NATURAL CONVECTION IN HEAT EXCHANGERS - A NEW INCENTIVE FOR MORE COMPACT HEAT EXCHANGERS?
|
|
- Ursula McCoy
- 6 years ago
- Views:
Transcription
1 Proceedings of Fifth International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology, Eds. R.K. Shah, M. Ishizuka, T.M. Rudy, and V.V. Wadekar, Engineering Conferences International, Hooken, NJ, USA, Septemer 25. CHE25 7 NATURAL CONVECTION IN HEAT EXCHANGERS - A NEW INCENTIVE FOR MORE COMPACT HEAT EXCHANGERS? Thomas Aicher and Holger Martin 2 Fraunhofer-Institut für Solare Energiesysteme ISE, Freiurg, Germany, thomas.aicher@ise.fraunhofer.de 2 Universität Karlsruhe (TH), Thermische Verfahrenstechnik, Karlsruhe, Germany, martin@tvt.uka.de ABSTRACT Natural convection in the la is very often studied at single surface elements or in single channels. The flow and heat transfer characteristics in these cases are more or less well understood and prediction of flow rates and heat transfer coefficients can usually e otained from standard textook formulae. While the ehaviour of a single channel can safely e used to predict what happens in a undle of parallel tues in forced flow, the same is not true for natural convection. Starting from relatively simple cases of natural convection in single channels as well as in undles of parallel ones, it is shown, that natural convection in undles does ehave completely differently. In the case of mixed convection in a vertical tue undle, the effect of natural convection may lead to severe reductions in overall performance, ut also depending on the operation parameters to an enhancement of heat transfer! Till now, the textooks and handooks on heat transfer do not even mention these possiilities, that may lead to a numer of prolems in heat exchanger operation practice. T T 2 one may call it a single phase heat i...andit isa direct contact alanced counter current h L single horizontal T d T 2 channel Fig. Natural Convection in a Single Horizontal Channel. WHAT IS THE PROBLEM? The natural convective flow situation in a single horizontal channel is shown in Fig.. This arrangement may e called a single phase heat pipe as it does create a circulating flow etween the cold side (T ) and the hot side (T 2 ) with the hotter fluid on top of the colder one in two horizontal layers. d T T Ra c =87 L=Z Ra c =5.6 Ra=gd 4 β T/(Lνκ) T *G. I. Taylor (954), * * J. Unger (98) * ** single vertical Fig. 2 Natural Convection in a Single Vertical Channel. While the circulating flow in case of the horizontal channel starts as soon as there is a temperature difference greater zero, this is not true for the case of a vertical channel as shown in Fig. 2. Only if a critical value Ra c of the (dimensionless) temperature difference Ra is surpassed, the circulating flow will start. For Ra<Ra c the fluid remains at rest. The critical Rayleigh numers (temperature differences) have een calculated from a staility analysis for a cylindrical vertical tue y Taylor (954) and for a vertical parallel plates duct y Unger (98). The definition of Ra, as well as the values of Ra c T 48
2 from the literature are given in Fig. 2. Diameter (or gap width) d and length L enter the Rayleigh numer as: d 4 /L. Nu Ra c [(Ra - Ra c) L/ d] Nu = + Ra 92 Ra c Ra Gz = Ra/96 7/3 Ra = c 96 7/3= 56.9 Fig. 3 Approximate solution to the natural convection prolem in a single vertical parallel plates channel. The single channel natural convection cases (Fig. and 2) may e solved in a much simpler way (approximately) y a -D-model, taking into account their nature as direct contact alanced counter current heat exchangers. This is shown for the parallel plates duct in Fig. 3. The -D model in this case leads to simple explicit formulae for the flow rate (or Graetz numer Gz) as a (linear) function of temperature difference (Rayleigh numer) and predicts the critical Rayleigh numer aout 3% higher than the more rigorous 2-D approach from the literature. Looking at a tue undle (or a numer of parallel plate ducts), the situation is different: No circulation will take place within each one of the single parallel tues, ut in pairs of tues in that case. 2 Ra c =5.6 counter current heat exchanger -D approximate model gives Ra c aout 3% larger than 2-D solution y Unger d L=Z Rayleigh-Bénard Convection Ra c =384* *for adiaatic tue walls g Determined Natural Convection Ra c = Fig. 4 Natural convection in tue undles. Z L L Rayleigh numer: Ra=gd 2 Zβ T/(νκ) d to e multiplied y (L/d) 2 to arrive at the correct form of Ra for the undle. From this we can find, that Ra c,single tue (L/d) 2 had to e less than Ra c,tue undle for circulation within a single tue to occur in a undle. Using the values from Figs. 2 and 4, namely Ra c,single tue =87 and Ra c,tue undle =384, we find (L/d) 2 < 384/87 or L/d <.59. So, in case of tues with lengths greater than.6 diameters, the single tue internal convection will never happen in a undle. Using again a - D approximate solution, which is certainly sufficient for an engineering approach, the temperature profiles in the tues of the undle as a function of the individual flow rates are shown in Fig.5. Θ m = (ρu)c p L/λ dimensionless mass velocity m= x.3 Fig. 5 Temperature profiles in the channels of tue undles (see Fig. 4) in natural convection as a function of flow rate m The heat transferred from the hot to the cold side y