Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
Heat gain through a composite cold-storage wall of brick (100 mm, k=0.30 W/m°C) and polyurethane foam insulation (150 mm, k=0.05 W/m°C); exposed surface temperatures are 45°C (brick) and 10°C (insulation). Find the temperature at the brick-insulation interface (°C). (Rounded to 1 decimal place)
Official Answer Key:
41.4 to 41.6
Step-by-Step Solution & Explanation
Equal heat flux through both layers: k1(T_brick−Ti)/L1 = k2(Ti−T_ins)/L2 ⇒ 0.30(45−Ti)/0.10 = 0.05(Ti−10)/0.15 ⇒ 3(45−Ti) = 0.3333(Ti−10) ⇒ 135−3Ti = 0.3333Ti−3.333 ⇒ Ti = 138.333/3.3333 ≈ 41.5°C.
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