Heat Transfer - California State University, Northridge
Final ReviewMay 16, 2006OutlineReview for Final Exam Larry CarettoMechanical Engineering 375Basic equations, thermal resistanceHeat sourcesConduction, steady and unsteadyComputing convection heat transferHeat Transfer– Forced convection, internal and external– Natural convection Radiation properties Radiative ExchangeMay 16, 20072Basic EquationsFinal Exam Wednesday, May 23, 3 – 5 pm Open textbook/one-page equation sheet Problems like homework, midterm andquiz problems Cumulative with emphasis on secondhalf of course Complete basic approach to allproblems rather than finishing details ofalgebra or arithmetic Fourier law for heat conduction (1D)k (T1 T2 )kA(T1 T2 )q& or Q& q&A LL Convection heat transferQ& conv hAs (Ts T ) Radiation (from small object, 1, inlarge enclosure, 2)(Q& rad ,1 2 A1ε 1σ T14 T24)3Heat Generation Variousphenomena insolids cangenerate heat Define e& genas the heatgenerated perunit volumeper unit timeRectangular Energy BalanceFigure 2-21 from Çengel,Heat and Mass Transferρc pStored energyρc p5ME 375 – Heat Transfer q& y q& z q& T x e&gen t x y zheat inflow –heat outflow heatgenerated T T T T k e&gen k k t x x y y z z TUsesq&ξ k ξFourier Law61
Final ReviewMay 16, 2006Cylindrical CoordinatesSpherical Coordinates T t1 T 1 Tkrk r r r r 2 φ φ T k e&gen z z T t1 2 Tkr rr 2 r1 T sink θ θr 2 sin θ θ1 Tk e&gen22 φ φr sin θρc pρc pFigure 2-3fromÇengel,Heat andMassTransferdQ& r q& r dA k Trdφdz rFigure 2-3fromÇengel,Heat andMassTransfer78Plot of (T - T0)/(TL - T0) for Heat Generation in a Slab1-D, Rectangular, Heat Generation21.8T T0 e&genx22k e&genxL2k(T T )x 0 LL e&gen 2x e&genL (T0 TL ) dT k q& k 2kL dx 2kq& 1.6TemperatureDifference Ratio Temperature profile for generation with T T0 at x 0 and T TL at x L1.4H 01.2H .01H .1H 11H 2H 50.8H 100.62H 0.40.2e&gen(2x L) k (T0 TL ) 2LL e&genk (TL T0 )000.10.20.30.40.50.60.70.80.91x/L910Slab With Heat GenerationThermal ResistanceBoth boundary temperatures TB2.42H 2.2L e& gen2kTBH 0T / TBH .011.8H .1H 11.6H 2H 51.4H 10 Conductionk A(T1 T2 )T T Q& 1 2Q& LRcond Convection(Q& hA Ts T f) Q& Ts T fRconv Rcond LkA Rconv 1hA Radiation1.2100.10.20.30.40.50.60.70.80.9Rrad 1Dimensionless Distance, x/L11ME 375 – Heat Transfer(1A1F12σ T13 T23 T22T1 T12T21) Ah1 rad122
Final ReviewMay 16, 2006CompositeCylindricalShellComposite Materials IIFigure 3-26 fromÇengel, Heat andMass Transfer11 h2 A4 h2 2πr4 L131 r2 1 r3 ln ln 11 k1L r1 k2 L r2 h1 A1 h1 2πr1LFin Results T T (Tb T )e x hp kAcfor uniformcross sectionQ& x 0 Ac q& x 0 kAc hp (Tb T )A fin Lc p Heat transfer at end (Lc A/p)θ T T θbcosh m( Lc x )cosh m( Lc x) (Tb T )cosh mLccosh mLQ& x 0 kAc hp (Tb T ) tanh mL15Overall Fin EffectivenessQ& finh(η fin A fin Aunfin )(Tb T ) &Qno finhAno fin (Tb T )Q& finno fin A finAunfin η fin Ano fin Ano fin Figure 3-45 fromÇengel, Heat TransferME 375 – Heat Transfer Compare actualheat transfer toideal case whereentire fin is atbase temperatureQ& finη fin & Q fin,maxQ& finhA fin (Tb T )Figure 3-39 fromÇengel, Heat Transfer16Lumped Parameter Model Original area, A (areawith fins, Afin) (areawithout fins, Aunfin)ε total &Q14Fin Efficiency Infinitely long finθ θb e mx1 r4 ln k3 L r3 17 Assumes same temperature in solid Use characteristic length Lc V/AhAhb ρc p V ρc p Lc(T T ) (Ti T )e btorT (Ti T )e bt T Must have Bi hLc/k 0.1 to use this183