the comined positive and negative flows in every second channel has een calculated from the same -D model y Martin (992) and the results are shown oth for the horizontal, and for the vertical tue undle as Nusselt numers versus Rayleigh numer in Fig. 6. For the sake of simplicity, the horizontal undle in this case consists of only two tues (or two tue rows) in a vertical distance Z as shown in Fig. 6. For sufficiently high Rayleigh numers, the heat transfer coefficient is directly proportional to the temperature difference. The heat flux therefore is proportional to the square of T. This of course is the same dependency as found for the single channels (see Fig. 3) in this limit. The difference in ehaviour of single tue versus tue undle can e seen in the fact, that the flow pattern occurring in a undle differs from that in a single tue, ecause the greater degree of freedom for the flow, as soon as more than one tue is availale for a circulation. m=3 temperature profiles in the tues with m as a parameter 3 Diameter (or gap width) d and length L enter the Rayleigh numer as: d 2 L, (for L=Z) i. e. the Rayleigh numers of the single channel cases, containing d 4 /L have 49
3 5 Z Q proportional T 2 + Nu Nu = Ra/28 - unexpected tueside ackflow in a vertical shell-and-tue heat exchanger 5 Z Ra 5 Ra=gd 2 Zβ T/(νκ) flow rate + Fig. 6. Nusselt vs. Rayleigh numers for natural convection in horizontal (upper curve) and vertical (lower curve) tue undles with adiaatic walls. MIXED CONVECTION IN BUNDLES Typically in a classical heat exchanger, we do have forced convection. Natural convection alone is rather unusual, ut mixed convection, i. e. fluid flow driven y pressure and density gradients, is exactly what happens in every heat exchanger. Usually, however, the effects due to density gradients are neglected in heat exchanger design. The question, whether natural convection may e safely neglected, is mainly answered on the asis of the well known single channel ehaviour. Judging from single channel ehaviour, an additional natural convection will usually increase (or only marginally decrease) the heat transfer coefficients compared to forced convection alone (see Aicher and Martin, 997). That s why neglecting natural convection in general is thought of eing justified y staying on the safe side in heat exchanger design. An example from industrial practice taught us, more than ten years ago, that this assumption may e completely wrong (Martin and Pajak, 994). A single tue pass vertical shell and tue heat exchanger with many segmental affles on the shell side had een designed and uilt for heat recovery to operate in counter flow at an efficiency of 9 to 97%. However, the efficiencies measured in operation were only 6 to 77%. The overall heat transfer coefficient, calculated from the measured temperatures, assuming ideal counter current operation reached only aout one third of the design value. After checking a numer of possile reasons for the unexpectedly low performance of that apparatus, we came to the conclusion, that superimposed natural convection might (see Fig. 7) e the reason of such a drastic deviation from the predicted design. Fig. 7. Unexpected tueside ackflow in a vertical shelland-tue heat exchanger This hypothesis has later een verified a) y tracer measurements of residence time distriutions in the undle, that actually showed, that ackflow existed in some of the tues. ) y -D model calculations on the flow and temperature distriutions in that shell-and-tue apparatus. c) y changing the flow directions of oth tue-side and shell-side fluid in the shell-and-tue apparatus, which indeed resulted in a stale situation avoiding ackflow and resulting in the high efficiencies of around 95% as expected from design. See Martin and Pajak (994) and Aicher et al. (999) for details. + z + NTU=5 = Fig. 8. Temperature distriution without ackflow in a vertical shell-and-tue heat exchanger ideal counter flow. To demonstrate the effect of unwanted ackflow in a part a of the tues in a vertical undle, the model equations from (Aicher et al., 999) have een used again here in a simpler form. We assume a alanced counter flow heat exchanger with NTU=5. If there is no ackflow (as shown in Fig. 8), the temperatures vary linearly with the tue 5
4 length, and the efficiency would e ε=5/6. The case with ackflow can e calculated analytically as the solution of three coupled ordinary differential equations for the temperatures in the tueside upflow (suscript, flow rate=+ in the fraction -a of the tues), the tue-side ackflow (suscript 2, flowrate in a fraction a of the tues), and the laterally mixed shell-side flow (suscript 3, assuming no ackflow or axial mixing). The (normalized) temperatures from this analytical solution can e written as: T j (z)=a j +B j exp(r 2 z)+ C j exp(r 3 z) j=,2,3 () Normalized axial coordinate: < z <. The roots of the characteristic equation (r =), r 2, r 3, and the coefficients A j, B j, and C j are listed in the appendix. These coefficients have een otained from the differential equations and from the oundary conditions: T ()=T 2 (), (+)T ()=+ T 2 (), T 3 ()= (2, 3, 4) The variation of the heat transfer coefficients with individual flowrates has not een taken into account in this calculation for the sake of simplicity. NTU, therefore, has een assumed to e