Thermodynamics, Fluid Dynamics, and Heat Transfer
|
|
- Bryce Collins
- 6 years ago
- Views:
Transcription
1 Chapter 2 Thermodynamics, Fluid Dynamics, and Heat Transfer 2. Introduction In this chapter we will review fundamental concepts from Thermodynamics, Fluid Dynamics, and Heat Transfer. Each section first begins with a review of the fundamentals. Subsequently, a review of important equations and solutions to fundamental problems from each of the three fields. This chapter is only intended to provide the necessary reference material for the course. It is not intended as a substitute for the basic texts used in the thermo-fluids courses. During this course extensive reference will be made to the following texts dealing with thermo-fluid fundamentals. These are: ) Fundamentals of Fluid Mechanics, Potter and Wiggert 2) Fundamentals of Engineering Thermodynamics, Moran and Shapiro 3) Fundamentals of Heat and Mass Transfer, Incropera and DeWitt Where possible, the use of robust design models or correlations which span a wide range of flow conditions will be encouraged. These comprehensive models allow for greater flexibility in the design and optimization of thermal systems. Whereas piecewise models, i.e. those which consider each different flow region separately, tend to detract from the integrated design approach developed in the notes. 3
2 4 Mechanical Equipment and Systems 2.2 Thermodynamics 2.2. First Law of Thermodynamics The First Law of Thermodynamics, better known as the conservation of energy will be utilized for both open and closed systems throughout this course. We shall begin by examining the different ways of stating the First Law for both open and closed systems. The First Law of Thermodynamics for a closed system states E 2 E = Q 2 + W 2 2.) This is understood to imply that the change in energy of a closed system is related to the net heat input and the net work done on the system. In terms of instantaneous transfer rates, the First Law may be written on a per unit time basis de dt = Q + Ẇ 2.2) The First Law of Thermodynamics may also be written for an open system containing a number of inlets and outlets de cv dt = ṁ i u i + p i v i + V ) i gz i ṁ e u e + p e v e + V ) e gz e + Q cv +Ẇcv 2.3) This equation states that the accumulation of energy within the control volume must equal the net inflow of energy into the control volume minus the net outflow of energy from the control volume plus the increase in energy due to work and heat transfers. The sign convention adopted in these notes is that any work done on a system is considered positive, while any work done by the system is considered negative. This convention reflects the notion that work done on a system increases the energy of the system, i.e. the use of a pump or compressor. Contemporary texts in Thermodynamics have preferred the use of the heat engine convention which reflects that useful work done by the system is considered positive. Either convention may be applied so long as consistency is applied throughout the analysis of a problem Second Law of Thermodynamics The Second Law of Thermodynamics deals with the irreversibility of thermodynamic processes. A reversible process is one in which there is no production of entropy. For a closed system the second law of thermodynamics states that 2 δq T S 2 S 2.4) We define the entropy production S gen as the difference between the entropy change and the entropy transfer such that
3 Fundamentals 5 S gen = S 2 S ) 2 δq T 0 2.5) The Second Law of Thermodynamics for an open system containing a number of inlets and outlets becomes ds cv dt = Q j T j + m i s i m e s e + Ṡgen 2.6) This equation states that the rate of entropy accumulation within the control volume is balanced by the net transfer of entropy through heat exchanges with the surroundings plus the net flow of entropy into the control volume and the rate of entropy production within the control volume. It should be noted that for a steady state analysis the entropy production rate is not zero except for reversible processes). Whereas the rate of accumulation of entropy within the control volume is zero for a steady state process Exergy The first and second laws of thermodynamics may be combined to develop a new relation which governs a new quantity Exergy. Exergy is a measure of the potential of a thermodynamic system to do work. Unlike energy, exergy can be destroyed. Exergy analysis, sometimes called availability analysis, is used quite frequently in the design and analysis of thermal systems. Exergy is defined as E = E U o ) + p o V V o ) T o S S o ) 2.7) Here E = U + P.E. + K.E.), the energy of the system, U is internal energy, S is entropy, and V is the volume of the system. The reference or dead state as it is referred is denoted by the subscript ) o. We may also define exergy as an intensive property, that is on a per unit mass basis, such that e = [u + V 2 /2 + gz) u o ] + p o v v o ) T o s s o ) 2.8) The change in exergy between any two states is merely E 2 E = E 2 E ) + p o V 2 V ) T o S 2 S ) 2.9) For a closed system the exergy balance yields E 2 E = 2 T ) o δq [W p o V 2 V )] E d 2.0) T b The term E d = T o S gen, is the exergy which is destroyed due to irreversibilities in the system. For an open system with a number of inlets and outlets the exergy balance yields:
