Page 1 PROBLEM 3.1 KNOWN: One-dimensional, plane wall ...

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PROBLEM 3.24KNOWN: Size and surface temperatures of a cubical freezer. Materials, thicknesses and interfaceresistances of freezer wall.FIND: Cooling load.SCHEMATIC:ASSUMPTIONS: (1) Steady-state, (2) One-dimensional conduction, (3) Constant properties.PROPERTIES: Table A-1, Aluminum 2024 (~267K): k al = 173 W/m⋅K. Table A-1, Carbon steelAISI 1010 (~295K): k st = 64 W/m⋅K. Table A-3 (~300K): k ins = 0.039 W/m⋅K.ANALYSIS: For a unit wall surface area, the total thermal resistance of the composite wall isLal Lins LR′′ sttot = + R′′ t,c + + R′′t,c +kal kins kst0.00635m2 24 m K 0.100m 4 m K 0.00635mRtot2.5 10− ⋅2.5 10− ⋅′′ = + × + + × +173 W / m⋅K W 0.039 W / m ⋅K W 64 W / m⋅K− − − −( )R′′ 5 4 4 5 2tot = 3.7× 10 + 2.5× 10 + 2.56 + 2.5× 10 + 9.9× 10 m ⋅K / WHence, the heat flux is( )Ts,o− Ts,i⎡22 − − 6 ⎤°C Wq′′ = =⎣ ⎦= 10.9R′′ 2 2tot 2.56 m ⋅ K / W mand the cooling load isq = A2 2 2s q′′ = 6 W q′′= 54m × 10.9 W / m = 590 W
PROBLEM 3.25KNOWN: Thicknesses and thermal conductivity of window glass and insulation. Contact resistance.Environmental temperatures and convection coefficients. Furnace efficiency and fuel cost.FIND: (a) Reduction in heat loss associated with the insulation, (b) Heat losses for prescribedconditions, (c) Savings in fuel costs for 12 hour period.SCHEMATIC:ASSUMPTIONS: (1) Steady-state, (2) One-dimensional heat transfer, (3) Constant properties.ANALYSIS: (a) The percentage reduction in heat loss isq′′ wo − q′′ with ⎛ q′′with ⎞ ⎛ R′′tot,wo ⎞Rq= × 100% = ⎜1− ⎟× 100% = ⎜1− ⎟×100%q′′ wo⎝ q′′ wo ⎠ ⎝ R′′tot, with ⎠where the total thermal resistances without and with the insulation, respectively, are1 Lw1R′′ tot,wo = R′′ cnv,o + R′′ cnd,w + R′′cnv,i = + +ho kw hi( )2 2R′′ tot,wo = 0.050 + 0.004 + 0.200 m ⋅ K / W = 0.254 m ⋅K / W1 LwLins1R′′ tot,with = R′′ cnv,o + R′′ cnd,w + R′′ t,c + R′′ cnd,ins + R′′ cnv,i = + + R′′t,c + +ho kw kins hi( )2 2R′′ tot,with = 0.050 + 0.004 + 0.002 + 0.926 + 0.500 m ⋅ K / W = 1.482 m ⋅K / WRq= ( 1− 0.254 /1.482)× 100% = 82.9%
Page 1 and 2: PROBLEM 3.1KNOWN: One-dimensional,
Page 3 and 4: PROBLEM 3.2 (Cont.)Surface temperat
Page 5 and 6: T∞,i − Ts,i 1hi0.10= = = 0.846,
Page 7 and 8: PROBLEM 3.4 (Cont.)7000Radiant heat
Page 9 and 10: PROBLEM 3.6KNOWN: Design and operat
Page 11 and 12: PROBLEM 3.7KNOWN: A layer of fatty
Page 13 and 14: PROBLEM 3.8KNOWN: Dimensions of a t
Page 15 and 16: PROBLEM 3.9KNOWN: Thicknesses of th
Page 17 and 18: PROBLEM 3.11KNOWN: Drying oven wall
Page 19 and 20: PROBLEM 3.13KNOWN: Composite wall o
Page 21 and 22: PROBLEM 3.15KNOWN: Dimensions and m
Page 23 and 24: PROBLEM 3.17KNOWN: Total floor spac
Page 25 and 26: PROBLEM 3.18KNOWN: Concrete wall of
Page 27 and 28: (2)(2)(2)Rcdm K/WPROBLEM 3.19 (Cont
Page 29 and 30: and with ′′ ( B B)( c,2 − s,2
Page 31 and 32: PROBLEM 3.22KNOWN: Temperatures and
Page 33: PROBLEM 3.23 (Cont.)1300Temperature
Page 37 and 38: PROBLEM 3.27KNOWN: Operating condit
Page 39 and 40: PROBLEM 3.28KNOWN: Dimensions, ther
Page 41 and 42: PROBLEM 3.29KNOWN: Conduction in a
Page 43 and 44: PROBLEM 3.31KNOWN: Temperature depe
Page 45 and 46: PROBLEM 3.33KNOWN: Steady-state tem
Page 47 and 48: PROBLEM 3.35KNOWN: Thickness and in
Page 49 and 50: PROBLEM 3.36KNOWN: Temperature and
Page 51 and 52: PROBLEM 3.37KNOWN: Inner and outer
Page 53 and 54: PROBLEM 3.38 (Cont.)2000016000Heat
Page 55 and 56: PROBLEM 3.39 (Cont.)and the heat ga
Page 57 and 58: PROBLEM 3.40 (Cont.)240Outer surfac
Page 59 and 60: PROBLEM 3.42KNOWN: Electric current
Page 61 and 62: PROBLEM 3.43KNOWN: Diameter of elec
Page 63 and 64: PROBLEM 3.44 (Cont.)(b) From an ene
Page 65 and 66: PROBLEM 3.45 (Cont.)The heat extrac
Page 67 and 68: PROBLEM 3.47KNOWN: Electric current
Page 69 and 70: PROBLEM 3.48KNOWN: Saturated steam
Page 71 and 72: PROBLEM 3.49KNOWN: Temperature and
Page 73 and 74: PROBLEM 3.50 (Cont.)20002Heat loss,
Page 75 and 76: PROBLEM 3.51KNOWN: Pipe wall temper
Page 77 and 78: PROBLEM 3.53KNOWN: Surface temperat
Page 79 and 80: PROBLEM 3.55KNOWN: Diameter of a sp
Page 81 and 82: PROBLEM 3.56KNOWN: Sphere of radius
Page 83 and 84: PROBLEM 3.58KNOWN: Dimensions of sp
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PROBLEM 3.60KNOWN: Inner diameter,
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PROBLEM 3.62KNOWN: Dimensions and m
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PROBLEM 3.63 (Cont.)To maintain T 1
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PROBLEM 3.65KNOWN: Thermal conducti
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PROBLEM 3.67KNOWN: Spherical tank o
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PROBLEM 3.69KNOWN: Critical and nor
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PROBLEM 3.70 (Cont.)Similarly, with
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PROBLEM 3.72KNOWN: Plane wall with
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PROBLEM 3.73 (Cont.)qT( − LB) = T
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PROBLEM 3.74 (Cont.)Substituting th
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PROBLEM 3.75KNOWN: Composite wall o
