benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 11707 / 200 Kg of water at T_i = 35°C is kept in an auxiliary reservoir tobe heated by…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

200 Kg of water at T_i = 35°C is kept in an auxiliary reservoir tobe heated by solar energy. The solar collector used has a surfacearea of A = 5m^2. The heat removal factor and the overallheat transfer coefficient are F_R = 0.80 and U_L = 8.0 W/m^2.°C, respectively. The ambient temperature T_a = 30°C. The product of the heat transfer coefficient and reservoirarea is (UA) = 1.80 W/°C. During an emergency, thewater will be used at a rate ṁ = 15 kg/hr and is refilled at atemperatureT_rf= 20°C. Determine the efficiency of this operationfrom 7 am to 5 pm. Refer to table 1 for hourly solar data. Table 1 I_T S T_a U_L(T_i - T_a) q = F_r S - U_L(T_i - T_a) \eta = (q / I_T) Time MJ/m^2 MJ/m^2 °C MJ/m^2 MJ/m^2 7 - 8 0.03 - - 12 1.35 - - 8 - 9 0.49 0.40 - 9 1.27 0 0 9 - 10 1.12 0.92 - 3 1.09 0 0 10 - 11 4.02 3.26 3 1.01 1.80 0.45 11 - 12 3.45 3.08 4 0.89 1.75 0.51 12 - 1 4.15 3.39 7 0.81 2.20 0.53 1 - 2 3.96 3.20 8 0.78 1.94 0.49 2 - 3 1.98 1.58 9 0.75 0.67 0.34 3 - 4 1.27 1.01 10 0.72 0.23 0.18 4 - 5 0.04 - 8 0.78 - - \sumI_T20.51 \sum_q = 8.59 I_T - energy gained per hour by the solar panel. T_a - ambient temperature each hour. S - Incident heat flux on the solar panel. The overall efficiency is \eta_day= [(\sumq) / (\sumI_T)] = [(8.59) / (20.42)] = 0.42 or 42% Table 2 I_T S T_a T_s^+ Q Loss Load Time MJ/m^2 MJ/m^2 °C °C MJ MJ MJ Begin 35.0 7 - 8 0.03 - - 12 33.2 0 0.021 0.83 8 - 9 0.49 0.40 - 9 31 .5 0 0.01 0.72 9 - 10 1.12 0.92 - 3 30.0 0 0 0.63 10 - 11 4.02 3.26 3 39.8 8.75 0.064 1.24 11 - 12 3.45 3.08 4 45.4 6.12 0.10 1.60 12 - 1 4.15 3.39 7 52.8 7.85 0.15 2.06 1 - 2 3.96 3.20 8 57.9 5.42 0.18 2.38 2 - 3 1.98 1.58 9 54.3 0 0.16 2.15 3 - 4 1.27 1.01 10 51 .6 0 0.14 1.98 4 - 5 0.04 - 8 48.6 0 0.12 1.80 \sumI_T \sumQ Losses \sumLoads = 20.51 = 28.14 = 0.945 = 15.39

category

engineering

options

  1. 55%
  2. 50%
  3. 42%
  4. 30%
  5. 35%
  6. 40%
  7. 22.2%
  8. 18.7%
  9. 33.3%
  10. 27.5%

src

stemez-HeatTransfer

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
11707
task_id
acccdf85-1a8c-5498-8121-ca2d81ab995a
task_key
default--test--11707
task_revision_id
1
config / split
default / test

Official source

initial import