4 6 Mechanical Equipment and Systems de cv dt = T ) o T j Q j ) dv cv Ẇ cv p o + ṁ i e i ṁ e e e E dt d 2.) e = h h o ) T o s s o ) + V 2 /2 + gz 2.2) is the flow exergy. Table Dimensionless Groups Group Biot Number Reynolds Number Prandtl Number Peclet Number Grashof Number Rayleigh Number Ra Nusselt Number Definition Bi hl k s Re ρv L µ Pr ν α Pe V L α RePr gβ T L3 Gr ν 2 gβ T L3 αν GrPr Nu q/a)l k f T hl k f Stanton Number St Nu RePr Colburn Factor j Nu RePr /3 Friction Coefficient C f τ 2 ρv 2 Fanning Friction Factor f p/l)a/p) 2 ρv 2
5 Fundamentals Dimensionless Groups Before proceeding to the review of fluid dynamics and heat transfer models, a brief discussion on the use of dimensionless quantities is required. A number of important dimensionless quantities appear throughout the text. The student should familiarize himself or herself with these parameters and their use. Table summarizes the most important groups that will be encountered during this course. 2.4 Fluid Dynamics 2.4. Conservation Equations Conservation of mass and momentum for a control volume will be applied throughout the course. Here we will merely state the general form as previously discussed in fluid mechanics courses. Conservation of Mass dm CV dt = ṁ i ṁ e 2.3) Conservation of Momentum F = Ve ρ V e A e ) Vi ρ V i A i ) 2.4) In addition, we will also apply Bernoulli s equation for a number of incompressible flows. Bernoulli s Equation P γ + V 2 2g + z = P 2 γ + V 2 2 2g + z 2 + h L 2.5) Internal Flows When analyzing flow in ducting or piping systems as well as flow through mechanical equipment, a number of design models and correlations are required for relating the mass flow rate to the pressure drop of the working fluid. The most common method is through the definition of the friction factor. The Fanning friction factor will be adopted for this course. It is defined as follows: A p f = τ = P L 2 ρu2 = 2 ρu2 D h 4 p L 2.6) 2 ρu2
6 8 Mechanical Equipment and Systems D h = 4A P 2.7) A is the cross-sectional area and P is the perimeter of the duct. In fully developed laminar flows the friction factor takes the following form: f = C Re Dh 2.8) C is a constant which is a function of the shape and aspect ratio of the duct. Table 2 summarizes a number of values for common duct shapes. Apparent friction factors for developing flows may be computed from the following formula f app Re Dh = [ 3.44 L ) 2 + fre Dh )2 ] /2 2.9) L = L D h Re Dh 2.20) In circular tubes the flow is developing in a region L < The entrance length for flow development is L e = 0.058DRe D 2.2) Table 2 Typical values of fre Dh = C for Non-Circular Ducts Shape fre Dh = C Equilateral Triangle 3.33 Square 4.23 Pentagon 4.74 Hexagon 5.05 Octagon 5.4 Circle 6 Elliptic 2: 6.82 Elliptic 4: 8.24 Elliptic 8: 9.5 Rectangular 2: 5.55 Rectangular 4: 8.23 Rectangular 8: Parallel Plates 24
7 Fundamentals 9 For turbulent flows the friction factor is predicted using the Colebrook relation. This correlation is the basis for the Moody diagram ǫ/d = 2 log fd ) 2.22) Re D fd the subscript d denotes the Darcy friction factor defined as: D p f d = L 2.23) 2 ρu2 The entrance length for turbulent flow in a tube is L e = 4.4DRe D ) /6 2.24) In non-circular ducts we use the concept of the hydraulic diameter D = D h = 4A/P to compute an equivalent duct diameter External Flows A number of important design equations for external fluid flows are required to relate the free stream velocity to the overall drag force. The three most common geometries are the flat plate, the cylinder, and the sphere. Flat Plate For laminar boundary layer flows, 000 < Re L < 500, 000, the important parameters are the boundary layer thickness and the friction coefficient: δx) = 5x Re /2 x 2.25) C f,x = ) Re /2 x C f = ) Re /2 L For turbulent boundary layer flows, 500, 000 < Re L < 0 7, the boundary layer thickness and friction coefficient are: δx) = 0.38x Re /5 x C f,x = Re /5 x C f = Re /5 L 2.28) 2.29) 2.30)
8 20 Mechanical Equipment and Systems If the boundary layer is composed of a combined laminar-turbulent flow, Re L > 500, 000, the friction coefficient is computed from the integrated value: C f = ) Re /5 Re L L Finally, a number of useful models for predicting drag on flat plates, cylinders, and spheres in low Reynolds number flows are also provided. These models will provide the building blocks for analysing a fluid component or system. Flat Plate 0.0 < Re L < 500, 000 C f = 2.66 Re 7/8 L Re /2 L 2.32) Cylinder 0. < Re D < 250, 000 C D = ) Re 2/3 D Sphere 0.0 < Re D < 250, 000 C D = 24 Re D Re /2 D ) C D, C f = F/A 2 ρu2 2.35) Note care must be taken to ensure the correct characteristic area A is chosen based upon the geometry. 2.5 Heat Transfer 2.5. Conduction -Dimensional Steady Conduction Steady one-dimensional conduction in plane walls, cylinders, and spheres is easily analyzed using the resistance concept. The thermal resistance is defined such that T = QR t 2.36) For a multi-component system containing j layers, the following thermal resistance results are useful.