inversely proportional to the flowrate. Figure 9 shows the results of such a calculation from eqns. (-4) and the coefficients as given in the appendix. In the paper y Aicher et al. (999) the calculations were carried out including the effects of flowrates on the heat transfer coefficients (htc), ut for a demonstration of the principle, the assumption of constant htc may e acceptale here. channels cannot e used directly in undles. The flow patterns occurring in undles differ from those in single channels in as far as flow in two opposite directions in these cases is not oserved within one channel, ut only in separate tues. From Figs. 8 and 9 we have seen, that ackflow in part of the tues, due to superimposed natural convection, may consideraly decrease the performance of a vertical counter current heat exchanger, especially so, if operated in the high NTU, high efficiency range. In order to avoid ackflow in these cases, it is to e recommended to have the hot end of the heat exchanger at the top, not the ottom. Internal circulation, however, does increase the local flowrates and, therefore, may increase the overall performance in other cases. In any case it is clear, that the influence of natural convection should e taken into account in heat exchanger design. Yet, so far nearly nothing on that topic is found in the textooks as well as in the handooks of heat transfer and heat exchanger design. To check, whether ackflow in some tues is possile, we need critical Rayleigh numers, which depend on the Graetz numer in laminar flow, and additionally on the Prandtl numer and d/l in turulent flow. Only recently, Nickolay (2) has developed a Ra I, Ra II vs. Graetz-chart from analytical calculations as well as experimental data with tue undles. Ra no stale steady state solution Ra II. no ackflow + NTU=5.8 = a=.7 =.7 Gz.6 Ra I + z T z Fig. 9. Temperature distriution with ackflow in a vertical shell-and-tue heat exchanger MAY BACKFLOW IN A TUBE BUNDLE ALSO BE USEFUL? It has een shown y a numer of relatively simple examples, that the results for natural convection in single Fig. Nickolay s staility chart for laminar mixed convection in vertical tue undles. The Rayleigh numer here is defined with d 4 /L as the characteristic volume. For Ra < Ra I no ackflow is oserved. For Ra > Ra II there exists no stale solution. In the range etween the two limits stale solutions with a certain numer of tues in ackflow do exist. The limiting value for low Graetz numers is Ra min =768. Extensions into the turulent flow regime have also een calculated y Nickolay (2). The curves in Fig. have een otained from the analytic formulae: 5
5 Ra I =32/(Θ/Gz) (5) Ra II =32/(dΘ/dGz) (6) and an empirical approximation for the volumetric mean temperature Θ = Θ vm, otained from a volume averaged enthalpy content which is different from the caloric mean temperature (corresponding to an average enthalpy flux): Θ=[+(24/Gz) 5 +(8/Gz) 5/3 +(3/Gz) 5/2 ] -/5 The derivative dθ/dgz in Ra II can e found analytically from this formula. This approximation has een shown to e in very good agreement to the more rigorous series calculations y Nickolay (2). Furthermore the experimental oservation of ackflow in tue undles verified the existence and importance of these two limiting Rayleigh numers. When increasing the temperature difference in Ra= gd 4 β T/(Lνκ), ackflow in one or more tues is oserved, when Ra II is reached. When reducing Ra, ackflow remains stale and only vanishes, when Ra I is reached! In the range etween the two critical Rayleigh numers, the actual flow pattern, and the performance of the apparatus depends on the history of its operation efore! A NEW INCENTIVE FOR MORE COMPACT HEAT EXCHANGERS? CONCLUSIONS Stale operation without ackflow can always e reached, if the Rayleigh numer stays elow Ra min =768. Scaling down an existing (shell-and-tue) heat exchanger to a smaller volume, when keeping its flowrates (nud 2 ), efficiency and pumping power constant, requires in the laminar flow range that (7) a) NTU and, therefore, Gz is kept constant Gz=(nud 2 /κ)/(nl), or nl=c t (8) ) p=32ηl(nud 2 )/(nd 4 ), or nd 4 /L=c h (9) From these scaling laws, one can see, that the length L decreases inversely with the numer n of parallel tues, while, eliminating L from eqns. (8) and (9) shows, that d 2, too, is inversely proportional to n. So douling the numer of parallel tues in a undle, will decrease L, d 2, and the Rayleigh-numer Ra y a factor of one half. Compact heat exchangers are definitely less affected y unwanted ackflow prolems, than the classical shelland-tue heat exchangers with tue diameters in the order of centimeters. NOMENCLATURE Latin symols a part of tues in ackflow, A area, m 2 ackflow ratio, c constants d diameter (gap width), m Gz Graetz numer, Gz=RePr d/l L length, m m dimensionless flowrate (Fig. 5), M shell-side NTU, n numer of parallel tues, N tue-side NTU, Nu Nusselt numer, αd/λ Pr Prandtl numer, Pr=ηc p /λ Ra Rayleigh numer, Ra=gL 3 β T/(νκ) (with L 3 replaced y d 4 /L or d 2 L if appropriate) Re Reynolds numer, Re=ud/ν u flow velocity, m/s z coordinate in flow direction, Greek symols α heat transfer coefficient, W/(m 2 K) λ thermal conductivity, W/(m K) κ thermal diffusivity, m 2 /s η viscosity, Pas ν kinematic viscosity, m²/s ρ density, kg/m 3 Suscripts tue-side upflow 2 tue-side ackflow 3 shell-side flow h hydrodynamic task t thermal task REFERENCES Aicher, T., Zur üerlagerten freien und erzwungenen Konvektion in lotrechten Rohründelwärmeüertragern, PhD Dissertation, Fortschr. Ber. VDI Reihe 9, Nr., Düsseldorf, 997. Aicher, T., Martin, H., New correlation for mixed turulent natural and forced convection heat transfer in vertical tues, Int. J. Heat Mass Transfer, 4 (997) 5, Aicher, T., Martin, H., Polt, A., Rayleigh-Bénard convection in vertical shell-and-tue heat exchangers, Chem. Eng. Process. 38 (999)