Final ReviewMay 16, 2006Slab Center-line (x 0) Temperature ChartTransient 1D ConvectionFigure 4-15(a) in Çengel, Heat and Mass TransferFigure 4-11 in Çengel,Heat and MassTransferAll problems have similar chart solutions19ΘT T Θ 0 T0 T Chart IIApproximate Solutions Can find T at anyx/L from thischart once T at x 0 is found fromprevious chart See basis for thischart on the nextpageFigure 4-15(b) in Çengel, Heatand Mass Transfer Plane thatextends toinfinity in alldirections Practicalapplications:large area forshort timesME 375 – Heat Transfer Valid for for τ 0.2 Slab Cylinder2T T A1e λ1τ cos λ1ξTi T 2 r T T Θ A1e λ1τ J 0 λ1 Ti T r0 Θ Sphere Θ 2 r T T r A1e λ1τ 0 sin λ1 Ti T λ1r r0 – Values of A1 and λ1 depend on Bi and aredifferent for each geometry (as is Bi)21Semi-Infinite SolidsFigure 4-24 in Çengel,Heat and Mass Transfer20– Example: earthsurface locally2322Multidimensional Solutions Can get multidimensional solutions asproduct of one dimensional solutions– All one-dimensional solutions have initialtemperature, Ti, with convection coefficient,h, and environmental temperature, T ,starting at t 0– General rule: ΘtwoD ΘoneΘtwo where Θoneand Θtwo are solutions from charts forplane, cylinder or sphere244
Final ReviewMay 16, 2006Multidimensional ExampleFlow Classifications T (r , x, t ) T Ti T x a/2finitecylinder T (r , t ) T Ti T infinitecylinderx -a/2Figure 4-35 inÇengel, Heatand MassTransfer T ( x, t ) T Ti T infiniteslab Forced versus free Internal (as in pipes) versus external (asaround aircraft)– Entry regions in pipes vs. fully-developed Unsteady (changing with time) versusunsteady (not changing with time) Laminar versus turbulent Compressible versus incompressible Inviscid flow regions (μ not important) One-, two- or three-dimensional25Flows26Boundary Layer Laminarflow islayered,turbulentflows arenot (buthave somestructure) Region near wall with sharp gradients– Thickness, δ, usually very thin compared tooverall dimension in y directionFigures 6-9 and 6-16. Çengel, Heatand Mass Transfer27Thermal Boundary Layer Nusselt number, Nu hLc/kfluid– Different from Bi hLc/ksolid Reynolds number, Re ρVLc/μ VLc/ν Prandtl number Pr μcp/k (in tables) Grashof number, Gr βgΔTLc3/ν2– g gravity, β expansion coefficient –(1/ρ)( ρ/ T)p, and ΔT Twall – T Thermal boundary layer thickness maybe less than, greater than or equal tothat of the momentum boundary layerME 375 – Heat Transfer28Dimensionless Convection Thin region nearsolid surface inwhich most oftemperaturechange occursFigure 6-15. Çengel, Heat and Mass TransferFigure 6-12 from Çengel, Heat and Mass Transfer Peclet, Pe RePr; Rayleigh, Ra GrPr29305