9 Fundamentals 2 Plane Wall R t = h i A + t j k j A + h o A 2.37) Cylinder R t = + lnr oj /r ij ) ) 2πr i L)h i 2πk j L) 2πr o L)h o Sphere R t = 4πr 2 i )h i + ) ) 4πk j r ij r oj 4πro)h 2 o Multi-Dimensional Steady Conduction In two or three dimensions, heat transfer by means of conduction is best analyzed using shape factors. Many multi-dimensional solutions of practical interest have been obtained and are outlined below. The conduction shape factor S, is defined such that: R = Sk 2.40) R is the thermal resistance and k is the thermal conductivity of the medium. The shape factor S, is only a function of the geometry of the system. The overall heat transfer rate is then related to an appropriate temperature difference: Q = Sk T 2.4) T is the temperature difference between two isothermal surfaces. A number of useful shape factors are tabulated in the handout. Transient Conduction Transient conduction in finite and semi-infinite regions are also of interest. The following solutions are useful for modelling a number of thermal systems. Semi-Infinite Regions Isothermal Wall Tx,t) T s T i T s ) x = erf 2 αt 2.42)
10 22 Mechanical Equipment and Systems q s t) = kt s T i ) παt 2.43) Isoflux Wall Tx,t) T i = 2q s αt/π exp k ) x 2 4αt q ) sx x k erfc 2 αt 2.44) Surface Convection Tx,t) T i T T i T s t) T i = 2q s k ) /2 αt 2.45) π ) [ )][ x hx = erfc 2 exp αt k + h2 αt x erfc k 2 2 αt + h )] αt k 2.46) T s t) T i T T i ) h 2 αt h αt = exp erfc k 2 k q s t) ) ) αt h 2 kt Ti) = exp αt h αt erfc k 2 k ) 2.47) 2.48) Finite Regions Transient conduction from finite one dimensional and multi-dimensional regions may be analyzed using the following solutions. In the solutions below = T T f, i = T i T f, and Q i = ρc p V T i T f ). The notation adopted in this section follows that of Yovanovich 999). Plane Wall i = A n exp δnfo) 2 cosδ n X) 2.49) n= A n = The eigenvalues δ n are determined from 4 sinδ n ) 2δ n + sin2δ n ) 2.50) δ n sinδ n ) = Bi cosδ n ) 2.5) In the expressions above, Fo = αt/l 2, X = x/l, and Bi = hl/k. The heat flow at the surface of the wall is determined from
11 Fundamentals 23 Q Q i = n= 2Bi 2 δ 2 nbi 2 + Bi + δ 2 n) ) exp δ 2 nfo) 2.52) Next if Fo > 0.24, the series solutions for temperature and heat flow reduce to single term approximations = A exp δ Fo) 2 cosδ X) i 2.53) ) Q 2Bi 2 = exp δ Q i δbi Bi + δ Fo) 2 ) ) δ =.5708 [ / Bi) 2.39 ] ) Finally, if the Biot number is small Bi < 0.2), spatial effects are no longer significant and the lumped capacitance model applies. For a plane wall this results in i = exp BiFo) 2.56) Infinite Cylinder Q Q i = exp BiFo) 2.57) i = A n exp δnfo)j 2 0 δ n R) 2.58) n= A n = The eigenvalues δ n are determined from 2J δ n ) δ n J 2 0δ n ) + J 2 δ n )) 2.59) δ n J δ n ) = J 0 δ n )Bi 2.60) In the expressions above, Fo = αt/a 2, R = r/a, and Bi = ha/k. The heat flow at the surface of the cylinder is determined from Q Q i = n= 4Bi 2 δ 2 nbi 2 + δ 2 n) ) exp δ 2 nfo) 2.6) Next if Fo > 0.2, the series solutions for temperature and heat flow reduce to single term approximations