6 Martin, H., Rayleigh-Bénard-Konvektion in Rohründeln, Archive of Applied Mechanics 62 (992) Martin, H., Pajak, D., Rayleigh-Bénard Convection in Tue Bundles, Heat Transfer 994, Proc. th Int. Heat Transf. Conf. Brighton, UK, Vol. 7, 6-NC-2A, pp Nickolay, M., Naturumlaufströmungen in durchströmten Rohr- und Spaltündeln, PhD Dissertation, Aachen, Shaker, 2. Taylor, G.I., cited from: Wooding, R. A., The staility of a viscous liquid in a vertical tue containing porous material. Proc. Roy. Soc. London, Ser. A 252 (959) Unger, J., Ausgeildete Kanalströmung zwischen Behältern unterschiedlicher Temperatur, ZAMM 6 (98) T23-T233. APPENDIX Coefficients, to e used in eqns. (-4) for the temperatures in a shell-and-tue hx with ackflow N_ = N a/(+) N_2 = N (-a)/ N_3 = M a N_4 = M (-a) NA = - (N_ N_2 N_3 N_4)/2 NB = ((N_ + N_2)^2 + (N_3 + N_4)^2-2 (N_ + N_2) (N_3 N_4))^(/2) r_2 = NA + NB/2 r_3 = NA NB/2 e_2 = exp(r_2) e_3 = exp(r_3) K_B = N_/(r_2 + N_) K_B2 = N_2/(r_2 N_2) K_C = N_/(r_3 + N_) K_C2 = N_2/(r_3 N_2) K = e_2 e_3 ((K_B + K_B2) (K_C + K_C2)) - e_2 (((+) K_C + K_C2) (K_B + K_B2)) + e_3 (((+) K_B + K_B2) (K_C + K_C2)) A_ = A_3 A_2 = A_3 A_2 = e_2 e_3 ((K_B + K_B2) (K_C + K_C2))/K B_ = K_B B_3 B_2 = - K_B2 B_3 B_3 = e_3 (K_C + K_C2)/K C_ = K_C C_3 C_2 = - K_C2 C_3 C_3 = - e_2 (K_B + K_B2)/K 53
cen29305_ch08.qxd 11/30/05 3:05 PM Page 451 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating
cen29305_ch08.qxd 11/30/05 3:05 PM Page 451 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications. The fluid in such applications
More informationEstimation of Hottest Spot Temperature in Power Transformer Windings with NDOF and DOF Cooling
Transactions D: Computer Science & Engineering and Electrical Engineering Vol. 16, No. 2, pp. 163{170 c Sharif University of Technology, Decemer 2009 Research Note Estimation of Hottest Spot Temperature
More informationCHME 302 CHEMICAL ENGINEERING LABOATORY-I EXPERIMENT 302-V FREE AND FORCED CONVECTION
CHME 302 CHEMICAL ENGINEERING LABOATORY-I EXPERIMENT 302-V FREE AND FORCED CONVECTION OBJECTIVE The objective of the experiment is to compare the heat transfer characteristics of free and forced convection.
More informationHeat processes. Heat exchange
Heat processes Heat exchange Heat energy transported across a surface from higher temperature side to lower temperature side; it is a macroscopic measure of transported energies of molecular motions Temperature
More informationHEAT EXCHANGER. Objectives
HEAT EXCHANGER Heat exchange is an important unit operation that contributes to efficiency and safety of many processes. In this project you will evaluate performance of three different types of heat exchangers
More informationStudies on flow through and around a porous permeable sphere: II. Heat Transfer
Studies on flow through and around a porous permeable sphere: II. Heat Transfer A. K. Jain and S. Basu 1 Department of Chemical Engineering Indian Institute of Technology Delhi New Delhi 110016, India
More informationPHYSICAL MECHANISM OF CONVECTION
Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter
More informationLAMINAR FORCED CONVECTION HEAT TRANSFER IN HELICAL COILED TUBE HEAT EXCHANGERS
LAMINAR FORCED CONVECTION HEAT TRANSFER IN HELICAL COILED TUBE HEAT EXCHANGERS Hesam Mirgolbabaei ia, Hessam Taherian b a Khajenasir University of Technology, Department of Mechanical Engineering, Tehran,
More informationA numerical study of heat transfer and fluid flow over an in-line tube bank
Fluid Structure Interaction VI 295 A numerical study of heat transfer and fluid flow over an in-line tube bank Z. S. Abdel-Rehim Mechanical Engineering Department, National Research Center, Egypt Abstract
More informationMYcsvtu Notes HEAT TRANSFER BY CONVECTION
www.mycsvtunotes.in HEAT TRANSFER BY CONVECTION CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in
More informationTransient Heat Transfer Experiment. ME 331 Introduction to Heat Transfer. June 1 st, 2017
Transient Heat Transfer Experiment ME 331 Introduction to Heat Transfer June 1 st, 2017 Abstract The lumped capacitance assumption for transient conduction was tested for three heated spheres; a gold plated
More informationNumerical Investigation of The Convective Heat Transfer Enhancement in Coiled Tubes
Numerical Investigation of The Convective Heat Transfer Enhancement in Coiled Tubes Luca Cattani* 1 1 Department of Industrial Engineering - University of Parma Parco Area delle Scienze 181/A I-43124 Parma,
More informationLecture 30 Review of Fluid Flow and Heat Transfer
Objectives In this lecture you will learn the following We shall summarise the principles used in fluid mechanics and heat transfer. It is assumed that the student has already been exposed to courses in
More informationConvection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.
Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,
More informationHeat Transfer Convection
Heat ransfer Convection Previous lectures conduction: heat transfer without fluid motion oday (textbook nearly 00 pages) Convection: heat transfer with fluid motion Research methods different Natural Convection
More informationHeat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay
Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Lecture No. 18 Forced Convection-1 Welcome. We now begin our study of forced convection
More informationKeywords: Spiral plate heat exchanger, Heat transfer, Nusselt number
EXPERIMENTAL AND NUMERICAL STUDIES OF A SPIRAL PLATE HEAT EXCHANGER Dr.RAJAVEL RANGASAMY Professor and Head, Department of Mechanical Engineering Velammal Engineering College,Chennai -66,India Email:rajavelmech@gmail.com
More informationConvection Workshop. Academic Resource Center
Convection Workshop Academic Resource Center Presentation Outline Understanding the concepts Correlations External Convection (Chapter 7) Internal Convection (Chapter 8) Free Convection (Chapter 9) Solving
More informationMOMENTUM TRANSPORT Velocity Distributions in Turbulent Flow
TRANSPORT PHENOMENA MOMENTUM TRANSPORT Velocity Distributions in Turbulent Flow Introduction to Turbulent Flow 1. Comparisons of laminar and turbulent flows 2. Time-smoothed equations of change for incompressible
More informationIntroduction to Heat and Mass Transfer. Week 14
Introduction to Heat and Mass Transfer Week 14 Next Topic Internal Flow» Velocity Boundary Layer Development» Thermal Boundary Layer Development» Energy Balance Velocity Boundary Layer Development Velocity
More informationCONVECTIVE HEAT TRANSFER
CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 4 HEAT TRANSFER IN CHANNEL FLOW BASIC CONCEPTS BASIC CONCEPTS Laminar
More informationEffect of Uniform Horizontal Magnetic Field on Thermal Instability in A Rotating Micropolar Fluid Saturating A Porous Medium
IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue Ver. III (Jan. - Fe. 06), 5-65 www.iosrjournals.org Effect of Uniform Horizontal Magnetic Field on Thermal Instaility
More informationEXPERIMENTAL AND NUMERICAL STUDIES OF A SPIRAL PLATE HEAT EXCHANGER
THERMAL SCIENCE: Year 2014, Vol. 18, No. 4, pp. 1355-1360 1355 EXPERIMENTAL AND NUMERICAL STUDIES OF A SPIRAL PLATE HEAT EXCHANGER by Rangasamy RAJAVEL Department of Mechanical Engineering, AMET University,
More informationTankExampleNov2016. Table of contents. Layout
Table of contents Task... 2 Calculation of heat loss of storage tanks... 3 Properties ambient air Properties of air... 7 Heat transfer outside, roof Heat transfer in flow past a plane wall... 8 Properties
More informationTransactions on Engineering Sciences vol 5, 1994 WIT Press, ISSN
Heat transfer at the outer surface of a rotating cylinder in the presence of axial flows R. Smyth & P. Zurita Department of Mechanical and Process Engineering, University of Sheffield, f. 0. Boz #00, Moppm
More informationGRAVITY EFFECT ON THE DISTRIBUTION OF REFRIGERANT FLOW IN A MULTI-CIRCUITED CONDENSER
Proceedings of Fifth International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology, Eds. R.K. Shah, M. Ishizuka, T.M. Rudy, and V.V. Wadekar, Engineering
More informationUNIT II CONVECTION HEAT TRANSFER
UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid
More informationS.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100
Total No. of Questions 12] [Total No. of Printed Pages 7 Seat No. [4162]-187 S.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100 N.B.
More informationPrinciples of Convection
Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid
More informationParallel Plate Heat Exchanger
Parallel Plate Heat Exchanger Parallel Plate Heat Exchangers are use in a number of thermal processing applications. The characteristics are that the fluids flow in the narrow gap, between two parallel
More informationChapter 7: Natural Convection
7-1 Introduction 7- The Grashof Number 7-3 Natural Convection over Surfaces 7-4 Natural Convection Inside Enclosures 7-5 Similarity Solution 7-6 Integral Method 7-7 Combined Natural and Forced Convection
More informationConvection Heat Transfer. Introduction
Convection Heat Transfer Reading Problems 12-1 12-8 12-40, 12-49, 12-68, 12-70, 12-87, 12-98 13-1 13-6 13-39, 13-47, 13-59 14-1 14-4 14-18, 14-24, 14-45, 14-82 Introduction Newton s Law of Cooling Controlling
More informationLaminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition
Sādhanā Vol. 40, Part 2, April 2015, pp. 467 485. c Indian Academy of Sciences Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition RAMBIR BHADOURIYA,
More informationIntroduction to Heat and Mass Transfer. Week 14
Introduction to Heat and Mass Transfer Week 14 HW # 7 prob. 2 Hot water at 50C flows through a steel pipe (thermal conductivity 14 W/m-K) of 100 mm outside diameter and 8 mm wall thickness. During winter,
More informationNatural Convection in a Trapezoidal Enclosure Heated from the Side with a Baffle Mounted on Its Upper Inclined Surface
Heat Transfer Engineering ISSN: 0145-7632 Print) 1521-0537 Online) Journal homepage: http://www.tandfonline.com/loi/uhte20 Natural Convection in a Trapezoidal Enclosure Heated from the Side with a Baffle
More informationAnalysis of Heat Transfer Enhancement in Spiral Plate Heat Exchanger
Vol. 2, No. 4 Modern Applied Science Analysis of Heat Transfer Enhancement in Spiral Plate Heat Exchanger Dr. Kaliannan Saravanan Professor & Head, Department of Chemical Engineering Kongu Engineering
More informationHeat Transfer Performance in Double-Pass Flat-Plate Heat Exchangers with External Recycle
Journal of Applied Science and Engineering, Vol. 17, No. 3, pp. 293 304 (2014) DOI: 10.6180/jase.2014.17.3.10 Heat Transfer Performance in Double-Pass Flat-Plate Heat Exchangers with External Recycle Ho-Ming
More informationHEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1
HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1 CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the
More informationProblem 4.3. Problem 4.4
Problem 4.3 Problem 4.4 Problem 4.5 Problem 4.6 Problem 4.7 This is forced convection flow over a streamlined body. Viscous (velocity) boundary layer approximations can be made if the Reynolds number Re
More informationExperimental Study on Port to Channel Flow Distribution of Plate Heat Exchangers
Proceedings of Fifth International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology, Eds. R.K. Shah, M. Ishizuka, T.M. Rudy, and V.V. Wadekar, Engineering
More informationSemi-Empirical 3D Rectangular Channel Air Flow Heat Transfer and Friction Factor Correlations
Purdue University Purdue e-pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 2006 Semi-Empirical 3D Rectangular Channel Air Flow Heat Transfer and Friction
More informationIf there is convective heat transfer from outer surface to fluid maintained at T W.
