A solar collector design consists of several parallel tubes each enclosed concentrically in an outer tube that is transparent to solar radiation. The tubes are thin walled with the inner and outer cylinder diameters of of 0.10 and 0.15 m respectively. The annular space between the tubes is filled with air at atmospheric pressure. Under operating condition the inner and outer tube surface temperatures are 70°C and 30°C respectively.

Question

(a) What is the convective heat loss per meter of tube length?

(b) If the emissivity of the outer surface of the inner tube is 0.2 and the outer cylinder

behaves as though it were a black body, estimate the radiation loss.

(c) Discuss design options for reducing the total heat loss.



GIVEN

? Thin walled concentric tubes with air atmospheric pressure between them

? Inner tube diameter (Di) = 0.1 m

? Outer tube diameter (Do) = 0.15 m

? Inner tube temperature (Ti) = 70°C = 343 K

? Outer tube temperature (To) = 30°C = 303 K

? Outer surface emissivity of inner tube (E) = 0.2

FIND

(a) The convective loss pe meter of tube (qc/L)

(b) The radiative loss (qr/L)

(c) Discuss design options for reducing the total heat loss

ASSUMPTIONS

? Steady state

? Tubes are horizontal

SKETCH



PROPERTIES AND CONSTANTS

Answer 1

(a) The characteristic length for the Problem is the air gap



The Rayleigh number based on the characteristic length is



The correlation for this geometry is given in Equation (8.33). Its use is restricted to the following condition



Therefore, the condition is met.

The effective thermal conductivity of the gap is



The convective heat transfer per unit length across the gap is given by Equation (2.38) and (2.39)



(b) Since the inner tube is completely surrounded by the outer tube, the radiative heat transfer is given by Equation (1.17)



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



(c) Evacuating the space between the tubes would eliminate the convective heat transfer and thereby reduce the total rate of heat transfer by 67%. The heat loss could be further decreased by decreasing the emissivity of both cylinders.