quiz_solutions

# quiz_solutions - 1 2 hr 3 R 2 = ln( r 3 /r 2 ) 2 k A R 3 =...

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Problem 2 Known: Plane wall with prescribed thermal conductivity, thickness, and surface tempera- tures Find: Heat ﬂux, q 00 , and the temperature gradient, d T/ d x , for the three different coordi- nate systems shown. Schematic: Assumptions: (1) One-dimensional heat ﬂow, (2) steady state, (3) No internal generation, (4) Constant properties. Basic equation: q 00 = - k d T d x (1) Simpliﬁed basic equations: d T d x = T ( L ) - T (0) L - 0 (2a) 1

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q 00 = - k ± T ( L ) - T (0) L ² (2b) Computing equations: For parts (a) and (c): d T d x = T 2 - T 1 L = 600 - 400 0 . 1 = 2000 K / m (3a) q 00 = - k ± T 2 - T 1 L ² = - 100 ± 600 - 400 0 . 1 ² = - 200 kW / m 2 (3b) For part (b): d T d x = T 1 - T 2 L = 400 - 600 0 . 1 = - 2000 K / m (4a) q 00 = - k ± T 1 - T 2 L ² = - 100 ± 400 - 600 0 . 1 ² = 200 kW / m 2 (4b) 2
Problem 3 Assumptions: (1) One-dimensional radial conduction, (2) steady state, (3) constant properties. Basic Equations: R cond = ln( r 2 /r 1 ) 2 πLk R conv = 1 hA = 1 2 hπrL q = Δ T R tot ˙ E in - ˙ E out + ˙ E gen = d ˙ E st dt Simpliﬁed Basic Equations: R 0 cond = ln( r 2 /r 1 ) 2 πk R 0 conv = 1 2 hπr q 0 = Δ T R 0 tot ˙ E in - ˙ E out = 0 3

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Step-by-Step Solution Procedure: a) R 1 =
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Unformatted text preview: 1 2 hr 3 R 2 = ln( r 3 /r 2 ) 2 k A R 3 = ln( r 2 /r 1 ) 2 k B R 4 = 1 2 hr 1 b) q i = T h-T i R 3 + R 4 q o = T h-T o R 1 + R 2 From conservation of energy: q o + q i = q h = 2 r 2 q 00 h T h-T o R 1 + R 2 + T h-T i R 3 + R 4 = 2 r 2 q 00 h T h 1 R 1 + R 2 + 1 R 3 + R 4 = T o R 1 + R 2 + T i R 3 + R 4 + 2 r 2 q 00 h T h = 1 R 1 + R 2 + 1 R 3 + R 4 -1 T o R 1 + R 2 + T i R 3 + R 4 + 2 r 2 q 00 h c) q o q i = ( T h-T o )( R 3 + R 4) ( T h-T i )( R 1 + R 2) 4 Computing equation in Algebraic Form: T h = 1 R 1 + R 2 + 1 R 3 + R 4 -1 T o R 1 + R 2 + T i R 3 + R 4 + 2 r 2 q 00 h q o q i = ( T h-T o )( R 3 + R 4) ( T h-T i )( R 1 + R 2) 5...
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## This note was uploaded on 01/10/2010 for the course MAE 19045 taught by Professor Dabirisatari during the Summer '08 term at UC Irvine.

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quiz_solutions - 1 2 hr 3 R 2 = ln( r 3 /r 2 ) 2 k A R 3 =...

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