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

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PROBLEM 3.26KNOWN: Surface area and maximum temperature of a chip. Thickness of aluminum coverand chip/cover contact resistance. Fluid convection conditions.FIND: Maximum chip power.SCHEMATIC:ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional heat transfer, (3)Negligible heat loss from sides and bottom, (4) Chip is isothermal.PROPERTIES: Table A.1, Aluminum (T ≈ 325 K): k = 238 W/m⋅K.ANALYSIS: For a control surface about the chip, conservation of energy yieldsorEg − Eout = 0( Tc− T∞) A( L/k) + R′′+ ( 1/ h)Pc− = 0⎣⎡ t,c ⎦⎤$( 85 − 25-4 2) C( 10 m )Pc,max=⎡ 4 2( 0.002 / 238) 0.5 10−( 1/1000)⎤⎢+ × + m ⋅K/W⎣⎥⎦60 10−4 $× C⋅m2Pc,max=8.4× 10-6+ 0.5× 104+ 103m2⋅K/W− −( )Pc,max= 5.7 W. Rt,c >> Rcond8.
PROBLEM 3.27KNOWN: Operating conditions for a board mounted chip.FIND: (a) Equivalent thermal circuit, (b) Chip temperature, (c) Maximum allowable heat dissipation fordielectric liquid (h o = 1000 W/m 2 ⋅K) and air (h o = 100 W/m 2 ⋅K). Effect of changes in circuit boardtemperature and contact resistance.SCHEMATIC:ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction, (3) Negligible chipthermal resistance, (4) Negligible radiation, (5) Constant properties.PROPERTIES: Table A-3, Aluminum oxide (polycrystalline, 358 K): k b = 32.4 W/m⋅K.ANALYSIS: (a)(b) Applying conservation of energy to a control surface about the chip ( E − E = 0)q′′ c −qi′′ − q′′o = 0Tc −T∞,i Tc −T∞,oq′′ c = +1hi + ( Lk)+ R′′b t,c 1hoWith q„„ c3–10 4 W m2 , h o = 1000 W/m 2 ⋅K, k b = 1 W/m⋅K and−4 2( 1 40 + 0.005 1+ 10 ) m ⋅K W ( ) ,inout4 2R′′ −t,c = 10 m ⋅ K W ,$ $4 2 Tc −20 C Tc−20 C3× 10 W m = +21 1000 m ⋅ K W3 4 2 2× 10 W m = ( 33.2T c − 664 + 1000T c − 20,000 ) W m ⋅ K1003T c = 50,664T c = 49°C.
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: PROBLEM 3.25KNOWN: Thicknesses and
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
Page 85 and 86: 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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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
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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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