Question

= The use of rock pile thermal energy storage systems has been considered for solar energy and industrial process heat applications. A particular system involves a cylindrical container, 2 m long by 1 m in diameter, in which nearly spherical rocks of 0.03-m diameter are packed. The bed has a void space of 0.42, and the density and specific heat of the rock are p = 2300 kg/m and cp = 879 J/kg-K, respectively. Consider conditions for which atmospheric air is supplied to the rock pile at a steady flow rate of 0.5 kg/s and a temperature of 90°C. The air flows in the axial direction through the container. If the rock is at a temperature of 25°C, what is the total rate of heat transfer from the air to the rock pile? Physical Properties Mathematical Functions Step 1 Your Answer Correct Answer (Used) * Your answer is incorrect. Jason from WileyPLUS What is the value of the Reynolds number based on the rock diameter? WileyPLUS Scheduled Maintenan As Wiley continues to fine tune w Re 8439,31

please show work

Answer 1

Ques) At Tz 90°C = 273 +90 = 363K, properties of air ma S= 0.963 Kyl K=0.031 W/mK V=22.35 x 100 m² 18. 1010. Ilkg k Pr=0.7 os a) 4 VS = ma s. 1 DB 8 TDR 4 x 0.5 0.963 x 11x (1)? V = 0.66108 m 16 Re Z VD v 0.66108 x 0.03 22.35x100 Re = 887.948 b) -0.575 h =2.06 Pr -2/3 suco R E void fraction -0.515 *0.963 x0-66108x1010 (887.248) 0.42 2/3 (0.7) Ñ 22.06

h=80.7 W/m²K c) Apt =(1-2)(DPL). 6 Фhock =(1-0.42) 11 (1) 2 xg 4 6 0:03 Apt = 182.21 m2 d) Tao-Ts To, in - Ts LbAt e SVC a hapit mo Cp = e Tao -25 90-25 80.7*182.21 0.581010 e -13 = 2.2616*10 Tao = 25°C e) o tem To, in -Ts)-(Tao-Ts) Tarin - Ts Togo Ts en s (90-25) - Osek 65x2.2616x10 -13 ln 190-25) 65x2.2616X163 Te 65 29.1175 m

OT),m = 2.2323°c f) q o Tam = h Apit = 80.7 *182.21722323 q= 32824.514 W Tin