12 24 Mechanical Equipment and Systems = A exp δ Fo)J 2 0 δ R) i 2.62) ) Q 4Bi 2 = exp δ Q i δbi δ Fo) 2 ) ) δ = [ / 2Bi) ] ) Finally, if the Biot number is small Bi < 0.2), spatial effects are no longer significant and the lumped capacitance model applies. For an infinite cylinder this results in i = exp 2BiFo) 2.65) Sphere Q Q i = exp 2BiFo) 2.66) i = n= The eigenvalues δ n are determined from A n exp δ 2 nfo) sinδ nr) δ n R A n = 4[sinδ n) δ n cosδ n )] 2δ n sin2δ n ) 2.67) 2.68) δ n cosδ n ) = Bi) sinδ n ) 2.69) In the expressions above, Fo = αt/a 2, R = a/l, and Bi = ha/k. The heat flow at the surface of the sphere is determined from Q Q i = n= 6Bi 2 δ 2 nbi 2 Bi + δ 2 n) ) exp δ 2 nfo) 2.70) Next if Fo > 0.8, the series solutions for temperature and heat flow reduce to single term approximations Q Q i = = A exp δ Fo) 2 sinδ R) i δ R 6Bi 2 δbi 2 2 Bi + δ) 2 2.7) ) exp δ 2 Fo) 2.72)
13 Fundamentals 25 δ = [ / 3Bi) 2.34 ] ) Finally, if the Biot number is small Bi < 0.2), spatial effects are no longer significant and the lumped capacitance model applies. For a sphere this results in Convection i = exp 3BiFo) 2.74) Q Q i = exp 3BiFo) 2.75) Convective heat transfer models for internal and external flows are required for modelling heat exchangers, heat sinks, electronic enclosures, etc. A number of useful design models and correlations are now presented for internal and external flows. Internal Forced Convection Circular and Non-Circular Ducts In laminar flow, Muzychka and Yovanovich 200) proposed the following model for developing laminar flows: { Nu A z ) = { )} ) fre 5 m/5 C A πǫ γ C C 2 fre A z { C4 fpr) z } ) } m /m 2.76) and m = Pr /3 2.77) z = z ARe A Pr 2.78) and fre A = 2 [ ǫ /2 + ǫ) 92ǫ π ) tanh ] 2.79) π 5 2ǫ
14 26 Mechanical Equipment and Systems In the above model, the characteristic length scale is the square root of the crosssectional duct area. The parameter γ is chosen based upon the duct geometry. The lower bound value is for ducts that have re-entrant corners, i.e. angles less than 90 degrees. The upper bound is for ducts with rounded corners, rectangular or elliptical shapes. The coefficients are tabulated in Table 3 for various conditions. For turbulent flows the most popular expression is the correlation developed by Gneilinski 976). Nu Dh = f/8)re Dh Pr f/8) /2 Pr 2/3 ) 2.80) f = 0.79 ln Re dh.64) 2 2.8) Table 3 Coefficients for General Model Boundary Condition Isothermal C 2 = 0.409, C 3 = 3.24 fpr) = Isoflux C 2 = 0.50, C 3 = 3.86 fpr) = [ +.664Pr /6 ) 9/2] 2/ [ +.909Pr /6 ) 9/2] 2/9 Nusselt Type Local C = C 4 = Average C = 3/2 C 4 = 2 Shape Parameter Upper Bound γ = /0 Lower Bound γ = 3/0 External Forced Convection Flate Plate For a flat plate in laminar boundary layer flow, 000 < Re L < 500, 000, the Nusselt number is obtained from the following expressions: Nu x = Re x Pr) /2 fpr) 2.82)
15 Fundamentals 27 Nu L = 2Re L Pr) /2 fpr) 2.83) for the constant surface temperature, T s, boundary condition fpr) = [ +.664Pr /6 ) 9/2] 2/9 2.84) and for the constant heat flux, q s, boundary condition fpr) = [ +.909Pr /6 ) 9/2] 2/9 2.85) In turbulent boundary layer flow, 500, 000 < Re L < 0 7, the following equations are often used: Nu x = Re 4/5 x Pr /3 2.86) Nu L = 0.037Re 4/5 L Pr/3 2.87) For a combined laminar/turbulent boundary layer, Re L > 500, 000, the following integrated expression is useful: Cylinder Pe D > 0.2 Nu L = 0.037Re 4/5 L 87)Pr/3 2.88) For a cylinder in crossflow Churchill and Bernstein 977) proposed the following correlation of experimental data: Nu D = [ ) ] 5/8 4/5 0.62Re/2 D Pr/3 ReD ) [ + 0.4/Pr) 2/3 ] /4 282, 000 Spheroids 0 < Re A < 2 05 and Pr > 0.7 For a sphere or spheroidal shaped body Yovanovich 988) recommends the following model Nu A = 2 π + [ ) ] /2 P 0.5 Re /2 A A Re A Pr /3 2.90) A is the surface area and P is the maximum equitorial perimeter.
