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

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PROBLEM 3.121 (Cont.)Case D (L → ∞): From Eqs. (3.80), (3.86), (3.81), (3.83) and (3.79)Mq′ f = = 450W/mw
PROBLEM 3.122KNOWN: Thickness, length, thermal conductivity, and base temperature of a rectangular fin. Fluidtemperature and convection coefficient.FIND: (a) Heat rate per unit width, efficiency, effectiveness, thermal resistance, and tip temperaturefor different tip conditions, (b) Effect of fin length and thermal conductivity on the heat rate.SCHEMATIC:ASSUMPTIONS: (1) Steady-state, (2) One-dimensional conduction along fin, (3) Constantproperties, (4) Negligible radiation, (5) Uniform convection coefficient, (6) Fin width is much longerthan thickness (w >> t).ANALYSIS: (a) The fin heat transfer rate for Cases A, B and D are given by Eqs. (3.72), (3.76) and(3.80), where M ≈ (2 hw 2 tk) 1/2 (T b - T ∞ ) = (2 × 100 W/m 2 ⋅K × 0.001m × 180 W/m⋅K) 1/2 (75°C) w =450 w W, m≈ (2h/kt) 1/2 = (200 W/m 2 ⋅K/180 W/m⋅K ×0.001m) 1/2 = 33.3m -1 , mL ≈ 33.3m -1 × 0.010m= 0.333, and (h/mk) ≈ (100 W/m 2 ⋅K/33.3m -1 × 180 W/m⋅K) = 0.0167. From Table B-1, it followsthat sinh mL ≈ 0.340, cosh mL ≈ 1.057, and tanh mL ≈ 0.321. From knowledge of q f , Eqs. (3.86),(3.81) and (3.83) yieldq′ fq′f θbηf ≈ , εf ≈ , R′t,f =h( 2L+t)θb htθb q ′fCase A: From Eq. (3.72), (3.86), (3.81), (3.83) and (3.70),( )( )M sinh mL + h / mk cosh mL0.340 + 0.0167 × 1.057q′ f = = 450 W / m = 151W / mw cosh mL + h / mk sinh mL 1.057 + 0.0167 × 0.340151W / mη f = = 0.962100 W / m ⋅ K 0.021m 75°Cεf( )151W / m75°C= = 20.1, R′2t,f = = 0.50 m ⋅K / W100 W / m ⋅ K 0.001m 75°C151W / m( )θb75°CT( L)= T∞+ = 25° C+ = 95.6°Ccosh mL + h / mk sinh mL 1.057 + 0.0167 0.340( ) ( )Case B: From Eqs. (3.76), (3.86), (3.81), (3.83) and (3.75)M′ = = ( ) =
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PROBLEM 3.1KNOWN: One-dimensional,
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PROBLEM 3.2 (Cont.)Surface temperat
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T∞,i − Ts,i 1hi0.10= = = 0.846,
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PROBLEM 3.4 (Cont.)7000Radiant heat
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PROBLEM 3.6KNOWN: Design and operat
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PROBLEM 3.7KNOWN: A layer of fatty
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PROBLEM 3.8KNOWN: Dimensions of a t
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PROBLEM 3.9KNOWN: Thicknesses of th
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PROBLEM 3.11KNOWN: Drying oven wall
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PROBLEM 3.13KNOWN: Composite wall o
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PROBLEM 3.15KNOWN: Dimensions and m
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PROBLEM 3.17KNOWN: Total floor spac
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PROBLEM 3.18KNOWN: Concrete wall of
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(2)(2)(2)Rcdm K/WPROBLEM 3.19 (Cont
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and with ′′ ( B B)( c,2 − s,2
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PROBLEM 3.22KNOWN: Temperatures and
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PROBLEM 3.23 (Cont.)1300Temperature
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PROBLEM 3.25KNOWN: Thicknesses and
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PROBLEM 3.27KNOWN: Operating condit
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PROBLEM 3.28KNOWN: Dimensions, ther
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PROBLEM 3.29KNOWN: Conduction in a
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PROBLEM 3.31KNOWN: Temperature depe
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PROBLEM 3.33KNOWN: Steady-state tem
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PROBLEM 3.35KNOWN: Thickness and in
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PROBLEM 3.36KNOWN: Temperature and