Final ReviewMay 16, 2006Characteristic LengthHow to Compute h Can use length as a subscript ondimensionless numbers to show correctlength to use in a problem Follow this general pattern– Find equations for h for the description ofthe flow given Correct flow geometry (local or average h?) Free or forced convection– ReD ρVD/μ, Rex ρVx/μ, ReL ρVL/μ– NuD hD/k, Nux hx/k, NuL hL/k– GrD ρ2βgΔTD3/μ2, Grx ρ2βgΔTx3/μ2,GrL ρ2βgΔTL3/μ2– Determine if flow is laminar or turbulent Different flows have different measures todetermine if the flow is laminar or turbulentbased on the Reynolds number, Re, for forcedconvection and the Grashof number, Gr, forfree convection Use not necessary if meaning is clear3132How to Compute hProperty Temperature Continue to follow this general pattern– Select correct equation for Nu (laminar orturbulent; range of Re, Pr, Gr, etc.)– Compute appropriate temperature forfinding properties– Evaluate fluid properties (μ, k, ρ, Pr) at theappropriate temperature– Compute Nusselt number from equation ofthe form Nu C Rea Prb or D Rac– Compute h k Nu / LC Find properties at correct temperature Some equations specify particulartemperatures to be used (e.g. μ/μw) External flows and natural convectionuse film temperature (Tw T )/2 Internal flows use mean fluidtemperature (Tin Tout)/23334Key Ideas of External FlowsFlat Plate Flow Equations The flow is unconfined Moving objects into still air are modeledas still objects with air flowing over them There is an approach condition ofvelocity, U , and temperature, T Far from the body the velocity andtemperature remain at U and T T is the (constant) fluid temperatureused to compute heat transfer35ME 375 – Heat Transfer Laminar flow (Rex, ReL 500,000, Pr .6)C fx τ wallρU 2Cf 2τwall 0.664 Re x1 / 2ρU 2 2 1.33 Re L1/ 2hx x 0.332 Re1x/ 2 Pr1/ 3khLNu L 0.664 Re1L/ 2 Pr1/ 3kNu x Turbulent flow (5x105 Rex, ReL 107)C fx Cf τ wallρU 2 2τwallρU 2 2 0.059 Re x1 / 5 0.074 Re L1 / 5hx x 0.0296 Re 0x.8 Pr1 / 3khLNu L 0.037 Re 0L.8 Pr1 / 3kNu x For turbulent Nu, .6 Pr 60366
Final ReviewMay 16, 2006Flat Plate Flow Equations IIHeat Transfer Coefficients Average properties for combined laminar and turbulentregions with transition at xc 500000 ν/U – Valid for 5x105 ReL 107 and0.6 Pr 60Cf τwallρU 2 2 0.074 1742 Re1L/ 5 Re LNu L ()hL 0.037 Re 0L.8 871 Pr1 / 3kFigure 7-10 from Çengel, Heat and Mass Transfer37 Cylinder average h (RePr 0.2; propertiesat (T Ts)/2[]38Tube Bank Heat Transfer39Table 7-2 from Çengel, Heat and Mass TransferKey Ideas of Internal Flows40Area TermsL The flow is confined There is a temperature and velocityprofile in the flow Acs is cross-sectional areafor the flowD– Use average velocity and temperature Wall fluid heat exchange will change theaverage fluid temperature– There is no longer a constant fluidtemperature like T for computing heattransferWL– Acs πD2/4 for circular pipe– Acs WH for rectangularduct Aw is the wall area for heattransferH41ME 375 – Heat Transfer1/ 4 μ hDNu 2 0.4 Re1 / 2 0.06 Re 2 / 3 Pr 0.4 k μs Other Shapes and EquationsPart of Table 7-1 from Çengel,Heat and Mass Transfer4/55/8hD0.62 Re1 / 2 Pr1 / 2 Re Nu 0.3 1 1/ 4k 0.4 2 / 3 282,000 1 Pr Sphere average h (3.5 Re 80,000; 0.7 Pr 380; μs at Ts; other properties at T )– Aw πDL for circular pipe– Aw 2(W H)L forrectangular ductFigure 8-1 from Çengel, Heat and Mass Transfer427