16 28 Mechanical Equipment and Systems Internal Natural Convection Parallel Plates The Nusselt number for laminar natural convection flow between parallel isothermal plates is obtained from the following correlation developed by Bar-Cohen and Rohsenow 984) [ ] /2 576 Nu b = [Ra b b/l)] ) 2 [Ra b b/l)] /2 The Nusselt number for laminar natural convection flow between parallel isoflux plates is obtained from the follow correlation developed by Bar-Cohen and Rohsenow 984) [ ] /2 48 Nu b = [Ra ) b b/l)]2 [Ra b b/l)]2/5 Ra b = gβ Tb 3 /αν) and Ra b = gβq b 4 /kαν), and b is the plate spacing. Circular and Non-Circular Ducts For laminar natural convection in vertical isothermal ducts, Yovanovich et al.200) recommend: Nu A = 2 Ra A A/L ) ) 2 A fre A P n Ra A ) /4 n A L /n and 2.93) n =.2 ǫ /9 2.94) fre A = 2 [ ǫ /2 + ǫ) 92ǫ π ) tanh ] 2.95) π 5 2ǫ In the above model, the characteristic length scale is the square root of the crosssectional duct area. External Natural Convection Flate Plate For a vertical isothermal wall the following correlation is recommended for laminar
17 Fundamentals 29 flow Gr L < 0 9 : Nu x = 0.503Ra /4 x fpr) 2.96) Nu L = 4 3 Ra/4 L fpr) 2.97) ) /4 Pr fpr) = 2.98) Pr Pr / ) A correlation which is valid for both the laminar and turbulent regions 0 < Ra L < 0 2 was proposed by Churchill and Chu 975). Their correlation takes the following form: Horizontal Cylinder Nu L = ) 0.387Ra /6 2 L 2.99) [ /Pr) 9/6 ] 8/27 A correlation which is valid for both the laminar and turbulent regions 0 5 < Ra L < 0 2 was proposed by Churchill and Chu 975). Their correlation takes the following form: Sphere Nu D = ) 0.387Ra /6 2 L 2.00) [ /Pr) 9/6 ] 8/27 For a sphere with Ra < 0, the following correlation is recommended: Nu D = 2 + Other Three Dimensional Bodies 0.589Ra /4 D [ /Pr) 9/6 ] 4/9 2.0) For three dimensional bodies in any orientation, Yovanovich 987) recommends the following correlation for 0 < Ra A < 08 : Nu A = 2 π + Ra /4 A fpr) 2.02) fpr) = and A is the surface area of the body [ /Pr) 9/6 ] 4/9 2.03)
18 30 Mechanical Equipment and Systems Radiation Radiative heat transfer transfer is determined using the Stefan-Boltzmann law: q 2 = ǫf 2 σt 4 T 4 2 ) 2.04) ǫ is the surface emissivity, F 2 is the view factor, and σ = 5.670e 8 W/m 2 K 4 ), the Stefan-Boltzmann constant. A number of common two surface enclosure problems are: Parallel Plates q 2 = σt 4 T 4 2 ) ǫ + ǫ ) Concentric Cylinders σt 4 T2 4 ) q 2 = + ǫ 2 ǫ ǫ 2 r r 2 ) 2.06) Concentric Spheres q 2 = σt 4 T 4 2 ) ǫ + ǫ 2 ǫ 2 r r 2 ) ) Additional enclosure problems are discussed in all basic heat transfer texts. For more information on radiative exchange and radiative properties, the student should refer to the course text on heat transfer.
