# heat-transfer-exercise-book

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dt TTd mCTThA fsfs )( )( \uf02d\uf02d\uf03d\uf02d (1) We know that nfs TTGh )( \uf02d\uf03d Where G is a constant. (Note that this relation arises from the usual Nusselt/Grashof relationship in free convection; for example: \uf028 \uf029 3/1Pr1.0 GrNu \uf03d in turbulent flow or \uf028 \uf029 4/1Pr54.0 GrNu \uf03d for laminar flow) Equation 1 then becomes: \uf028 \uf029 dt TTd A mCTTTTG fsfs n fs )( )( \uf02d\uf02d\uf03d\uf02d\uf02d \uf0f2 \uf0f2 \uf03d \uf02d \uf02b\uf02d \uf02d\uf03d\uf02d t t t t n fs fs TT TTd dt mC GA 0 0 1)( )( \uf028 \uf029 \uf028 \uf029 n tfs n fs TTTTmC GnAt \uf02d \uf03d \uf02d \uf02d\uf02d\uf02d\uf03d 0 (2) At \uf028 \uf029 \uf028 \uf029fisfs TTTTt \uf02d\uf03d\uf02d\uf03d ,,0 If we divide equation 2 by \uf028 \uf029 nfis TT \uf02d\uf02d, And use the definition \uf028 \uf029 \uf028 \uf029fis fs TT TT \uf02d \uf02d\uf03d , \uf071 We obtain \uf028 \uf029 \uf028 \uf029nfisnnfis TTmC GnAt TTmC GnAt \uf02d\uf03d\uf02d\uf03d\uf02d \uf02d \uf02d , , 1\uf071 Since \uf028 \uf029 ifis hTTG \uf03d\uf02d, , the heat transfer coefficient at time t = 0, then 1\uf02b\uf03d\uf02d mC Athin\uf071 Download free eBooks at bookboon.com Click on the ad to read more Heat Transfer: Exercises 31 Conduction Or 1\uf02b\uf03d\uf02d tnhin \uf06c\uf071 For aluminium KkgJCmkg /870,/2750 3 \uf03d\uf03d\uf072 For laminar free convection, n = ¼ kgXAm 22.0002.004.02750 \uf03d\uf0b4\uf0b4\uf03d\uf03d \uf072 JKm mC A /101.2 87022.0 04.0 24\uf02d\uf0b4\uf03d\uf0b4\uf03d\uf03d\uf06c 1\uf02b\uf03d\uf02d tnhin \uf06c\uf071 which gives www.mastersopenday.nl Visit us and find out why we are the best! Master\u2019s Open Day: 12 October 2013 Join the best at the Maastricht University School of Business and Economics! Top master\u2019s programmes \u2022 33rd place Financial Times worldwide ranking: MSc International Business \u2022 1st place: MSc International Business \u2022 1st place: MSc Financial Economics \u2022 2nd place: MSc Management of Learning \u2022 2nd place: MSc Economics \u2022 2nd place: MSc Econometrics and Operations Research \u2022 2nd place: MSc Global Supply Chain Management and Change Sources: Keuzegids Master ranking 2013; Elsevier \u2018Beste Studies\u2019 ranking 2012; Financial Times Global Masters in Management ranking 2012 Maastricht University is the best specialist university in the Netherlands (Elsevier) Download free eBooks at bookboon.com Heat Transfer: Exercises 32 Conduction \uf028 \uf029 \uf06c \uf071 i n nh t 1\uf02d\uf03d \uf02d When 2.0 20120 204040 \uf03d\uf02d \uf02d\uf03d\uf0b0\uf03d \uf071CT Then \uf028 \uf029 \uf028 \uf029 st 590101.2164/1 12.0 4 4/1 \uf03d\uf0b4\uf0b4\uf0b4 \uf02d\uf03d \uf02d \uf02d For the equation the \uf06c\uf071 \uf02d\uf03d which assumes that the heat transfer coefficient is independent of surface-to-fluid temperature difference. s h t 479 101.216 2.0lnln 4 \uf03d\uf0b4\uf0b4\uf02d\uf03d\uf02d\uf03d \uf02d\uf06c \uf071 Percentage error = %19100 590 479590 \uf03d\uf0b4\uf02d Example 2.11 A 1 mm diameter spherical thermocouple bead (C = 400 J/kg K, \ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd) is required to respond to 99.5% change of the surrounding