problem4-22 - PROBLEM 4.22 KNOWN: Long constantan wire...

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Unformatted text preview: PROBLEM 4.22 KNOWN: Long constantan wire butt-welded to a large copper block forming a thermocouple junction n the surface of the block. o FIND: (a) The measurement error (T j- T o ) for the thermocouple for prescribed conditions, and (b) Compute and plot (T j- T o ) for h = 5, 10 and 25 W/m 2 ⋅ K for block thermal conductivity 15 ≤ k ≤ 400 /m ⋅ K. When is it advantageous to use smaller diameter wire? W SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Thermocouple wire behaves as a fin with constant eat transfer coefficient, (3) Copper block has uniform temperature, except in the vicinity of the junction. h P ROPERTIES: Table A-1 , Copper (pure, 400 K), k b = 393 W/m ⋅ K; Constantan (350 K), k t ≈ 25 W/m ⋅ K. ANALYSIS: The thermocouple wire behaves as a long fin permitting heat to flow from the surface thereby depressing the sensing junction temperature below that of the block T o . In the block, heat flows into the circular region of the wire-block interface; the thermal resistance to heat flow within the block is...
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