19 Fundamentals References Bar-Cohen, A. and Rohsenow, W.M., Thermally Optimum Spacing of Vertical Natural Convection Cooled Parallel Plates, Journal of Heat Transfer, Vol. 06, 984. Bejan, A. Heat Transfer, 993, Wiley, New York. Bejan, A., Advanced Engineering Thermodynamics, 997, Wiley, New York, NY. Bejan, A., G. Tsatsaronis, and Moran, M., Thermal Design and Optimization, 996, Wiley, New York, NY. Churchill, S.W. and Chu, H.H.S., Correlating Equations for Laminar and Turbulent Free Convection from a Horizontal Cylinder, International Journal of Heat and Mass Transfer, Vol. 8, 975, pp Churchill, S.W. and Bernstein, M., A Correlating Equation for Forced Convection from gases and Liquids to a Circular Cylinder in Cross Flow, Journal of Heat Transfer, Vol. 99, 977, pp Churchill, S.W., A Comprehensive Correlating Equation for Forced Convection from Flat Plates, American Institute of Chemical Engineers, Vol. 22, 976, pp Gnielinski, V., New Equations for Heat and Mass Transfer in Turbulent Pipe and Channel Flow, International Chemical Engineering, Vol. 6, 976, pp Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, 996, Wiley, New York, NY. Moran, M.J. and Shapiro, H.N., Fundamentals of Engineering Thermodynamics, 2000, Wiley, New York, NY. Munson, B.R., Young, D.F., Okiishi, T.H., Fundamentals of Fluid Mechanics, 998, Wiley, New York, NY. Muzychka, Y.S. and Yovanovich, M.M., Forced Convection Heat Transfer in the Combined Entry Region of Non-Circular Ducts, Submitted to the 200 International Mechanical Engineering Congress and Exposition, New York, NY, November, 200. Rohsenow, W.M., Hartnett, J.P., and Cho, Y.I., Handbook of Heat Transfer, 999, McGraw-Hill, New York. Yovanovich, M.M., General Expression for Forced Convection Heat and Mass Transfer from Isopotential Spheroids, AIAA Paper , AIAA 26th Aerospace Sciences Meeting and Exhibit, Reno, NV, January -4, 988.
20 32 Mechanical Equipment and Systems Yovanovich, M.M., On the Effect of Shape, Aspect Ratio, and Orientation Upon natural Convection from Isothermal Bodies of Complex Shape, ASME HTD Vol. 82, 987, pp Yovanovich, M.M., Teertstra, P.M., and Muzychka, Y.S. Natural Convection Inside Vertical Isothermal Ducts of Constant Arbitrary Cross-Section, AIAA Paper , AIAA 39th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 8-, 200.
ENGR Heat Transfer II
ENGR 7901 - Heat Transfer II Convective Heat Transfer 1 Introduction In this portion of the course we will examine convection heat transfer principles. We are now interested in how to predict the value
More informationENGR Heat Transfer II
ENGR 7901 - Heat Transfer II External Flows 1 Introduction In this chapter we will consider several fundamental flows, namely: the flat plate, the cylinder, the sphere, several other body shapes, and banks
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 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 informationFORMULA SHEET. General formulas:
FORMULA SHEET You may use this formula sheet during the Advanced Transport Phenomena course and it should contain all formulas you need during this course. Note that the weeks are numbered from 1.1 to
More informationSummary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer
1. Nusselt number Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer Average Nusselt number: convective heat transfer Nu L = conductive heat transfer = hl where L is the characteristic
More informationDipak P. Saksena Assistant Professor, Mechancial Engg. Dept.Institute of Diploma Studies.Nirmaunieversity
International Journal of Engineering Science Invention ISSN (Online): 2319 6734, ISSN (Print): 2319 6726 Volume 2 Issue 7 ǁ July. 2013 ǁ PP.17-29 Entropy generation analysis for fully developed laminar
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 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 informationEntropy Generation Analysis for Various Cross-sectional Ducts in Fully Developed Laminar Convection with Constant Wall Heat Flux
Korean Chem. Eng. Res., 52(3), 294-301 (2014) http://dx.doi.org/10.9713/kcer.2014.52.3.294 PISSN 0304-128X, EISSN 2233-9558 Entropy Generation Analysis for Various Cross-sectional Ducts in Fully Developed
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 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 informationExternal Forced Convection :
External Forced Convection : Flow over Bluff Objects (Cylinders, Spheres, Packed Beds) and Impinging Jets Chapter 7 Sections 7.4 through 7.8 7.4 The Cylinder in Cross Flow Conditions depend on special
