Solar One, located near Barstow, CA, was the first large-scale (10 MW electric) solar- thermal electric-power-generating plant in the United States. A schematic diagram of the plant is shown below. The receiver may be treated as a cylinder 7 m in diameter and 13.5-m-tall. At the design operating conditions, the average outer surface temperature of the receiver is about 675°C and ambient air temperature is about 40°C. Estimate the rate of heat loss, in MW, from the receiver—via natural convection only—for the temperatures given. What are other mechanisms by which heat may be lost from the receiver?

Question

GIVEN

• A vertical cylinder in air

• Height of cylinder (L) = 13.5 m

• Diameter (D) = 7 m

• Surface temperature (Ts) = 675°C

• Ambient air temperature (T?) = 40°C

FIND

(a) The rate of convective heat loss (qc) in MW

(b) What other mechanisms for heat loss exist?

ASSUMPTIONS

• Air is still

• Surface temperature is uniform and constant

PROPERTIES AND CONSTANTS

for dry air at the mean temperature of 357.5°C

Thermal expansion coefficient (?) = 0.00160 1/K

Thermal conductivity (k) = 0.0461 W/(m K)

Kinematic viscosity (?) = 58.1 × 10–6 m2/s

Prandtl number (Pr) = 0.72

Answer 1

The Grashof number is



Therefore, the flow is turbulent.

gives the Nusselt number for a turbulent boundary layer



(a) The rate of convective heat transfer is



(b) Other mechanisms for heat transfer from the surface are

1. Radiation to the surroundings.

2. Conduction to the interior of the cylinder where the heat can be removed by a working

fluid.

3. Conduction to the support structure.

4. Forced convection to the ambient air when breezes occur.