Chapter 9, Problem 9.33P

In the central receiver concept of a solar power plant, many heliostats at ground level are used to direct a concentrated solar flux $q_s^n$ to the receiver, which is positioned at the top of a tower. However, even with absorption of all the solar flux by the outer surface of the receiver, losses due to free convection and radiation reduce the collection efficiency below the maximum possible value of 100%. Consider a cylindrical receiver of diameter $D=7\text{m}$ , length $L=12\text{m}$ , and emissivity $\epsilon =0.20$ .

(a) If all of the solar flux is absorbed by the receiver and a surface temperature of $T_s=800\text{K}$ is maintained, what is the rate of heat loss from the receiver? The ambient air is quiescent at a temperature of $T_{\infty }=300\text{K}$ , and irradiation from the surroundings may be neglected. If the corresponding value of the solar flux is $q_S^n={10}^5{\text{W/m}}^2$ , what is the collector efficiency?
(b) The surface temperature of the receiver is affected by design and operating conditions within the power plant. Over the range from 600 to 1000 K, plot the variation of the convection, radiation, and total heat rates as a function of $T_s$ . For a fixed value of $q_S^n={10}^5{\text{W/m}}^2$ , plot the corresponding variation of the receiver efficiency.