air \ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd \ufffd \ufffd\ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd , \ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\u2044 and Pr = 0.77) temperature in 10 ms. What is the minimum air speed at which this will occur? Download free eBooks at bookboon.com Heat Transfer: Exercises 33 Conduction Solution Spherical bead: \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd 6\u2044 Assume this behaves as a lumped mass, then \ufffd\ufffd \ufffd \ufffd\ufffd \ufffd\ufffd \ufffd \ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd (given) For lumped mass on cooling from temperature Ti \ufffd\ufffd \ufffd \ufffd\ufffd \ufffd\ufffd \ufffd \ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd \ufffd \ufffd \ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd \ufffd \ufffd\ufffd\ufffd Which gives the required value of heat transfer coefficient \ufffd\ufffd \ufffd\ufffd\ufffd \ufffd \ufffd\ufffd\ufffd So Download free eBooks at bookboon.com Heat Transfer: Exercises 34 Conduction \ufffd \ufffd 0.\ufffd \ufffd\ufffd \ufffd 6 \ufffd\ufffd \ufffd\ufffd\ufffd \ufffd 0.\ufffd \ufffd \ufffd \ufffd 6 \ufffd \ufffd 0.\ufffd \ufffd 10 \ufffd\ufffd \ufffd 400 \ufffd 7800 6 \ufffd 260 \ufffd \ufffd \ufffd \ufffd\u2044 \ufffd\ufffd\ufffd \ufffd \ufffd\ufffd\ufffd \ufffd 260 \ufffd 10\ufffd\ufffd 0.0262 \ufffd \ufffd.\ufffd For a sphere \ufffd\ufffd\ufffd \ufffd 2 \ufffd \ufffd0.4\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd 0.06\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd.\ufffd From which with Pr = 0.707 \ufffd \ufffd 0.4\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd 0.06\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd \ufffd.4 \ufffd 0 \ufffd\ufffd \ufffd 0.2\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd 0.04\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd Using Newton iteration \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd \ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd Starting with ReD = 300 \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd 300 \ufffd \ufffd0.4\u221a300 \ufffd 0.06\ufffd300\ufffd\ufffd\ufffd\ufffd \ufffd \ufffd.4\ufffd \ufffd 0.2\u221a300 \ufffd 0.04 300\ufffd\ufffd\ufffd\ufffd \ufffd 300 \ufffd 0.2220.01782 Which is close enough to 300 From which \ufffd\ufffd \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd \ufffd 4.\ufffd \ufffd\ufffd\ufffd Download free eBooks at bookboon.com Click on the ad to read more Heat Transfer: Exercises 35 Convection 3. Convection Example 3.1 Calculate the Prandtl number (Pr = \uf06dCp/k) for the following a) Water at 20\uf0b0C: \uf06d = 1.002 x 10\uf02d3 kg/m s, Cp = 4.183 kJ/kg K and k = 0.603 W/m K b) Water at 90\uf0b0C: \uf072 = 965 kg/m3, \uf06e = 3.22 x 10\uf02d7 m2/s, Cp = 4208 J/kg K and k = 0.676 W/m K c) Air at 20\uf0b0C and 1 bar: R = 287 J/kg K, \uf06e = 1.563 x 10\uf02d5 m2/s, Cp = 1005 J/kg K and k = 0.02624 W/m K d) Air at 100\uf0b0C: \uf028 \uf029T T \uf02b \uf0b4\uf03d \uf02d 110 1046.1 236\uf06d kg/m s KkgkJTTC p /1098.31058.2917.0 284 \uf02d\uf02d \uf0b4\uf02d\uf0b4\uf02b\uf03d (Where T is the absolute temperature in K) and k = 0.03186 W/m K. e) Mercury at 20\uf0b0C: \uf06d = 1520 x 