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PROBLEM 3.77KNOWN: Geometry and bou
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PROBLEM 3.78KNOWN: Thermal conducti
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PROBLEM 3.78 (Cont.)qL ⎛1 b ⎞Ts
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and from Eq. (3) with x = L and T(L
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PROBLEM 3.80 (Cont.)Surface energy
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PROBLEM 3.82KNOWN: Distribution of
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PROBLEM 3.84KNOWN: Cylindrical shel
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PROBLEM 3.86KNOWN: Diameter, resist
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PROBLEM 3.87KNOWN: Energy generatio
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PROBLEM 3.88KNOWN: Radii and therma
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PROBLEM 3.88 (Cont.)Clearly, the ab
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PROBLEM 3.89 (Cont.)(b) Using the o
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PROBLEM 3.90KNOWN: Electric current
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PROBLEM 3.91KNOWN: Materials, dimen
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PROBLEM 3.92KNOWN: Long rod experie
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PROBLEM 3.94KNOWN: Radial distribut
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Henceq2 2() = s,i + ( i − )PROBLE
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PROBLEM 3.96 (Cont.)(b) With the co
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PROBLEM 3.97 (Cont.)(b) The sphere
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PROBLEM 3.98KNOWN: Radius, thicknes
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The boundary conditions are:( ) = w
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PROBLEM 3.101KNOWN: Dimensions of a
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PROBLEM 3.102 (Cont.)Substituting f
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PROBLEM 3.103 (Cont.)Hence, the tem
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PROBLEM 3.105KNOWN: Electric power
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PROBLEM 3.107KNOWN: TC wire leads a
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PROBLEM 3.108KNOWN: Rod (D, k, 2L)
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PROBLEM 3.109KNOWN: Long rod in ove
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( ) θ ( )PROBLEM 3.110 (Cont.)1/2
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PROBLEM 3.111 (Cont.)−( ) 1/21/22
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PROBLEM 3.112 (Cont.)The gradient a
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PROBLEM 3.114KNOWN: Dimensions, end
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PROBLEM 3.116KNOWN: Dimensions and
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PROBLEM 3.117 (Cont.)Continued...dT
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PROBLEM 3.119KNOWN: Long, aluminum
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PROBLEM 3.121KNOWN: Thickness, leng
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PROBLEM 3.122KNOWN: Thickness, leng
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PROBLEM 3.123KNOWN: Length, thickne
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PROBLEM 3.126KNOWN: Pin fin of ther
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PROBLEM 3.128KNOWN: Slender rod of
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PROBLEM 3.130KNOWN: Arrangement of
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PROBLEM 3.131KNOWN: Conditions asso
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PROBLEM 3.132 (Cont.)N t(mm) η f R
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2( ) ( )PROBLEM 3.133 (Cont.)25 0.0
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The fin heat rate is( )( )PROBLEM 3
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PROBLEM 3.135 (CONT.)Heat rate, qt(
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PROBLEM 3.136 (Cont.)With w = 0.25
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where( )( )sinh(mL) + h mk cosh(mL)
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( )PROBLEM 3.138 (Cont.)C1 = 1+ η
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PROBLEM 3.139 (Cont.)Heat generatio
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PROBLEM 3.140 (Cont.)5000Heat rate,
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PROBLEM 3.142KNOWN: Dimensions, bas
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PROBLEM 3.146KNOWN: Dimensions, bas
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PROBLEM 3.147 (Cont.)5 2 3/2( ) 1/2
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PROBLEM 3.148 (Cont.)Once the heat
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PROBLEM 3.149 (Cont.)R′′ t,c to
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PROBLEM 3.151KNOWN: Internal and ex
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PROBLEM 3.152 (Cont.)(c) For the pr
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