Chris Long & Naser Sayma Heat Transfer: Exercises Download free eBooks at bookboon.com Heat Transfer: Exercises © 2010 Chris Long, Naser Sayma & Ventus Publishing ApS ISBN 978-87-7681-433-5 Download free eBooks at bookboon.com Heat Transfer: Exercises Contents Contents Preface Introduction Conduction 11 Convection 35 Radiation 60 Heat Exchangers 79 e Graduate Programme for Engineers and Geoscientists I joined MITAS because I wanted real responsibili Maersk.com/Mitas Real work International Internationa al opportunities ree work wo or placements Month 16 I was a construction supervisor in the North Sea advising and helping foremen he solve problems s Download free eBooks at bookboon.com Click on the ad to read more Preface Heat Transfer: Exercises Preface Worked examples are a necessary element to any textbook in the sciences, because they reinforce the theory (i.e the principles, concepts and methods) Once the theory has been understood, well chosen examples can be used, with modification, as a template to solve more complex, or similar problems This work book contains examples and full solutions to go with the text of our e-book (Heat Transfer, by Long and Sayma) The subject matter corresponds to the five chapters of our book: Introduction to Heat Transfer, Conduction, Convection, Heat Exchangers and Radiation They have been carefully chosen with the above statement in mind Whilst compiling these examples we were very much aware of the need to make them relevant to mechanical engineering students Consequently many of the problems are taken from questions that have or may arise in a typical design process The level of difficulty ranges from the very simple to challenging Where appropriate, comments have been added which will hopefully allow the reader to occasionally learn something extra We hope you benefit from following the solutions and would welcome your comments Christopher Long Naser Sayma Brighton, UK, February 2010 Download free eBooks at bookboon.com Introduction Heat Transfer: Exercises Introduction Example 1.1 The wall of a house, m wide and m high is made from 0.3 m thick brick with k 0.6 W / m K The surface temperature on the inside of the wall is 16oC and that on the outside is 6oC Find the heat flux through the wall and the total heat loss through it Solution: For one-dimensional steady state conduction: q k q dT k Ti To dx L 16 6 20 W / m Q qA 20 6 840 W The minus sign indicates heat flux from inside to outside Download free eBooks at bookboon.com Introduction Heat Transfer: Exercises Example 1.2 A 20 mm diameter copper pipe is used to carry heated water, the external surface of the pipe is subjected to a convective heat transfer coefficient of h W / m K , find the heat loss by convection per metre length of the pipe when the external surface temperature is 80oC and the surroundings are at 20oC Assuming black body radiation what is the heat loss by radiation? Solution qconv h Ts T f 680 20 360 W / m For metre length of the pipe: Qconv q conv A q conv 2 r 360 0.01 22.6 W / m For radiation, assuming black body behaviour: q rad Ts4 T f4 q rad 5.67 10 8 353 293 q rad 462 W / m For metre length of the pipe Qrad q rad A 462 0.01 29.1 W / m A value of h = W/m2 K is representative of free convection from a tube of this diameter The heat loss by (black-body) radiation is seen to be comparable to that by convection Download free eBooks at bookboon.com Introduction Heat Transfer: Exercises Example 1.3 A plate 0.3 m long and 0.1 m wide, with a thickness of 12 mm is made from stainless steel ( k 16 W / m K ), the top surface is exposed to an airstream of temperature 20oC In an experiment, the plate is heated by an electrical heater (also 0.3 m by 0.1 m) positioned on the underside of the plate and the temperature of the plate adjacent to the heater is maintained at 100oC A voltmeter and ammeter are connected to the heater and these read 200 V and 0.25 A, respectively Assuming that the plate is perfectly insulated on all sides except the top surface, what is the convective heat transfer coefficient? Solution Heat flux equals power supplied to electric heater divided by the exposed surface area: q V I V I 200 0.25 1666.7 W / m A W L This will equal the conducted heat through the plate: k T2 T1 t 1666.7 0.012 98.75C qt T1 T2 100 16 k q (371.75 K) The conducted heat will be transferred by convection and radiation at the surface: q hT1 T f T14 T f4 h q T14 T f4 T Tf 1666.7 5.67 10 371.75 8 371.75 293 Download free eBooks at bookboon.com 293 12.7 W / m K Introduction Heat Transfer: Exercises Example 1.4 An electronic component dissipates 0.38 Watts through a heat sink by convection and radiation (black body) into surrounds at 20oC What is the surface temperature of the heat sink if the convective heat transfer coefficient is W/m2 K, and the heat sink has an effective area of 0.001 m2 ? Solution q Q hTs T Ts4 T4 A 0.38 6Ts 293 5.67 10 3 Ts4 293 0.001 5.67 10 8 Ts4 6Ts 2555.9 This equation needs to be solved numerically Newton-Raphson’s method will be used here: f 5.67 10 8 Ts4 6Ts 2555.9 df 22.68 10 8 Ts3 dTs T n 1 s 5.67 10 8 Ts4 6Ts 2555.9 T T 22.68Ts3 df dTs n s f n s Start iterations with Ts0 300 K Ts1 300 5.67 10 8 300 300 2555.9 324.46 K 22.68 300 5.67 10 8 324.46 324.46 2555.9 323 K T 324.46 22.68 324.46 s Download free eBooks at bookboon.com Introduction Heat Transfer: Exercises The difference between the last two iterations is small, so: Ts0 323 K 50C The value of 300 K as a temperature to begin the iteration has no particular significance other than being above the ambient temperature www.job.oticon.dk Download free eBooks at bookboon.com 10 Click on the ad to read more [...]