Heat Transfer 1. What are the different modes of heat transfer? Explain with examples. 2. State Fourier s Law of heat conduction? Write some of their applications. 3. State the effect of variation of temperature
More informationCFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel
CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel *1 Hüseyin Kaya, 2 Kamil Arslan 1 Bartın University, Mechanical Engineering Department, Bartın, Turkey
More informationPHYSICAL MECHANISM OF NATURAL CONVECTION
1 NATURAL CONVECTION In this chapter, we consider natural convection, where any fluid motion occurs by natural means such as buoyancy. The fluid motion in forced convection is quite noticeable, since a
More informationAnalytical Modeling of Forced Convection in Slotted Plate Fin Heat Sinks
Analytical Modeling of Forced Convection in Slotted Plate Fin Heat Sinks P. Teertstra, J. R. Culham & M. M. Yovanovich Department of Mechanical Engineering Waterloo, Ontario, Canada http://www.mhtl.uwaterloo.ca
More informationIn order to optimize the shell and coil heat exchanger design using the model presented in Chapter
1 CHAPTER FOUR The Detailed Model In order to optimize the shell and coil heat exchanger design using the model presented in Chapter 3, one would have to build several heat exchanger prototypes, and then
More informationThe Effect of Mass Flow Rate on the Effectiveness of Plate Heat Exchanger
The Effect of Mass Flow Rate on the of Plate Heat Exchanger Wasi ur rahman Department of Chemical Engineering, Zakir Husain College of Engineering and Technology, Aligarh Muslim University, Aligarh 222,
More informationOUTCOME 2 - TUTORIAL 1
Unit 4: Heat Transfer and Combustion Unit code: K/60/44 QCF level: 5 Credit value: 5 OUTCOME - TUTORIAL Heat transfer coefficients Dimensional analysis: dimensionless groups; Reynolds, Nusselt, Prandtl,
More informationPerformance evaluation of heat transfer enhancement for internal flow based on exergy analysis. S.A. Abdel-Moneim and R.K. Ali*
Int. J. Exergy, Vol. 4, No. 4, 2007 401 Performance evaluation of heat transfer enhancement for internal flow based on exergy analysis S.A. Abdel-Moneim and R.K. Ali* Faculty of Engineering (Shoubra),
More informationTechnological design and off-design behavior of heat exchangers 26
Technological design and off-design behavior of heat exchangers 26 2.2 MODELING OF HEAT TRANSFER The overall heat transfer coefficient U depends on the distribution of thermal resistances in the exchanger.
More informationTutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k)
Tutorial 1 1. Explain in detail the mechanism of forced convection. Show by dimensional analysis (Rayleigh method) that data for forced convection may be correlated by an equation of the form Nu = φ (Re,
More informationExamination Heat Transfer
Examination Heat Transfer code: 4B680 date: 17 january 2006 time: 14.00-17.00 hours NOTE: There are 4 questions in total. The first one consists of independent sub-questions. If necessary, guide numbers
More informationINSTRUCTOR: PM DR MAZLAN ABDUL WAHID
SMJ 4463: HEAT TRANSFER INSTRUCTOR: PM ABDUL WAHID http://www.fkm.utm.my/~mazlan TEXT: Introduction to Heat Transfer by Incropera, DeWitt, Bergman, Lavine 5 th Edition, John Wiley and Sons Chapter 9 Natural
More information1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used?
1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used?. During unsteady state heat transfer, can the temperature
More informationNumerical Study of Free Convection Heat Transfer in a Square Cavity with a Fin Attached to Its Cold Wall
Heat Transfer Research, 2011, Vol. 42, No. 3 Numerical Study of Free Convection Heat Transfer in a Square Cavity with a Fin Attached to Its Cold Wall SAEID JANI, 1* MEYSAM AMINI, 2 and MOSTAFA MAHMOODI
More informationAnalysis of Turbulent Free Convection in a Rectangular Rayleigh-Bénard Cell
Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows Lyon, July 2007 Paper reference : ISAIF8-00130 Analysis of Turbulent Free Convection
More informationNatural Convection in Vertical Channels with Porous Media and Adiabatic Extensions
Natural Convection in Vertical Channels with Porous Media and Adiabatic Extensions Assunta Andreozzi 1,a, Bernardo Buonomo 2,b, Oronzio Manca 2,c and Sergio Nardini 2,d 1 DETEC, Università degli Studi
More informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011
Experimental and Numerical comparison between the performance of Helical cone coils and ordinary helical coils used as dehumidifier for humidification dehumidification in desalination units Abo Elazm M.M.
More informationTrue/False. Circle the correct answer. (1pt each, 7pts total) 3. Radiation doesn t occur in materials that are transparent such as gases.
ME 323 Sample Final Exam. 120pts total True/False. Circle the correct answer. (1pt each, 7pts total) 1. A solid angle of 2π steradians defines a hemispherical shell. T F 2. The Earth irradiates the Sun.
