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

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PROBLEM 3.64KNOWN: Representation of the eye with a contact lens as a composite spherical system subjected toconvection processes at the boundaries.FIND: (a) Thermal circuits with and without contact lens in place, (b) Heat loss from anteriorchamber for both cases, and (c) Implications of the heat loss calculations.SCHEMATIC:r 1 =10.2mmr 2 =12.7mmr 3 =16.5mmT ∞,i =37°CT ∞,o =21°Ck 1 =0.35 W/m⋅Kk 2 =0.80 W/m⋅Kh i =12 W/m 2 ⋅Kh o =6 W/m 2 ⋅KASSUMPTIONS: (1) Steady-state conditions, (2) Eye is represented as 1/3 sphere, (3) Convectioncoefficient, h o , unchanged with or without lens present, (4) Negligible contact resistance.ANALYSIS: (a) Using Eqs. 3.9 and 3.36 to express the resistance terms, the thermal circuits are:Without lens:
PROBLEM 3.65KNOWN: Thermal conductivity and inner and outer radii of a hollow sphere subjected to auniform heat flux at its outer surface and maintained at a uniform temperature on the innersurface.FIND: (a) Expression for radial temperature distribution, (b) Heat flux required to maintainprescribed surface temperatures.SCHEMATIC:ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional radial conduction, (3)No generation, (4) Constant properties.ANALYSIS: (a) For the assumptions, the temperature distribution may be obtained byintegrating Fourier’s law, Eq. 3.33. That is,q rr r dr Tqr1k dT or k ( T T s,1).4π∫ =−r1 2 ∫− =− −r Ts,1 4πr r1Hence,qr⎡1 1⎤T() r = Ts,1+ ⎢ − ⎥4 π k ⎣r r1⎦or, with q′′ 22 ≡ q r /4 π r2,q′′ 22r ()2 ⎡1 1⎤T r = Ts,1+ ⎢ − ⎥k ⎣r r1⎦(b) Applying the above result at r 2 ,$k( Ts,2 − Ts,1) 10 W/m⋅K ( 50 −20)Cq′′ 22 = = =−3000 W/m .2 ⎡ 1 1⎤ 2 ⎡ 1 1 ⎤ 1r( 0.1m )2 ⎢ −r2 r⎥ ⎢−1⎣0.1 0.05⎦⎥⎣ ⎦mCOMMENTS: (1) The desired temperature distribution could also be obtained by solvingthe appropriate form of the heat equation,d ⎡ 2 dT⎤ r 0dr ⎢ =⎣ dr ⎥⎦and applying the boundary conditions ( )dT ⎤T r = T and − k = q ′′ .1 s,1 2dr ⎥⎦r2(2) The negative sign on q′′2 implies heat transfer in the negative r direction.
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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
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 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: PROBLEM 3.63 (Cont.)To maintain T 1
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
Page 105 and 106: PROBLEM 3.75KNOWN: Composite wall o
Page 107 and 108: PROBLEM 3.77KNOWN: Geometry and bou
Page 109 and 110: PROBLEM 3.78KNOWN: Thermal conducti
Page 111 and 112: PROBLEM 3.78 (Cont.)qL ⎛1 b ⎞Ts
Page 113 and 114: and from Eq. (3) with x = L and T(L
Page 115 and 116: PROBLEM 3.80 (Cont.)Surface energy
Page 117 and 118: PROBLEM 3.82KNOWN: Distribution of
Page 119 and 120: PROBLEM 3.84KNOWN: Cylindrical shel
Page 121 and 122: PROBLEM 3.86KNOWN: Diameter, resist
Page 123 and 124: PROBLEM 3.87KNOWN: Energy generatio
Page 125 and 126: 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 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
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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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