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PROBLEM 3.37KNOWN: Inner and outer
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PROBLEM 3.38 (Cont.)2000016000Heat
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PROBLEM 3.39 (Cont.)and the heat ga
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PROBLEM 3.40 (Cont.)240Outer surfac
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PROBLEM 3.42KNOWN: Electric current
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PROBLEM 3.43KNOWN: Diameter of elec
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PROBLEM 3.44 (Cont.)(b) From an ene
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PROBLEM 3.45 (Cont.)The heat extrac
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PROBLEM 3.47KNOWN: Electric current
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PROBLEM 3.48KNOWN: Saturated steam
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PROBLEM 3.49KNOWN: Temperature and
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PROBLEM 3.50 (Cont.)20002Heat loss,
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PROBLEM 3.51KNOWN: Pipe wall temper
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PROBLEM 3.53KNOWN: Surface temperat
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PROBLEM 3.55KNOWN: Diameter of a sp
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PROBLEM 3.56KNOWN: Sphere of radius
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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
Page 127 and 128: PROBLEM 3.88 (Cont.)Clearly, the ab
Page 129 and 130: PROBLEM 3.89 (Cont.)(b) Using the o
Page 131 and 132: PROBLEM 3.90KNOWN: Electric current
Page 133 and 134: PROBLEM 3.91KNOWN: Materials, dimen
Page 135 and 136: PROBLEM 3.92KNOWN: Long rod experie
Page 137 and 138: PROBLEM 3.94KNOWN: Radial distribut
Page 139 and 140: Henceq2 2() = s,i + ( i − )PROBLE
Page 141 and 142: PROBLEM 3.96 (Cont.)(b) With the co
Page 143 and 144: PROBLEM 3.97 (Cont.)(b) The sphere
Page 145 and 146: PROBLEM 3.98KNOWN: Radius, thicknes
Page 147 and 148: The boundary conditions are:( ) = w
Page 149 and 150: PROBLEM 3.101KNOWN: Dimensions of a
Page 151 and 152: PROBLEM 3.102 (Cont.)Substituting f
Page 153 and 154: PROBLEM 3.103 (Cont.)Hence, the tem
Page 155 and 156: PROBLEM 3.105KNOWN: Electric power
Page 157 and 158: PROBLEM 3.107KNOWN: TC wire leads a
Page 159 and 160: PROBLEM 3.108KNOWN: Rod (D, k, 2L)
Page 161 and 162: PROBLEM 3.109KNOWN: Long rod in ove
Page 163 and 164: ( ) θ ( )PROBLEM 3.110 (Cont.)1/2
Page 165 and 166: PROBLEM 3.111 (Cont.)−( ) 1/21/22
Page 167 and 168: PROBLEM 3.112 (Cont.)The gradient a
Page 169 and 170: PROBLEM 3.114KNOWN: Dimensions, end
Page 171 and 172: PROBLEM 3.116KNOWN: Dimensions and
Page 173 and 174: PROBLEM 3.117 (Cont.)Continued...dT
Page 175 and 176: PROBLEM 3.119KNOWN: Long, aluminum
Page 177: PROBLEM 3.121KNOWN: Thickness, leng
Page 181 and 182: PROBLEM 3.123KNOWN: Length, thickne
Page 185 and 186: PROBLEM 3.126KNOWN: Pin fin of ther
Page 187 and 188: PROBLEM 3.128KNOWN: Slender rod of
Page 189 and 190: PROBLEM 3.130KNOWN: Arrangement of
Page 191 and 192: PROBLEM 3.131KNOWN: Conditions asso
Page 193 and 194: PROBLEM 3.132 (Cont.)N t(mm) η f R
Page 195 and 196: 2( ) ( )PROBLEM 3.133 (Cont.)25 0.0
Page 197 and 198: The fin heat rate is( )( )PROBLEM 3
Page 199 and 200: PROBLEM 3.135 (CONT.)Heat rate, qt(
Page 201 and 202: PROBLEM 3.136 (Cont.)With w = 0.25
Page 203 and 204: where( )( )sinh(mL) + h mk cosh(mL)
Page 205 and 206: ( )PROBLEM 3.138 (Cont.)C1 = 1+ η
Page 207 and 208: PROBLEM 3.139 (Cont.)Heat generatio
Page 209 and 210: PROBLEM 3.140 (Cont.)5000Heat rate,
Page 211 and 212: PROBLEM 3.142KNOWN: Dimensions, bas
Page 215 and 216: PROBLEM 3.146KNOWN: Dimensions, bas
Page 217 and 218: PROBLEM 3.147 (Cont.)5 2 3/2( ) 1/2
Page 219 and 220: PROBLEM 3.148 (Cont.)Once the heat
Page 221 and 222: 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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