Final ReviewMay 16, 2006Average Temperature Change Let T represent the average fluidtemperature (instead of Tavg, Tm or T ) T will change from inlet to outlet ofconfined flow– This gives a variable driving force (Twall –Tfluid) for heat transfer– Can accommodate this by using the first& m& cp(Tout – Tin)law of thermodynamics: Q– Two cases: fixed wall heat flux and fixedwall temperatureFixed Wall Heat Flux Fixed wall heat flux, q& wall, over given wallarea, Aw, gives total heat input which isrelated to Tout – Tin by thermodynamicsq&AQ& q& wall Aw m& c p (Tout Tin ) Tout Tin wall wm& c p “Outlet” can be any point along flow pathwhere area from inlet is Aw We can compute Tw at this point as Tw Tout q& wall /h43Constant Wall Temperature(Tout Ts ) (Tin Ts )e Log-mean Temperature Diff This is usually written as a set oftemperature differenceshAwm& c p& cp NTU, the hAw / mnumber of transferunits This is generalequation forcomputing Tout ininternal flowsFigure 8-14 from Çengel, Heat and Mass TransferLMΔT (Tout Tin ) T T ln out s Tin Ts (Tout Ts ) (Tin Ts ) T T ln out s Tin Ts hA (T T )Q& w out in hAw ( LMΔT ) T T ln out s Tin Ts Çengel usesΔTlm for LMΔT45Developing Flows46Fully Developed ylayerdevelopment47ME 375 – Heat Transfer44 Temperature profile does not changewith x if flow is fully developed thermally This means that T/ r does not changewith downstream distance, x, so heatflux (and Nu) do not depend on x Laminar entry Lh 0.05 ReDlengths Turbulententry lengthsLt 0.05 Re PrDLt Lh 1.359 Re1 4 10D D488
Final ReviewMay 16, 2006Entry Region Nusselt NumbersInternal Flow Pressure Drop General formula: Δp f (L/D) ρV2/2 Friction factor, f, depends on Re ρVD/μ and relative roughness, ε/D For laminar flows, f 64/Re– No dependence on relative roughness For turbulent flowsColebrook ε D12.51 2.0 log10 3.7 Re ff 6.9 ε D 1.11 1.8 log10 Re 3.7 f Haaland 1Eggs from Figure8-9 in Çengel,Heat and MassTransfer49Moody Diagram50Laminar Nusselt Number Laminar flow if Re ρVD/μ 2,300 Fully-developed, constant heat flux, Nu 4.36 Fully-developed, constant walltemperature: Nu 3.66 Entry region, constant wall temperature:Fundamentals ofFluid Mechanics, 5/Eby Bruce Munson,Donald Young, andTheodore Okiishi.Copyright 2005 byJohn Wiley & Sons,Inc. All rightsreserved.Nu 3.66 0.065 (D L ) Re Pr1 0.04[(D L ) Re Pr ]2 35152Noncircular Ducts Define hydraulic diameter, Dh 4A/P– A is cross-sectional area for flow– P is wetted perimeter– For a circular pipe where A pD2/4 and P πD, Dh 4(πD2/4) / (πD) DFrom Çengel,Heat and MassTransfer For turbulent flows use Moody diagramwith D replaced by Dh in Re, f, and ε/D For laminar flows, f A/Re and Nu B(all based on Dh) – A and B next slide53ME 375 – Heat Transfer549
