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

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PROBLEM 3.36 (Cont.)q =( )( − )55 20 Cln 0.417 0.392 1+2π0.026 W m K 0.784 m 2 W m K 2 0.417 m 0.784 m( ⋅ ) 2( ⋅ ) π ( )$+( − )2 55 20 C0.025 m 1+2 22( 0.026 W m ⋅ K) π 4( 0.784 m) ( 2 W m ⋅ K) π 4( 0.784 m)( )$$( )$35 C2 35 Cq = + = ( 48.2 + 23.1)W = 71.3 W0.483 + 0.243 K W 1.992 + 1.036 K WThe annual energy loss is therefore( )−3( )( )( )Qannual= 71.3W 365days 24 h day 10 kW W = 625 kWhWith a unit electric power cost of $0.08/kWh, the annual cost of the heat loss isC = ($0.08/kWh)625 kWh = $50.00Hence, an insulation thickness ofδ = 25 mm
PROBLEM 3.37KNOWN: Inner and outer radii of a tube wall which is heated electrically at its outer surfaceand is exposed to a fluid of prescribed h and T ∞ . Thermal contact resistance between heaterand tube wall and wall inner surface temperature.FIND: Heater power per unit length required to maintain a heater temperature of 25°C.SCHEMATIC:ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction, (3) Constantproperties, (4) Negligible temperature drop across heater.ANALYSIS: The thermal circuit has the formApplying an energy balance to a control surface about the heater,q′ = q′ a + q′bTo −Ti To−Tq′ = + ∞ln( r o / ri) ( 1/hπDo)+ R′t,c2πk$$( 25-5)C⎡25 −( −10)⎤ Cq= ′ +⎣ ⎦ln ( 75mm/25mm ) m ⋅ K ⎡ 1/20.01 ( 100 W/m K π 0.15m)⎤+ ⋅ × ×2π× 10 W/m ⋅K W⎢⎣⎥⎦( )q′ = 728 + 1649 W/mq ′ =2377 W/m.
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 and 34: PROBLEM 3.23 (Cont.)1300Temperature
Page 35 and 36: PROBLEM 3.25KNOWN: Thicknesses and
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: PROBLEM 3.36KNOWN: Temperature and
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
Page 85 and 86: PROBLEM 3.60KNOWN: Inner diameter,
Page 87 and 88: PROBLEM 3.62KNOWN: Dimensions and m
Page 89 and 90: PROBLEM 3.63 (Cont.)To maintain T 1
Page 91 and 92: PROBLEM 3.65KNOWN: Thermal conducti
Page 93 and 94: PROBLEM 3.67KNOWN: Spherical tank o
Page 95 and 96: PROBLEM 3.69KNOWN: Critical and nor
Page 97 and 98: PROBLEM 3.70 (Cont.)Similarly, with
Page 99 and 100: PROBLEM 3.72KNOWN: Plane wall with
Page 101 and 102:
PROBLEM 3.73 (Cont.)qT( − LB) = T
Page 103 and 104:
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
Page 135 and 136:
PROBLEM 3.92KNOWN: Long rod experie
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PROBLEM 3.94KNOWN: Radial distribut
Page 139 and 140:
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
Page 155 and 156:
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
Page 165 and 166:
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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Page 185 and 186:
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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Page 215 and 216:
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
Page 223 and 224:
PROBLEM 3.151KNOWN: Internal and ex
Page 225:
PROBLEM 3.152 (Cont.)(c) For the pr
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