More informationC ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127
C ONTENTS Preface xviii Nomenclature xxvi CHAPTER ONE BASICS OF HEAT TRANSFER 1 1-1 Thermodynamics and Heat Transfer 2 Application Areas of Heat Transfer 3 Historical Background 3 1-2 Engineering Heat
More information6. Laminar and turbulent boundary layers
6. Laminar and turbulent boundary layers John Richard Thome 8 avril 2008 John Richard Thome (LTCM - SGM - EPFL) Heat transfer - Convection 8 avril 2008 1 / 34 6.1 Some introductory ideas Figure 6.1 A boundary
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 Transfer II ENGR 7901 Spring, Dr. Y. Muzychka EN 3058
Heat Transfer II ENGR 7901 Spring, 2010 Dr. Y. Muzychka EN 3058 Course Materials Text: Fundamentals of Heat Transfer Incropera and DeWiP, 6 th EdiRon Course Notes and Handouts Most Course Material on Webpage
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 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 informationChapter 9 NATURAL CONVECTION
Heat and Mass Transfer: Fundamentals & Applications Fourth Edition in SI Units Yunus A. Cengel, Afshin J. Ghajar McGraw-Hill, 2011 Chapter 9 NATURAL CONVECTION PM Dr Mazlan Abdul Wahid Universiti Teknologi
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 information1 R-value = 1 h ft2 F. = m2 K btu. W 1 kw = tons of refrigeration. solar = 1370 W/m2 solar temperature
Quick Reference for Heat Transfer Analysis compiled by Jason Valentine and Greg Walker Please contact greg.alker@vanderbilt.edu ith corrections and suggestions copyleft 28: You may copy, distribute, and
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 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 informationMECH 375, Heat Transfer Handout #5: Unsteady Conduction
1 MECH 375, Heat Transfer Handout #5: Unsteady Conduction Amir Maleki, Fall 2018 2 T H I S PA P E R P R O P O S E D A C A N C E R T R E AT M E N T T H AT U S E S N A N O PA R T I - C L E S W I T H T U
More informationMechanical Engineering. Postal Correspondence Course HEAT TRANSFER. GATE, IES & PSUs
Heat Transfer-ME GATE, IES, PSU 1 SAMPLE STUDY MATERIAL Mechanical Engineering ME Postal Correspondence Course HEAT TRANSFER GATE, IES & PSUs Heat Transfer-ME GATE, IES, PSU 2 C O N T E N T 1. INTRODUCTION
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 information6 Empirical and Practical
6 Empirical and Practical Forced-Convection Relations for Heat Transfer CHAPTER 6-1 INTRODUCTION The discussion and analyses of Chapter 5 have shown how forced-convection heat transfer may be calculated
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 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 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 informationENG Heat Transfer II 1. 1 Forced Convection: External Flows Flow Over Flat Surfaces... 4
ENG7901 - Heat Transfer II 1 Contents 1 Forced Convection: External Flows 4 1.1 Flow Over Flat Surfaces............................. 4 1.1.1 Non-Dimensional form of the Equations of Motion.......... 4
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 informationChemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017
Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering
More informationMODULE CODE: ENGG08021 INTRODUCTION TO THERMOFLUIDS. Date: 15 January 2016 Time: 10:00 12:00
School of Engineering & Computing Session 2015-16 Paisley Campus Trimester 1 MODULE CODE: ENGG08021 INTRODUCTION TO THERMOFLUIDS Date: 15 January 2016 Time: 10:00 12:00 Attempt FOUR QUESTIONS IN TOTAL
More informationInternal Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Internal Forced Convection Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Introduction Pipe circular cross section. Duct noncircular cross section. Tubes small-diameter
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 informationCooling by Free Convection at High Rayleigh Number of Cylinders Positioned Above a Plane
16 th Australasian Fluid Mechanics Conference Crown Plaza, Gold Coast, Australia 2-7 December 2007 Cooling by Free Convection at High Rayleigh Number of Cylinders Positioned Above a Plane B.P. Huynh Faculty
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 informationExternal Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
External Forced Convection Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Drag and Heat Transfer in External flow Fluid flow over solid bodies is responsible
More informationFundamental Concepts of Convection : Flow and Thermal Considerations. Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.