More informationINDIAN INSTITUTE OF TECHNOOGY, KHARAGPUR Date: -- AN No. of Students: 5 Sub. No.: ME64/ME64 Time: Hours Full Marks: 6 Mid Autumn Semester Examination Sub. Name: Convective Heat and Mass Transfer Instructions:
More informationEffect of an adiabatic fin on natural convection heat transfer in a triangular enclosure
American Journal of Applied Mathematics 2013; 1(4): 78-83 Published online November 10, 2013 (http://www.sciencepublishinggroup.com/j/ajam) doi: 10.11648/j.ajam.20130104.16 Effect of an adiabatic fin on
More informationWorld Journal of Engineering Research and Technology WJERT
wjert, 2016, Vol. 2, Issue 3, 108-119 Research Article ISSN 2454-695X Yadav et al. WJERT www.wjert.org SJIF Impact Factor: 3.419 INVESTIGATION OF AXIAL HEAT CONDUCTION FLUX IN RECTANGULAR PARALLEL FLOW
More informationForced Convection: Inside Pipe HANNA ILYANI ZULHAIMI
+ Forced Convection: Inside Pipe HANNA ILYANI ZULHAIMI + OUTLINE u Introduction and Dimensionless Numbers u Heat Transfer Coefficient for Laminar Flow inside a Pipe u Heat Transfer Coefficient for Turbulent
More informationCircle one: School of Mechanical Engineering Purdue University ME315 Heat and Mass Transfer. Exam #2. April 3, 2014
Circle one: Div. 1 (12:30 pm, Prof. Choi) Div. 2 (9:30 am, Prof. Xu) School of Mechanical Engineering Purdue University ME315 Heat and Mass Transfer Exam #2 April 3, 2014 Instructions: Write your name
More informationNumerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15-Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis
More informationNUMERICAL INVESTIGATION OF COUNTER FLOW ISOSCELES RIGHT TRIANGULAR MICROCHANNEL HEAT EXCHANGER
International Journal of Mechanical Engineering and Technology IJMET) Volume 8, Issue 1, January 217, pp. 81 87, Article ID: IJMET_8_1_9 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=8&itype=1
More informationAxial profiles of heat transfer coefficients in a liquid film evaporator
Axial profiles of heat transfer coefficients in a liquid film evaporator Pavel Timár, Ján Stopka, Vladimír Báleš Department of Chemical and Biochemical Engineering, Faculty of Chemical and Food Technology,
More informationPIPE FLOW. General Characteristic of Pipe Flow. Some of the basic components of a typical pipe system are shown in Figure 1.
PIPE FLOW General Characteristic of Pipe Flow Figure 1 Some of the basic components of a typical pipe system are shown in Figure 1. They include the pipes, the various fitting used to connect the individual
More informationY. L. He and W. Q. Tao Xi an Jiaotong University, Xi an, China. T. S. Zhao Hong Kong University of Science and Technology, Kowloon, Hong Kong, China
Numerical Heat Transfer, Part A, 44: 399 431, 2003 Copyright # Taylor & Francis Inc. ISSN: 1040-7782 print=1521-0634 online DOI: 10.1080/10407780390206625 STEADY NATURAL CONVECTION IN A TILTED LONG CYLINDRICAL
More informationطراحی مبدل های حرارتی مهدي کریمی ترم بهار HEAT TRANSFER CALCULATIONS
طراحی مبدل های حرارتی مهدي کریمی ترم بهار 96-97 HEAT TRANSFER CALCULATIONS ١ TEMPERATURE DIFFERENCE For any transfer the driving force is needed General heat transfer equation : Q = U.A. T What T should
More informationHeat and Mass Transfer
1 Comments on six papers published by S.P. Anjali Devi and R. Kandasamy in Heat and Mass Transfer, ZAMM, Mechanics Research Communications, International Communications in Heat and Mass Transfer, Communications
More informationA NUMERICAL STUDY OF NATURAL CONVECTIVE HEAT TRANSFER FROM A HORIZONTAL ISOTHERMAL SQUARE ELEMENT WITH AN UNHEATED ADIABATIC INNER SECTION
A NUMERICAL STUDY OF NATURAL CONVECTIVE HEAT TRANSFER FROM A HORIZONTAL ISOTHERMAL SQUARE ELEMENT WITH AN UNHEATED ADIABATIC INNER SECTION Oosthuizen P.H. Department of Mechanical and Materials Engineering,
More informationCHAPTER 3 SHELL AND TUBE HEAT EXCHANGER
20 CHAPTER 3 SHELL AND TUBE HEAT EXCHANGER 3.1 INTRODUCTION A Shell and Tube Heat Exchanger is usually used for higher pressure applications, which consists of a series of tubes, through which one of the
More informationTHE INFLUENCE OF INCLINATION ANGLE ON NATURAL CONVECTION IN A RECTANGULAR ENCLOSURE
THE INFLUENCE OF INCLINATION ANGLE ON NATURAL CONVECTION IN A RECTANGULAR ENCLOSURE Thamer Khalif Salem Mechanical Engineering, College of Engineering, Tikrit University, IRAQ. thamer_khalif@yahoo.com
More informationConvection. U y. U u(y) T s. T y
Convection Heat transfer in the presence of a fluid motion on a solid surface Various mechanisms at play in the fluid: - advection physical transport of the fluid - diffusion conduction in the fluid -
More informationFINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT OF A HEATED SQUARE HOLLOW CYLINDER IN A LID-DRIVEN RECTANGULAR ENCLOSURE
Proceedings of the International Conference on Mechanical Engineering 2011 (ICME2011) 18-20 December 2011, Dhaka, Bangladesh ICME11-TH-014 FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT
More information5th WSEAS Int. Conf. on Heat and Mass transfer (HMT'08), Acapulco, Mexico, January 25-27, 2008
Numerical Determination of Temperature and Velocity Profiles for Forced and Mixed Convection Flow through Narrow Vertical Rectangular Channels ABDALLA S. HANAFI Mechanical power department Cairo university
More informationLevel 7 Post Graduate Diploma in Engineering Heat and mass transfer
9210-221 Level 7 Post Graduate Diploma in Engineering Heat and mass transfer 0 You should have the following for this examination one answer book non programmable calculator pen, pencil, drawing instruments
More informationEffect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below
International Journal of Discrete Mathematics 017; (): 43-47 http://www.sciencepublishinggroup.com/j/dmath doi: 10.11648/j.dmath.01700.13 Effect of Buoyancy Force on the Flow Field in a Square Cavity with
More informationJournal of Solid and Fluid Mechanics. An approximate model for slug flow heat transfer in channels of arbitrary cross section
Vol. 2, No. 3, 2012, 1 7 Journal of Solid and Fluid Mechanics Shahrood University of Technology An approximate model for slug flow heat transfer in channels of arbitrary cross section M. Kalteh 1,*, A.