10\uf02d6 kg/m s, Cp = 0.139 kJ/kg K and k = 0.0081 kW/m K f) Liquid Sodium at 400 K: \uf06d = 420 x 10\uf02d6 kg/m s, Cp = 1369 J/kg K and k = 86 W/m K g) Engine Oil at 60\uf0b0C: \uf06d = 8.36 x 10\uf02d2 kg/m s, Cp = 2035 J/kg K and k = 0.141 W/m K Designed for high-achieving graduates across all disciplines, London Business School\u2019s Masters in Management provides specific and tangible foundations for a successful career in business. This 12-month, full-time programme is a business qualification with impact. In 2010, our MiM employment rate was 95% within 3 months of graduation*; the majority of graduates choosing to work in consulting or financial services. As well as a renowned qualification from a world-class business school, you also gain access to the School\u2019s network of more than 34,000 global alumni \u2013 a community that offers support and opportunities throughout your career. For more information visit www.london.edu/mm, email mim@london.edu or give us a call on +44 (0)20 7000 7573. Masters in Management The next step for top-performing graduates * Figures taken from London Business School\u2019s Masters in Management 2010 employment report Download free eBooks at bookboon.com Heat Transfer: Exercises 36 ConvectionSolution a) 95.6 603.0 418310002.1Pr 3 \uf03d\uf0b4\uf0b4\uf03d\uf03d \uf02d k Cp\uf06d b) 93.1 676.0 42081022.3965Pr 7 \uf03d\uf0b4\uf0b4\uf0b4\uf03d\uf03d\uf03d \uf02d k C k C pp \uf072\uf06e\uf06d c) k Cp\uf072\uf06e\uf03dPr 3/19.1 293287 100000 mkg RT P \uf03d\uf0b4\uf03d\uf03d\uf072 712.0 02624.0 100510563.119.1Pr 5 \uf03d\uf0b4\uf0b4\uf0b4\uf03d \uf02d d) \uf028 \uf029 smkgT T /1018.2 373110 3731046.1 110 1046.1 52/36236 \uf02d\uf02d\uf02d \uf0b4\uf03d\uf02b \uf0b4\uf0b4\uf03d\uf02b \uf0b4\uf03d\uf06d KkgJ TTCp /7.1007 3731098.33731058.2917.01098.31058.2917.0 284284 \uf03d \uf0b4\uf0b4\uf02d\uf0b4\uf0b4\uf02b\uf03d\uf0b4\uf02d\uf0b4\uf02b\uf03d \uf02d\uf02d\uf02d\uf02d 689.0 03186.0 7.10071018.2Pr 5 \uf03d\uf0b4\uf0b4\uf03d \uf02d e) 0261.0 100081.0 139101520Pr 3 6 \uf03d\uf0b4 \uf0b4\uf0b4\uf03d\uf03d \uf02d k Cp\uf06d Solution a) 95.6 603.0 418310002.1Pr 3 \uf03d\uf0b4\uf0b4\uf03d\uf03d \uf02d k Cp\uf06d b) 93.1 676.0 42081022.3965Pr 7 \uf03d\uf0b4\uf0b4\uf0b4\uf03d\uf03d\uf03d \uf02d k C k C pp \uf072\uf06e\uf06d c) k Cp\uf072\uf06e\uf03dPr 3/19.1 293287 100000 mkg RT P \uf03d\uf0b4\uf03d\uf03d\uf072 712.0 02624.0 100510563.119.1Pr 5 \uf03d\uf0b4\uf0b4\uf0b4\uf03d \uf02d d) \uf028 \uf029 smkgT T /1018.2 373110 3731046.1 110 1046.1 52/36236 \uf02d\uf02d\uf02d \uf0b4\uf03d\uf02b \uf0b4\uf0b4\uf03d\uf02b \uf0b4\uf03d\uf06d KkgJ TTCp /7.1007 3731098.33731058.2917.01098.31058.2917.0 284284 \uf03d \uf0b4\uf0b4\uf02d\uf0b4\uf0b4\uf02b\uf03d\uf0b4\uf02d\uf0b4\uf02b\uf03d \uf02d\uf02d\uf02d\uf02d 689.0 03186.0 7.10071018.2Pr 5 \uf03d\uf0b4\uf0b4\uf03d \uf02d e) 0261.0 100081.0 139101520Pr 3 6 \uf03d\uf0b4 \uf0b4\uf0b4\uf03d\uf03d \uf02d k Cp\uf06d Solution a) 95.6 603.0 418310002.1Pr 3 \uf03d\uf0b4\uf0b4\uf03d\uf03d \uf02d k Cp\uf06d b) 93.1 676.0 42081022.3965Pr 7 \uf03d\uf0b4\uf0b4\uf0b4\uf03d\uf03d\uf03d \uf02d k C k C pp \uf072\uf06e\uf06d c) k Cp\uf072\uf06e\uf03dPr 3/19.1 293287 100000 mkg RT P \uf03d\uf0b4\uf03d\uf03d\uf072 712.0 02624.0 100510563.119.1Pr