M otivation tivation and and Hi Highlig hli ghts M otivation: tivation: I n thi this course course,, we we are prim primaril ri ly inte i ntereste rested d in in heat, heat, which which is is the form of of energy than can can be transferred transferred from from one system to another another as a result result of temperature perature dif difference. The The sci scien ence ce that deals with the rates of such energy transfers is called Heat Transfer. Transfer. Why do we need need to undertake a detai detailled study on hea heat transfer? A fter all all, we we can determ determine the amount of heat heat transfer for any system system undergoing rgoi ng any process process using using thermodyna thermodynamic analysis ysis al alone. The The reason reason is is that thermodyna thermodynamics is is concerned concerned with with the amount of heat heat transfer as a system undergoes a process ffrom rom one equil quilibrium bri um state to another, nother, and it gives gives no no indic indica ation tion about about how how long l ong the the process process should should take or what is is the mode of heat transfer. But engi engine neers ers are more concerned wi with th the rate of heat heat transf transfer than the amount. For example, it is relatively simple to calculate, using principle of thermodyna thermodynamics, the amount of heat heat that is is transferred transferred when when water in i n a thermos thermos flask fl ask cools cools from 90 ºC to 60 ºC. But a typical user is more interested in knowing how quickly the liquid in the therm thermos bottle bottle cools, cools, and an an engine gineer er who designs designs the thermos thermos tries tries to understan understand d the mode of heat heat transfer transfer and then designs signs the bottle bottle appropr appropriiately for for low l ow rate rates of heat transf transfer. er. R elevance of heat heat trans tr ansffer : I n the vernacular vernacular of the tim time, heat transf transfer er is is inde indeed a releva relevant subj subject, not to menti ention on an inherently fascinating part of engineering sciences. We will devote much time to acquire an understanding rstanding of heat heat transfer transfer ef effects and to deve developing oping the the skil ski lls needed eded to predict predict heat heat transfer rates. What is the value of this knowledge and to what kinds of problems may be applied? Heat transfer transfer phenomenon enon plays plays an im important role role in many any industri industrial al and envi environme ronmental ntal problem problems. As A s an example, ple, conside considerr the vital vital area of energy production production and conversion. There is not a single application in this area that does not involve heat transfer effects in in some way. In I n the the generation ration of ele electrical ctri cal power, whe whether it i t is is through through nucle clear fission or fusion, the combustion of fossil fuels, magneto hydrodynamic processes, or the use of geotherm geothermal energy energy sources, sources, there are numerous heat tran transfer sfer probl problem ems that must must be solved. solved. The These problem lems inv involve lve conduction ion, co convection ion, an and ra radiat iation ion pr processes an and re relat late to th the design sign of systems such as boil boilers, condensers, and turbi turbine nes. One One is ofte often n confronte confronted d with with the need need to maxim aximize heat transfer transfer rates rates and to mainta aintaiin the integri ntegrity ty of material ri al in i n high high temperature enviro environm nments. On a small aller scale scale there are many any heat transfer problem problems rel relate ated to the devel development ent of solar energy conversion systems for space heating, as well as for electric power production. Heat transfer processes also affect the performance of propulsion systems, such as the internal nternal combusti combustion, on, gas turbine turbine,, and rocket rocket engine ngines. s. Hea Heat transfer transfer problem problemarise arise in the desi design gn of conven conventi tional onal space and and water heating ting system systems, in i n the desi design gn of conventi conventiona onall space and and water heating ting system systems, in i n the desi design gn of inci i ncine nerators rators and cryogenic cryogenic storage equi equipm pment, ent, in in the cooling of electronic equipment, in the design of refrigeration and air conditioning systems, and in in many any man manuf ufacturi acturing ng processes. Hea Heat transfer transfer is is al also releva relevant nt to ai air and water water pollution and strongly influences local and global climate. Highlights: Classification of heat transfer problems: The heat transfer problems typically encountered in practive can be broadly classified into two groups: (1) rating and (2) sizing problems. The rating rating probl problem ems deal with wi th the determination tion of heat transfer transfer rate for an existi xi sting ng system at a specified temperature difference. The sizing problems deal with the determination of the size
Problem 8: The back side of a metallic plate is perfectly insulated while the front side absorbs a solar radiant flux of 800 W/m2. The convection coefficient between the plate and the ambient air is 112 w /m2. K.
(a) Neg Negllecting ecting radi radiati ation on exchange with with the surroundings, surroundings, calcul calculate ate the temperature perature of the 0 plate plate under steadysteady-sta state te conditi conditions ons if if the ambien bientt air air temperature perature is is 20C. (b) For the same ambient bient air temperature, perature, calcul calcula ate the temperature perature of the plate plate if its surface surface 0 emissivity is 0.8 and the temperature of the surroundings is also20 C. surfa ace of insu i nsullated ted pl plate absorbs bsorbs sol sola ar fl flux, qs” and experi xperien ences for case case Known: front surf (a) Convection process with air at T and for case (b): (b): the sam same convecti convection on process and radiati radiation on exchange exchange with with surroundings surroundings at Tsur
Find: temperature of the plate, plate, Ts, for the two cases. Schematic:
As s um pt io ns : (1) steady state conditions, (2) no heat loss out backside of plate, (3) surroundings large in comparison plate. An alys al ys is : (a) apply a surface energy balance, identifying the control surface as shown on .