Final ReviewMay 16, 2006Turbulent FlowFree (Natural) Convection Smooth tubes (Gnielinski) 0.5 Pr 2000 ( f 8)(Re 1000) Pr Nu 36 0.5231 12.7( f 8) (Pr 1) 3 x10 Re 5 x10 Petukhov :f [0.790 ln (Re ) 1.64] 2 Flow is induced by temperaturedifference3000 Re 5 x10 Tubes with roughnessFree(Natural)– Use correlations developed for this case– As approximation use Gnielinski equationwith f from Moody diagram or f equation Danger! h does not increase for f 4fsmooth– No external source of fluid motion– Temperature differences causedensity differences– Density differences induce flowForced6 “Warm air rises”– Volume expansion coefficient: β [–(1/ρ)( ρ/ T)]Eggs from Figure1-33 in Çengel,Heat and MassTransfer For ideal gases β 1/T5556Grashof and Rayleigh NumbersEquations for Nu Dimensionless groups for free (natural)convectionRa Gr Pr β gΔTL3c ρ 2βgΔTL3cGr βgΔTL3cν2μ2να-2 Equations have form of AGraPrb or BRac Since Gr and Ra contain Twall – Tfluid ,an iterative process is required if one ofthese temperatures is unknown Transition from laminar to turbulentoccurs at given Ra values– g acceleration of gravity (LT )– β –(1/ρ)( ρ/ T) called the volumeexpansion coefficient (dimensions: 1/Θ)– For vertical plate transition Ra 109– ΔT Twall – Tfluid (dimensions: Θ)– Other terms same as previous use Evaluate properties at “film” (average)temperature, (Twall Tfluid)/25758Vertical Plate Free ConvectionVertical Plate Free Convection10000 Simplified equations on previous chartfor constant wall temperature1000Nu hL 100k 0.387 Ra1L/ 6 Nu L 0.825 9 / 16 8 / 27 1 (0.492 Pr )109 Ra 10131011.E 00– More accurate: Churchill and Chu, any RaNu 0.10 Ra1/ 3[Nu 0.59 Ra1 / 4104 Ra 1091.E 021.E 041.E 061.E 101.E 121.E 14Nu L 0.68 ME 375 – Heat TransferβgΔTL3Ra Any RaL– More accurate laminar Churchill/Chu1.E 08Rayleigh NumberPlate figure from Table9-1 in Çengel, Heatand Mass Transfer]2ν2βgΔTL3Pr να590.670 Ra1L/ 4[1 (0.492 Pr ) ]9 / 16 4 / 90 Ra L 1096010
Final ReviewMay 16, 2006Vertical Plate Free ConvectionVertical Cylinder Constant wall heat flux Apply equations for verticalplate from previous charts ifD/L 35/Gr1/4 For this D/L effects ofcurvature are not important Thin cylinder results of Cebeciand Minkowcyz and Sparrowavailable in ASMETransactions– Use q& hA(Tw – T ) to compute anunknown temperature (Tw or T ) fromknown wall heat flux and computed h– Tw varies along wall, but the average heattransfer uses midpoint temperature, TL/2q&q& wall hAwall (TL / 2 T ) TL / 2 T wallhAwall– Use trial and error solution with TL/2 – T asΔT in Ra used to compute h kNu/LCylinder figurefrom Table 9-1 inÇengel, Heat andMass Transfer6162Horizontal PlateHorizontal Plate IICold surfaceCold surface Hot surface facing up or cold surfacefacing down Lc area / perimeter (As/p) Cold surface facing up or hot surfacefacing down Lc area / perimeter (As/p)– For a rectangle of length, L, and width, W,Lc (LW) / (2L 2W) 1 / ( 2 / W 2 / L)– For a circle, Lc πR2 / 2πR R/2 D/4Figures from Table 9-1 inÇengel, Heat and MassTransfer– For a rectangle of length, L, and width, W,Lc (LW) / (2L 2W) 1 / ( 2 / W 2 / L)– For a circle, Lc πR2 / 2πR R/2 D/4Figures from Table 9-1 inÇengel, Heat and MassTransferNu 0.54 Ra1L/c 4 10 4 Ra 107Nu 0.15 Ra1L/c310 Ra 1071163Sphere and Horizontal Cylinder 0.387 Ra1D/ 6 Nu D 0.6 1 (0.559 Pr )9 / 16[] 8 / 27 Nu D 2 L0.589 Ra1D/ 4[1 (0.469 Pr ) ]Figures from Çengel, Heat and Mass TransferME 375 – Heat Transfer9 / 16 4 / 96564Horizontal Enclosures2 NuD results are average valuesNu 0.27 Ra1L/c 4 105 Ra 1011 Top side warmer:no convection Conduction only, Nu hL/k 1 Bottom warmer:convection becomessignificant when RaL (Pr)βgΔTL3/ν2 βgΔTL3/να 1708Figure 9-22 in Çengel,Heat and Mass Transfer6611
