John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook, страница 9

Plot Tsphere as a function of t. Verify the lumpedcapacity assumption.1.27A 3 cm diameter, black spherical heater is kept at 1100◦ C. It radiates through an evacuated space to a surrounding sphericalshell of Nichrome V. The shell has a 9 cm inside diameter andis 0.3 cm thick. It is black on the inside and is held at 25◦ C onthe outside. Find (a) the temperature of the inner wall of theshell and (b) the heat transfer, Q.

(Treat the shell as a planewall.)1.28The sun radiates 650 W/m2 on the surface of a particular lake.At what rate (in mm/hr) would the lake evaporate away if all ofthis energy went to evaporating water? Discuss as many otherChapter 1: Introduction44ways you can think of that this energy can be distributed (hfgfor water is 2,257,000 J/kg). Do you suppose much of the 650W/m2 goes to evaporation?1.29It is proposed to make picnic cups, 0.005 m thick, of a newplastic for which k = ko (1 + aT 2 ), where T is expressed in ◦ C,ko = 0.15 W/m·K, and a = 10−4 ◦ C−2 . We are concerned withthermal behavior in the extreme case in which T = 100◦ C inthe cup and 0◦ C outside. Plot T against position in the cupwall and find the heat loss, q.1.30A disc-shaped wafer of diamond 1 lb is the target of a very highintensity laser.

The disc is 5 mm in diameter and 1 mm deep.The flat side is pulsed intermittently with 1010 W/m2 of energyfor one microsecond. It is then cooled by natural convectionfrom that same side until the next pulse. If h = 10 W/m2 K andT∞ =30◦ C, plot Tdisc as a function of time for pulses that are 50s apart and 100 s apart. (Note that you must determine thetemperature the disc reaches before it is pulsed each time.)1.31A 150 W light bulb is roughly a 0.006 m diameter sphere. Itssteady surface temperature in room air is 90◦ C, and h on theoutside is 7 W/m2 K.

What fraction of the heat transfer fromthe bulb is by radiation directly from the filament through theglass? (State any additional assumptions.)1.32How much entropy does the light bulb in Problem 1.31 produce?1.33Air at 20◦ C flows over one side of a thin metal sheet (h = 10.6W/m2 K). Methanol at 87◦ C flows over the other side (h = 141W/m2 K). The metal functions as an electrical resistance heater,releasing 1000 W/m2 . Calculate (a) the heater temperature, (b)the heat transfer from the methanol to the heater, and (c) theheat transfer from the heater to the air.1.34A planar black heater is simultaneously cooled by 20◦ C air (h =14.6 W/m2 K) and by radiation to a parallel black wall at 80◦ C.What is the temperature of the heater if it delivers 9000 W/m2 ?1.35An 8 oz. can of beer is taken from a 3◦ C refrigerator and placedin a 25◦ C room.

The 6.3 cm diameter by 9 cm high can is placedon an insulated surface (h = 7.3 W/m2 K). How long will ittake to reach 12◦ C? Ignore thermal radiation, and discuss yourother assumptions.Problems451.36A resistance heater in the form of a thin sheet runs parallelwith 3 cm slabs of cast iron on either side of an evacuatedcavity. The heater, which releases 8000 W/m2 , and the castiron are very nearly black.

The outside surfaces of the castiron slabs are kept at 10◦ C. Determine the heater temperatureand the inside slab temperatures.1.37A black wall at 1200◦ C radiates to the left side of a parallelslab of type 316 stainless steel, 5 mm thick. The right side ofthe slab is to be cooled convectively and is not to exceed 0◦ C.Suggest a convective process that will achieve this.1.38A cooler keeps one side of a 2 cm layer of ice at −10◦ C. Theother side is exposed to air at 15◦ C. What is h just on theedge of melting? Must h be raised or lowered if melting is toprogress?1.39At what minimum temperature does a black heater deliver itsmaximum monochromatic emissive power in the visible range?Compare your result with Fig.

10.2.1.40The local heat transfer coefficient during the laminar flow offluid over a flat plate of length L is equal to F /x 1/2 , where F isa function of fluid properties and the flow velocity. How doesh compare with h(x = L)? (x is the distance from the leadingedge of the plate.)1.41An object is initially at a temperature above that of its surroundings. We have seen that many kinds of convective processes will bring the object into equilibrium with its surroundings.

Describe the characteristics of a process that will do sowith the least net increase of the entropy of the universe.1.42A 250◦ C cylindrical copper billet, 4 cm in diameter and 8 cmlong, is cooled in air at 25◦ C. The heat transfer coefficientis 5 W/m2 K. Can this be treated as lumped-capacity cooling?What is the temperature of the billet after 10 minutes?1.43The sun’s diameter is 1,392,000 km, and it emits energy as ifit were a black body at 5777 K. Determine the rate at which itemits energy.

Compare this with a value from the literature.What is the sun’s energy output in a year?Chapter 1: Introduction46Bibliography of Historical and Advanced TextsWe include no specific references for the ideas introduced in Chapter 1since these may be found in introductory thermodynamics or physicsbooks. References 1–6 are some texts which have strongly influencedthe field. The rest are relatively advanced texts or handbooks which gobeyond the present textbook.References[1.1] J. Fourier. The Analytical Theory of Heat. Dover Publications, Inc.,New York, 1955.[1.2] L.