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the schem schematic. atic. For an instant nstant of tim time the conversation conversation requirem requirement ent is Ein − E out =0. The releva relevant nt processes processes are convection convection between the plate plate and and the air, qconv, and absorbed solar flux, qs”. Consi Conside deri ring ng the plate plate to have an area As solve for Ts and substitute numerical values to find q''s.A s − hA s ( Ts − T∞ ) = 0 Ts = T∞ + q"s / h 0
Ts = 20 C +
800W / m2 12W /
2
.K
= 200 C + 66.70 C = 870 C
(b) Conside onsideri ring ng now the radiati radiation on exchange exchange between tween the surface surface and and iits ts surr surroundi oundings, ngs, the .
.
surface surface energy balance balance has the form orm Ein − E out =0.
Sol Solving He Heat Tr T r ans nsffer Pr obl ble ems: Gener ner al Gui uide dellines nes
A major obje objective ctive of this this le learning rning materi aterial al is i s to prepa prepare you to to solve solve engi ngineering ri ng proble problems that invol involve ve heat transf transfer proce processe sses. In I n vie view of this, this, several problem problems are provide provided and and worked worked out out at the end end of each module. odule. In In worki working these these problem problems you wil will gai gain a deep deeper er appreciation of the fundamentals of the subject, and you will gain confidence in your ability to appl apply y these these fundamentals to the soluti solution on of engine gineering ri ng probl problem ems. It I t is is strongly strongly recommended that the stude student trie tri es to work work out the problem problems fi first by him himsel self/hersel /herself, before looking at the solutions provided. I n solvi solving ng heat transfer transfer problem problems, use of a systematic atic procedure is advocated. dvocated. Our experien ri ence shows that that most most heat tran transf sfer er problem probl ems can be tackled tackled by by a soluti solution on procedure characteri racterized zed by a prescri prescribe bed fforma ormat. This his procedure procedure has been been consi consiste stently ntly employed ployed in in all all the solutions provided, and we require the students to use it in their problem solutions in the future. The general solution procedure consists of the following steps: 1. K nown: nown: A fter ter caref carefull ully readi reading ng the the proble roblem, state state brie briefly and and conci concise sely what what is is known about about the problem problem. Do not rep repeat eat the probl problem emstatement ent verbatim verbati m. 2. Find: State briefly and concisely what must be found. 3. Schematic: tic: Draw Draw a schematic tic of the physical system. If I f appli plicati cation on of the conservation laws is anticipated, represent the required control surface by dashed lines on the sche schemati atic. I dentif ntify re relevant hea heat tran transfe sfer processe processes s by appropria ppropriatel tely labeled arrows rrows on the sche schemati atic. Treat this this enti entire re step step seriously ri ously,, as a good picture paints a thousand words! words! 4. A ssum ssumptions: Li L ist all pertine rtinent s siimplif pli fying ying assumptions. 5. Properties: Compile property values need for calculations, and identify sources from where you obtai obtain the value values. s. Make sure that the source is reliable. 6. A nalysis: ysis: Be B egin gin your ana analysis ysis by appl applyi ying ng appropri ppropria ate cons conse ervati rvation la laws, and and introduce rate equa equati tions ons as needed eded.. Deve Develop the anal analysi ysis s as as complete pletely as possi possibl ble e before substituting numerical values. Check the units before substituting any numerical value. Perform erform the the calcul calculati ations ons nee needed ded to obtain obtain thedesi desired red resul results. 7. Comments: Discuss your results (even if you are not asked do to so, specifically). Such a discussion may include a summary of key conclusions, a critique of the original assumptions, and an inference of trends obtained. This step will give you additional insights.
M odul odule e 1: L earni arning ng obj obj ectives ctives •
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Overvie Overview: Al A lthough though much of of the mate ateria rial of this modu modulle will wil l be discu discusse ssed iin n greater detail, the objective of this module is to give you a reasonable overview of heat trans transffer. Heat transfer transfer modes: Y ou should should be aware of the several modes of transfer transfer modes of transfer and their physical origins. Physical insight: Given a physical situation, you should be able to perceive the releva relevant transport transport phenomena. na. The im importance portance of developing velopi ng this this insi insight ght must not be undere underestim stimated. Y ou wil will be investi nvesting ng a lot of tim time to to acqui acquire the the tool tools s neede eded to calcul calculate ate heat heat transfer transfer phenomena. ena. However, However, before before you can begin to to use these tools to solve practical problems, you must have the intuition to determine what is happe happening ning physi physicall cally. y. In I n short, short, you must be be abl able to look look at a proble problem and and ide identif ntify the pertinen rti nentt transp transport ort phenom phenomenon. enon. The example ple and problem probl ems at the end of this this module should help you to begin developing this intuition. Rateequa equati tions ons and conse conservati rvation on laws laws:: Y ou shoul should d al also appre appreci ciate atethe signi signifficance cance of the rate equations quations and and fee feel comfortabl comfortable e in using using them to compute compute transport transport rates. Y ou must must al also recognize recognize the importance portance of the conse conservation rvation laws laws and and the need to carefully identify control volumes. With the rate equations, the conservation conservation laws laws may be used used to solve solve numerous heat transfer transfer probl problem ems.
