Problem 1 (40 Points): The Solana Generating Station is a solar power plant near Gila Bend,Arizona. It has a parabolic trough design, using concentrated solar energy and molten salt thermal

energy storage. A field of mirrors focus the solar energy onto a central receiver in order to elevate the temperature of the molten salt which then provides heat input to an electricity-generating power cycle. You are to be involved in the engineering of the central receiver. The receiver can be modeled as a cylinder with diameter D = 4 m and height H = 8 m. The surface emissivity is 1. The collector field has an area of Af = 20 acres and the mirrors have an efficiency of 76% for transferring the incident solar flux to the receiver surface. It is estimated that the solar flux incident on the field is between 50 and 1000 W/m². The receiver absorbs all of the radiation that strikes its surface. The temperature of the receiver surface is T,. The molten salt enters the receiver at Tin = 320° C and leaves at the receiver surface temperature.The efficiency of the power cycle is given by: \eta_{c}=0.25\left(1-\frac{T_{\infty}}{T_{r}}\right) The receiver experiences losses that are related to forced and natural convection to the surrounding air at T = 10° C. The natural convection heat transfer coefficient is hn = 6.5 W/m²-K and the forced convection heat transfer coefficient is hf = 8.5 W/m^2-K. The combined effect of natural and forced convection can be approximated by: h=\left(h_{n}^{3}+h_{f}^{3}\right)^{1 / 3} The receiver also experiences a radiative loss to surroundings at To. Assume that the top and bottom surfaces are well-insulated so that losses only occur from the sides. a.) 10 Points. By performing an energy balance, determine an analytic expression that rep-resents the total rate of heat loss from the receiver. b.) 8 Points. If the receiver temperature must be between 400° C and 800° C, plot the overall efficiency as a function of the receiver temperature for at least 4 different values of the incident solar flux within the estimated range of 50 < q" < 1000 W/m?. The overall efficiency is defined as the ratio of the power produced to the total solar energy incident on the field, 7 = W/qin, and the power produced is related to the heat input to the salt by the cycle efficiency, W = nc qsalt . c.) 2 Points. Explain the physics behind the salient features of your plot from part (b). d.) 2 Points. The owner of the facility requires the overall efficiency of the system to be atleast 12%. What incident solar flux is required for this condition? e.) 3 Points. What receiver temperature is required to satisfy the conditions of part (d)? f.) 2 Points. What mass flow rate is required to satisfy the conditions of part (d)? g.) 3 Points. How much power will the facility produce under the conditions of part (d)? h.) 5 Points. In an effort to convince the owner of the consequences of off-design operation,plot the overall efficiency vs. incident solar flux for the fixed receiver temperature that you determined in part (e) above. i.) 5 Points. What is the percent reduction in efficiency and power output if the incident solar flux is reduced by half? Take the specific heat of molten salt to be 557 J/kg-K and 1 acre 4046.86 m².