M. K. Boelter, V. H. Cherry, H. A. Johnson, and R. C. Martinelli.Heat Transfer Notes. McGraw-Hill Book Company, New York, 1965.Originally issued as class notes at the University of California atBerkeley between 1932 and 1941.[1.3] M. Jakob. Heat Transfer. John Wiley & Sons, New York, 1949.[1.4] W. H. McAdams. Heat Transmission. McGraw-Hill Book Company,New York, 3rd edition, 1954.[1.5] W. M. Rohsenow and H. Y. Choi. Heat, Mass and Momentum Transfer. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1961.[1.6] E. R. G.

Eckert and R. M. Drake, Jr. Analysis of Heat and MassTransfer. Hemisphere Publishing Corp., Washington, D.C., 1987.[1.7] H. S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. Oxford University Press, New York, 2nd edition, 1959. Very comprehenisve, but quite dense.[1.8] D. Poulikakos. Conduction Heat Transfer. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1994. This book’s approach is very accessible.Good coverage of solidification.[1.9] V. S. Arpaci. Conduction Heat Transfer. Ginn Press/Pearson Custom Publishing, Needham Heights, Mass., 1991. Abridgement ofthe 1966 edition, omitting numerical analysis.References[1.10] W.

M. Kays and M. E. Crawford. Convective Heat and Mass Transfer. McGraw-Hill Book Company, New York, 3rd edition, 1993.Coverage is mainly of boundary layers and internal flows.[1.11] F.M. White. Viscous Fluid Flow. McGraw-Hill, Inc., New York, 2ndedition, 1991. Excellent development of fundamental results forboundary layers and internal flows.[1.12] J.A. Schetz.

Foundations of Boundary Layer Theory for Momentum,Heat, and Mass Transfer. Prentice-Hall, Inc., Englewood Cliffs, NJ,1984. This book shows many experimental results in support ofthe theory.[1.13] A. Bejan. Convection Heat Transfer. John Wiley & Sons, New York,2nd edition, 1995. This book makes good use of scaling arguments.[1.14] M. Kaviany. Principles of Convective Heat Transfer.

SpringerVerlag, New York, 1995. This treatise is wide-ranging and quiteunique. Includes multiphase convection.[1.15] H. Schlichting and K. Gersten. Boundary-Layer Theory. SpringerVerlag, Berlin, 8th edition, 2000. Very comprehensive development of boundary layer theory. A classic.[1.16] H. C. Hottel and A. F. Sarofim. Radiative Transfer. McGraw-HillBook Company, New York, 1967.[1.17] R. Siegel and J. R. Howell. Thermal Radiation Heat Transfer. Taylorand Francis-Hemisphere, Washington, D.C., 4th edition, 2001.[1.18] M.

F. Modest. Radiative Heat Transfer. McGraw-Hill, New York,1993.[1.19] P. B. Whalley. Boiling, Condensation, and Gas-Liquid Flow. OxfordUniversity Press, Oxford, 1987.[1.20] J. G. Collier and J. R. Thome. Convective Boiling and Condensation.Oxford University Press, Oxford, 3rd edition, 1994.[1.21] Y. Y. Hsu and R. W. Graham. Transport Processes in Boiling andTwo-Phase Systems Including Near-Critical Systems. American Nuclear Society, LaGrange Park, IL, 1986.4748Chapter 1: Introduction[1.22] W.

M. Kays and A. L. London. Compact Heat Exchangers. McGrawHill Book Company, New York, 3rd edition, 1984.[1.23] G. F. Hewitt, editor. Heat Exchanger Design Handbook 1998. BegellHouse, New York, 1998.[1.24] R. B. Bird, W. E. Stewart, and E. N. Lightfoot. Transport Phenomena.John Wiley & Sons, Inc., New York, 2nd edition, 2002.[1.25] A. F. Mills. Mass Transfer. Prentice-Hall, Inc., Upper Saddle River,2001. Mass transfer from a mechanical engineer’s perpective withstrong coverage of convective mass transfer.[1.26] D. S.

Wilkinson. Mass Transfer in Solids and Fluids. CambridgeUniversity Press, Cambridge, 2000. A systematic development ofmass transfer with a materials science focus and an emphasis onmodelling.[1.27] D. R. Poirier and G. H. Geiger. Transport Phenomena in MaterialsProcessing.

The Minerals, Metals & Materials Society, Warrendale,Pennsylvania, 1994. A comprehensive introduction to heat, mass,and momentum transfer from a materials science perspective.[1.28] W. M. Rohsenow, J. P. Hartnett, and Y. I. Cho, editors. Handbookof Heat Transfer. McGraw-Hill, New York, 3rd edition, 1998.2.Heat conduction concepts,thermal resistance, and theoverall heat transfer coefficientIt is the fire that warms the cold, the cold that moderates the heat.

. .thegeneral coin that purchases all things. . .Don Quixote, M. de Cervantes, 16152.1The heat diffusion equationObjectiveWe must now develop some ideas that will be needed for the design ofheat exchangers. The most important of these is the notion of an overallheat transfer coefficient. This is a measure of the general resistance of aheat exchanger to the flow of heat, and usually it must be built up fromanalyses of component resistances.