Final ReviewMay 16, 2006Horizontal Enclosures IIVertical EnclosuresBerkovsky and Polevikov, any PrJakob, for 0.5 Pr 2 Pr Nu L 0.18 Ra L 0.2 Pr Nu 0.195Ra1L/ 4 10 4 RaL 4 x105Nu 0.068Ra1L/ 34 x105 Ra L 107Globe and Dropkin fora range of liquidsNu 0.069 Ra1L/ 3 Pr 0.0743x105 Ra L 7 x109Hollands et al. for air; also for other fluids if RaL 105 1708 Ra max 0, L 1 RaL 108Nu 1 1.44 max 0, 1 RaL 18 67Figure 923 inÇengel,Heat andMassTransfer0.291 H / L 2Ra L Pr 0.2 Pr 1030.281/ 42 H / L 10 Pr Ra L L Nu L 0.22 RaL 10100.2 PrH MacGregor and Emery L Nu L 0.42 Ra1L/ 4 Pr 0.012 H 1 H / L 401 Pr 2010 RaL 1060.310 H / L 401 Pr 2 x10 410 4 RaL 107Nu L 0.46 Ra1L/ 3968Heat Exchangers Used to transfer energy from one fluidto another One fluid, the hot fluid, is cooled whilethe other, the cold fluid, is heated May have phase change: temperatureof one or both fluids is constant Simplest is double pipe heat exchanger– Parallel flow and counter flowFigure 11-1 from Çengel,Heat and Mass Transfer69Compact Heat Exchangers70Shell-and-Tube Exchanger Counter flow exchanger with largersurface area; baffles promote mixingFigure 11-3 from Çengel, Heat and Mass TransferME 375 – Heat Transfer71Figure 11-4 from Çengel, Heat and Mass Transfer7212
Final ReviewMay 16, 2006Shell and Tube PassesOverall U U is overall heattransfer coefficient Analyzed here fordouble-pipe heatexchangerTube flow hasthree completechanges ofdirection givingfour tubepassesShell flowchangesdirection togive two shellpasses7311 Rwall hi Aiho Ao111 U o Ao U i Ai UAR Figure 11-5(b) from Çengel, Heat and Mass TransferHeat Exchange Analysis Heat transfer fromhot to cold fluidParallel Flow Parallel flow Q& UAΔTlmheat exchangerQ& UAΔT(())Q& m& c c pc Tc,out Tc,in First lawenergyQ& m& h c ph Th,in Th,outbalances Assumes no heat loss to surroundingsΔTlm ΔTlm – Subscripts c and h denote cold and hotfluids, respectively– Alternative analysis for phase change75ΔT2 Th,out – Tc,inCounter FlowΔT ΔT1Q& UAΔTlm UA 2 ΔT ln 2 ΔT1 (Th,out Tc,in ) (Th,in Tc,out )Figure 11-16 from Çengel,Heat and Mass TransferME 375 – Heat Transfer T T ln h,out c,in T T h,in c,out (Th,out Tc,out ) (Th,in Tc,in ) T Tln h,out c,out T T h,in c,in Figure 11-14 from Çengel, Heat and Mass Transfer76 With ΔTlm method we want to find U orA when all temperatures are known If we know three temperatures, we canfind the fourth by an energy balancewith known mass flow rates (and cp’s)– Difference in ΔT1 andΔT2 definitionsΔTlm ΔT2 ΔT1 ΔT1 ΔT2 ΔT ΔT ln 2 ln 1 ΔT1 ΔT2 Heat Exchanger Problems Same basic equationsΔT1 Th,in – Tc,out74Figure 11-7 from Çengel, Heat and Mass TransferQ& m& c c pc (Tc,out Tc,in ))Q& m& c (T Th ph77h,inh,out& from twoCan find Qtemperatures for onestream and then findunknown temperature7813