More informationThe Mean Version One way to write the One True Regression Line is: Equation 1 - The One True Line
Chapter 27: Inferences for Regression And so, there is one more thing which might vary one more thing aout which we might want to make some inference: the slope of the least squares regression line. The
More informationThe Effect Of MHD On Laminar Mixed Convection Of Newtonian Fluid Between Vertical Parallel Plates Channel
The Effect Of MH On Laminar Mixed Convection Of Newtonian Fluid Between Vertical Parallel Plates Channel Rasul alizadeh,alireza darvish behanbar epartment of Mechanic, Faculty of Engineering Science &
More informationFALLING FILM FLOW ALONG VERTICAL PLATE WITH TEMPERATURE DEPENDENT PROPERTIES
Proceedings of the International Conference on Mechanical Engineering 2 (ICME2) 8-2 December 2, Dhaka, Bangladesh ICME-TH-6 FALLING FILM FLOW ALONG VERTICAL PLATE WITH TEMPERATURE DEPENDENT PROPERTIES
More informationTowards a Numerical Benchmark for 3D Low Mach Number Mixed Flows in a Rectangular Channel Heated from Below
Copyright 2008 Tech Science Press FDMP, vol.4, no.4, pp.263-269, 2008 Towards a Numerical Benchmark for 3D Low Mach Number Mixed Flows in a Rectangular Channel Heated from Below G. Accary 1, S. Meradji
More informationSpecific heat capacity. Convective heat transfer coefficient. Thermal diffusivity. Lc ft, m Characteristic length (r for cylinder or sphere; for slab)
Important Heat Transfer Parameters CBE 150A Midterm #3 Review Sheet General Parameters: q or or Heat transfer rate Heat flux (per unit area) Cp Specific heat capacity k Thermal conductivity h Convective
More informationNatural convection heat transfer around a horizontal circular cylinder near an isothermal vertical wall
Natural convection heat transfer around a horizontal circular cylinder near an isothermal vertical wall Marcel Novomestský 1, Richard Lenhard 1, and Ján Siažik 1 1 University of Žilina, Faculty of Mechanical
More informationMIXED CONVECTION HEAT TRANSFER FROM A PARTICLE IN SUPERCRITICAL WATER
THERMAL SCIENCE, Year 2016, Vol. 20, No. 2, pp. 483-492 483 MIXED CONVECTION HEAT TRANSFER FROM A PARTICLE IN SUPERCRITICAL WATER by Liping WEI, Youjun LU*, and Jinjia WEI State Key Laboratory of Multiphase
More informationWTS Table of contents. Layout
Table of contents Thermal and hydraulic design of shell and tube heat exchangers... 2 Tube sheet data... 4 Properties of Water and Steam... 6 Properties of Water and Steam... 7 Heat transfer in pipe flow...
More informationFLUID MECHANICS PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES Liquid or gas flow through pipes
More informationAdvanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell
Laminar external natural convection on vertical and horizontal flat plates, over horizontal and vertical cylinders and sphere, as well as plumes, wakes and other types of free flow will be discussed in
More informationNATURAL CONVECTIVE HEAT TRANSFER FROM A RECESSED NARROW VERTICAL FLAT PLATE WITH A UNIFORM HEAT FLUX AT THE SURFACE
HEFAT2007 5 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics Sun City, South Africa Paper number: OP2 NATURAL CONVECTIVE HEAT TRANSFER FROM A RECESSED NARROW VERTICAL FLAT
More informationNUMERICAL ANALYSIS OF PARALLEL FLOW HEAT EXCHANGER
NUMERICAL ANALYSIS OF PARALLEL FLOW HEAT EXCHANGER 1 Ajay Pagare, 2 Kamalnayan Tripathi, 3 Nitin Choudhary 1 Asst.Profesor at Indore institute of science and technology Indore, 2 Student at Indore institute
More informationConvective Mass Transfer
Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface
More informationMIXED CONVECTION OF NEWTONIAN FLUID BETWEEN VERTICAL PARALLEL PLATES CHANNEL WITH MHD EFFECT AND VARIATION IN BRINKMAN NUMBER
Bulletin of Engineering Tome VII [14] ISSN: 67 389 1. Rasul ALIZADEH,. Alireza DARVISH BAHAMBARI, 3. Komeil RAHMDEL MIXED CONVECTION OF NEWTONIAN FLUID BETWEEN VERTICAL PARALLEL PLATES CHANNEL WITH MHD
More informationHeat transfer enhancement in natural convection in micropolar nanofluids
Arch. Mech., 68, 4, pp. 327 344, Warszawa 2016 Heat transfer enhancement in natural convection in micropolar nanofluids K. RUP, K. NERING Faculty of Mechanical Engineering Cracow University of Technology
More informationInternal Flow: Heat Transfer in Pipes
Internal Flow: Heat Transfer in Pipes V.Vuorinen Aalto University School of Engineering Heat and Mass Transfer Course, Autumn 2016 November 15 th 2016, Otaniemi ville.vuorinen@aalto.fi First about the
More informationHeat Transfer F12-ENG Lab #4 Forced convection School of Engineering, UC Merced.
1 Heat Transfer F12-ENG-135 - Lab #4 Forced convection School of Engineering, UC Merced. October 23, 2012 1 General purpose of the Laboratory To gain a physical understanding of the behavior of the average
More informationOutlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer
Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer
More informationConstructal multi-scale design of compact micro-tube heat sinks and heat exchangers
JID:THESCI AID:2493 /FLA [m5+; v 1.60; Prn:29/06/2006; 9:31] P.1 (1-8) International Journal of Thermal Sciences ( ) www.elsevier.com/locate/ijts Constructal multi-scale design of compact micro-tube heat
More informationChapter 3 NATURAL CONVECTION
Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGraw-Hill Companies,
More information