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MMLU-Pro / 11634 / A furnace is lined with a refractory material whose ther-mal conductivity varies…

Problem

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question

A furnace is lined with a refractory material whose ther-mal conductivity varies with temperature k = 0.12 + 5 × 10-5T where T is in °F. If the thickness of the re-fractory layer is 5 in. and the inner and outer surface temperatures of it are 2000°F and200°F, determine the heat flux and the 2000 200 temperature distribution in the refrac-tory material layer.

category

engineering

options

  1. The heat flux is 800 Btu/hr-ft^2 and the temperature distribution is 0.5 - 1.6 × 10^-4T - 3.3 × 10^-8T^2
  2. The heat flux is 765 Btu/hr-ft^2 and the temperature distribution is 0.46 - 1.61 × 10^-4T - 3.32 × 10^-8T^2
  3. The heat flux is 720 Btu/hr-ft^2 and the temperature distribution is 0.44 - 1.57 × 10^-4T - 3.29 × 10^-8T^2
  4. The heat flux is 756 Btu/hr-ft^2 and the temperature distribution is 0.45 - 1.59 × 10^-4T - 3.31 × 10^-8T^2
  5. The heat flux is 735 Btu/hr-ft^2 and the temperature distribution is 0.43 - 1.55 × 10^-4T - 3.28 × 10^-8T^2
  6. The heat flux is 780 Btu/hr-ft^2 and the temperature distribution is 0.47 - 1.60 × 10^-4T - 3.35 × 10^-8T^2
  7. The heat flux is 800 Btu/hr-ft^2 and the temperature distribution is 0.49 - 1.62 × 10^-4T - 3.34 × 10^-8T^2
  8. The heat flux is 750 Btu/hr-ft^2 and the temperature distribution is 0.45 - 1.6 × 10^-4T - 3.31 × 10^-8T^2
  9. The heat flux is 810 Btu/hr-ft^2 and the temperature distribution is 0.48 - 1.58 × 10^-4T - 3.30 × 10^-8T^2
  10. The heat flux is 700 Btu/hr-ft^2 and the temperature distribution is 0.4 - 1.5 × 10^-4T - 3.2 × 10^-8T^2

src

stemez-TransportPhenomena

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Source and history

upstream_id / Original problem ID
11634
task_id
5f755f78-3dc6-5bcb-978a-b8f9d9771a4f
task_key
default--test--11634
task_revision_id
1
config / split
default / test

Official source

initial import