... fin So total heat flow: Q Qu Q f 0.461 9 2.03 18.7 W Finn effectiveness fin Qf Fin heat transfer rate Heat transfer rate that would occur in the absence of the fin hAc Tb T f fin 2.03 106 12 40 10 6 60 20 Download free eBooks at bookboon.com 20 Conduction Heat Transfer: Exercises Fin efficiency: Actual heat transfer through the fin Heat that would be transferred... speed at which this will occur? Download free eBooks at bookboon.com 32 Conduction Heat Transfer: Exercises Solution Spherical bead: Assume this behaves as a lumped mass, then (given) For lumped mass on cooling from temperature Ti ��� Which gives the required value of heat transfer coefficient So Download free eBooks at bookboon.com 33 Conduction Heat Transfer: Exercises For a sphere From which with Pr... thickness Download free eBooks at bookboon.com 14 Conduction Heat Transfer: Exercises i ii Calculate the heat loss by convection and conduction per metre length of uninsulated pipe when the water temperature is 15oC, the outside air temperature is -10oC, the water side heat transfer coefficient is 30 kW/m2 K and the outside heat transfer coefficient is 20 W/m2 K Calculate the corresponding heat loss when the... mL where m 2 hP and Ac is the cross sectional area kAc Determine the total convective heat transfer from the heat sink, the fin effectiveness and the fin efficiency Download free eBooks at bookboon.com 18 Conduction Heat Transfer: Exercises Solution Total heat fluxed is that from the un-finned surface plus the heat flux from the fins Q Qu Q f Qu Au h (Tb T f ) w s N 1) h Tb T f... the time estimated from the equation ( e ht ) which assumes a constant value of heat transfer coefficient Solution Low Biot number approximation for free convection for Bi 1 Heat transfer by convection = rate of change of internal energy Download free eBooks at bookboon.com 29 Conduction Heat Transfer: Exercises hA(Ts T f ) mC d (Ts T f ) (1) dt n We know that h G (Ts T f ) Where... insulation material with k = 0.07 W/m K Find the width of the insulation that is required to reduce the convective heat loss to 15 W/m2 Download free eBooks at bookboon.com 13 Click on the ad to read more Conduction Heat Transfer: Exercises Solution q UT U where U is the overall heat transfer coefficient given by: q 15 0.333W / m 2 K T 25 (20) 1 L p Li Ls 1 U hi k p k... balance on an annular control volume as shown the figure above The heat balance in the control volume is given by: Heat in + Heat out = rate of change of internal energy Q r Q z Q r r Q z z Q r r Q r Q r r Q z z Q z Q z z u t (2.1) Download free eBooks at bookboon.com 11 Conduction Heat Transfer: Exercises u mcT Substituting in equation 2.1: (mcT ) Q Q r... vestas.com/jobs Application period will open March 1 2012 Download free eBooks at bookboon.com 16 Click on the ad to read more Conduction Heat Transfer: Exercises Q L 2 15 (10) 7.3W / m 1 ln0.052 / 0.05 ln(0.15 / 0.052) 1 30000 0.05 50 0.05 20 0.15 For the plain pipe, the heat loss is governed by the convective heat transfer coefficient on the outside, which provides the highest thermal... overall heat loss Example 2.4 Water at 80oC is pumped through 100 m of stainless steel pipe, k = 16 W/m K of inner and outer radii 47 mm and 50 mm respectively The heat transfer coefficient due to water is 2000 W/m2 K The outer surface of the pipe loses heat by convection to air at 20oC and the heat transfer coefficient is 200 W/m2 K Calculate the heat flow through the pipe Also calculate the heat flow... and a heat transfer coefficient of h = 15 W/m2 K acts over the remaining surfaces Estimate the number of fins required to ensure the base temperature does not exceed 120oC Are you remarkable? Win one of the six full tuition scholarships for International MBA or MSc in Management Download free eBooks at bookboon.com 22 register now rode www.Nyen lenge.com MasterChal Conduction Heat Transfer: Exercises ... Sayma Heat Transfer: Exercises Download free eBooks at bookboon.com Heat Transfer: Exercises © 2010 Chris Long, Naser Sayma & Ventus Publishing ApS ISBN 978-87-7681-433-5 Download free eBooks at bookboon.com... convective heat transfer from the heat sink, the fin effectiveness and the fin efficiency Download free eBooks at bookboon.com 18 Conduction Heat Transfer: Exercises Solution Total heat fluxed... 6 60 20 Download free eBooks at bookboon.com 20 Conduction Heat Transfer: Exercises Fin efficiency: Actual heat transfer through the fin Heat that would be transferred if all the fin area