Final ReviewMay 16, 2006Correction FactorsCorrection Factor Chart I Correction factor parameters, R and P– Shell and tube definitions belowTtube,
Final Review May 16, 2006 ME 375 – Heat Transfer 1 Review for Final Exam . midterm and quiz problems . half of course Complete basic approach to all problems rather than finishing details of algebra or arithmetic Basic Equations Fourier law for heat conduction (1D) ( ) L kA T T
Basic Heat and Mass Transfer complements Heat Transfer,whichispublished concurrently. Basic Heat and Mass Transfer was developed by omitting some of the more advanced heat transfer material fromHeat Transfer and adding a chapter on mass transfer. As a result, Basic Heat and Mass Transfer contains the following chapters and appendixes: 1.
Feature Nodes for the Heat Transfer in Solids and Fluids Interface . . . 331 The Heat Transfer in Porous Media Interface 332 Feature Nodes for the Heat Transfer in Porous Media Interface . . . . 334 The Heat Transfer in Building Materials Interface 338 Settings for the Heat Transfer in Building Materials Interface . . . . . 338
Both temperature and heat transfer can change with spatial locations, but not with time Steady energy balance (first law of thermodynamics) means that heat in plus heat generated equals heat out 8 Rectangular Steady Conduction Figure 2-63 from Çengel, Heat and Mass Transfer Figure 3-2 from Çengel, Heat and Mass Transfer The heat .
1 INTRODUCTION TO HEAT TRANSFER AND MASS TRANSFER 1.1 HEAT FLOWS AND HEAT TRANSFER COEFFICIENTS 1.1.1 HEAT FLOW A typical problem in heat transfer is the following: consider a body “A” that e
Relevance of heat transfer and heat exchangers for the development of sustainable energy systems B. Sundén1 & L. Wang2 1Division of Heat Transfer, Department of Energy Sciences, Lund University, Lund, Sweden. 2Siemens Industrial Turbines, Finspong, Sweden. Abstract There are many reasons why heat transfer and heat exchangers play a key role in the
Holman / Heat Transfer, 10th Edition Heat transfer is thermal energy transfer that is induced by a temperature difference (or gradient) Modes of heat transfer Conduction heat transfer: Occurs when a temperature gradient exists through a solid or a stationary fluid (liquid or gas). Convection heat transfer: Occurs within a moving fluid, or
Young I. Cho Principles of Heat Transfer Kreith 7th Solutions Manual rar Torrent Principles.of.Heat.Transfer.Kreith.7th.Sol utions.Manual.rar (Size: 10.34 MB) (Files: 1). Fundamentals of Heat and Mass Transfer 7th Edition - Incropera pdf. Principles of Heat Transfer_7th Ed._Frank Kreith, Raj M. Manglik Principles of Heat Transfer. 7th Edition
J. P. Holman, “Heat Transfer . Heat transfer (or heat) is thermal energy in transit due to a spatial temperature difference. Whenever a temperature difference exists in a medium or between media, heat transfer must occur. As shown in Figure 1.1, we refer to different types of heat transfer processes as
