A solar thermal central receiver generates heat by focusing sunlight with a field of mirrors on a bank of tubes through which a coolant flows. Solar energy absorbed by the tubes is transferred to the coolant which can then deliver useful heat to a load. Consider a receiver fabricated from multiple horizontal tubes in parallel. Each tube is 1-cm-ID and 1-m-long. The coolant is molten salt which enters the tubes at 370°C. Under start-up conditions, the salt flow is 10 gm/s in each tube and the net solar flux absorbed by the tubes is 104 W/m2. The tube wall material will tolerate temperatures up to 600°C. Will the tubes survive start-up? What is the salt outlet temperature?

Question

GIVEN

• Molten salt flowing through a horizontal tube that is absorbing solar energy

• Tube inside diameter (D) = 1 cm = 0.01 m

• Tube length (L) = 1 m

• Entering salt temperature (Tb,in) = 370°C

• Start-up mass flow rate (m) = 10 gm/s = 0.01 kg/s

• Net solar energy absorbed by the tube (qs) = 104 W/m2

• Maximum tube wall temperature (Ts) = 600°C

FIND

(a) Salt outlet temperature (Tb,out)

(b) Will the tubes survive start-up?

SKETCH



PROPERTIES AND CONSTANTS

for molten salt at 370°C

Specific heat (c) = 1629 J/(kg K)

Answer 1

(a) By the conservation of energy



Evaluating the molten salt properties at the average bulk temperature of 380°C

Density (?) = 1849 kg/m3

Absolute viscosity (?) = 1970 × 10–6 (Ns)/m2

Thermal expansion coefficient (?) = 3.55 × 10–4 1/K

Thermal conductivity (k) = 0.516 W/(m K)

Kinematic viscosity (?) = 1.065 × 10–6 m2/s

Prandtl number (Pr) = 6.18

(b) The Reynolds number is



With laminar flow and the high temperature differences possible, natural convection may be

important. Since we do not know the tube wall temperature needed to evaluate the Grashof number,

an iterative procedure must be used. For the first iteration, let the average tube wall temperature be

10°C above the average bulk salt temperature (Ts = 390°C).

at the tube temperature of 390°C ?s = 1882 × 10–6 (Ns)/m2

The Graetz number is



The Grashof number based on the diameter,



For this value and ReD = 6.5 × 102, indicates the flow is in the mixed convection regime, therefore, will be used to estimate the Nusselt number. Note that this will be a rough estimate since is technically only for isothermal tubes.



The rate of heat transfer to the molten salt is



Further iterations are necessary. However, the fluid properties will not change appreciably. Therefore,

ReD, Pr, and Gz will not change.



The maximum tube wall temperature is therefore



which is well below the tube melting point. The tube will have no problems surviving the start-up in

good shape.