMPTIONS

? Sphere temperatures are constant and uniform

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

? The nitrogen behaves as an ideal gas

PROPERTIES AND CONSTANTS



From Appendix 2, Table 33, for Nitrogen at atmospheric pressure and the mean temperature of 300 K



The density of the nitrogen at 500 kPa can be calculated from the ideal gas law

Answer 1

(a) The effective thermal conductivity of the nitrogen is given by Equation (8.34)



The thermal resistance of the nitrogen is given by Equation (2.51)



The rate of convective heat transfer is given by



(b) The radiative heat transfer from a black body to a black body enclosure is given by Equation

(1.16)



The total rate of heat transfer is the sum of the radiative and convective heat transfer



(c) The rate of heat transfer could be reduced in several ways, including

? Coating the spheres to reduce their emissivity, thereby decreasing the rate of radiative heat

transfer.

? Partially or totally evacuating the space between the spheres to decrease the rate of

convective heat transfer