Fundamental Concepts of Convection : Flow and Thermal Considerations Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.3 6.1 Boundary Layers: Physical Features Velocity Boundary Layer
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 informationChapter 7: External Forced Convection
Chapter 7: External Forced Convection Yoav Peles Department of Mechanical, Aerospace and Nuclear Engineering Rensselaer Polytechnic Institute Copyright The McGraw-Hill Companies, Inc. Permission required
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 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 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 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 informationECE309 INTRODUCTION TO THERMODYNAMICS & HEAT TRANSFER. 10 August 2005
ECE309 INTRODUCTION TO THERMODYNAMICS & HEAT TRANSFER 0 August 2005 Final Examination R. Culham & M. Bahrami This is a 2 - /2 hour, closed-book examination. You are permitted to use one 8.5 in. in. crib
More informationPhone: , For Educational Use. SOFTbank E-Book Center, Tehran. Fundamentals of Heat Transfer. René Reyes Mazzoco
8 Fundamentals of Heat Transfer René Reyes Mazzoco Universidad de las Américas Puebla, Cholula, Mexico 1 HEAT TRANSFER MECHANISMS 1.1 Conduction Conduction heat transfer is explained through the molecular
More informationChapter 7: External Forced Convection. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University
Chapter 7: External Forced Convection Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Objectives When you finish studying this chapter, you should be able to: Distinguish between
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 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 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 informationENTROPY GENERATION DUE TO EXTERNAL FLUID FLOW AND HEAT TRANSFER FROM A CYLINDER BETWEEN PARALLEL PLANES
ENTROPY GENERATION UE TO EXTERNAL FLUI FLOW AN HEAT TRANSFER FROM A CYLINER BETWEEN PARALLEL PLANES Omar A. MELHEM, Ahmet Z. SAHIN*, and Bekir S. YILBAS Mechanical Engineering epartment King Fahd University
More informationSimplified Analytical Models for Forced Convection Heat Transfer From Cuboids of Arbitrary Shape
J. R. Culham Associate Professor and Director Mem. ASME M. M. Yovanovich Distinguished Professor Emeritus Fellow ASME P. Teertstra Research Associate Microelectronics Heat Transfer Laboratory, Department
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 informationQUESTION ANSWER. . e. Fourier number:
QUESTION 1. (0 pts) The Lumped Capacitance Method (a) List and describe the implications of the two major assumptions of the lumped capacitance method. (6 pts) (b) Define the Biot number by equations and
More informationMicroelectronics Heat Transfer Laboratory
Microelectronics Heat Transfer Laboratory Department of Mechanical Engineering University of Waterloo Waterloo, Ontario, Canada http://www.mhtl.uwaterloo.ca Outline Personnel Capabilities Facilities Research
More informationUniversity of Macau Department of Electromechanical Engineering MECH316 Heat Transfer Syllabus 2 nd Semester 2011/2012 Part A Course Outline
University of Macau Department of Electromechanical Engineering MECH316 Heat Transfer Syllabus 2 nd Semester 2011/2012 Part A Course Outline Compulsory course in Electromechanical Engineering Course description:
More informationInternational Journal of Heat and Mass Transfer
International Journal of Heat and Mass Transfer 54 (2011) 1441 1447 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
More informationLumped Mass Heat Transfer Experiment
Lumped Mass Heat Transfer Experiment Thermal Network Solution with TNSolver Bob Cochran Applied Computational Heat Transfer Seattle, WA TNSolver@heattransfer.org ME 331 Introduction to Heat Transfer University
More informationECE309 INTRODUCTION TO THERMODYNAMICS & HEAT TRANSFER. 3 August 2004
ECE309 INTRODUCTION TO THERMODYNAMICS & HEAT TRANSFER 3 August 004 Final Examination R. Culham This is a 3 hour, closed-book examination. You are permitted to use one 8.5 in. in. crib sheet (both sides),
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 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 informationENTROPY GENERATION OF CONVECTION HEAT TRANSFER IN AN ASYMMETRICALLY HEATED PACKED DUCT
University of Nebraska - Lincoln From the SelectedWorks of YASAR DEMIREL 1997 ENTROPY GENERATION OF CONVECTION HEAT TRANSFER IN AN ASYMMETRICALLY HEATED PACKED DUCT YASAR DEMIREL H.H. Ali B.A. Abu-Al-Saud
More informationIsentropic Efficiency in Engineering Thermodynamics
June 21, 2010 Isentropic Efficiency in Engineering Thermodynamics Introduction This article is a summary of selected parts of chapters 4, 5 and 6 in the textbook by Moran and Shapiro (2008. The intent
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 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 informationFin Convection Experiment
Fin Convection Experiment Thermal Network Solution with TNSolver Bob Cochran Applied Computational Heat Transfer Seattle, WA TNSolver@heattransfer.org ME 331 Introduction to Heat Transfer University of
More informationELEC9712 High Voltage Systems. 1.2 Heat transfer from electrical equipment
ELEC9712 High Voltage Systems 1.2 Heat transfer from electrical equipment The basic equation governing heat transfer in an item of electrical equipment is the following incremental balance equation, with
More informationLecture 28. Key words: Heat transfer, conduction, convection, radiation, furnace, heat transfer coefficient
Lecture 28 Contents Heat transfer importance Conduction Convection Free Convection Forced convection Radiation Radiation coefficient Illustration on heat transfer coefficient 1 Illustration on heat transfer
More informationCeiling mounted radiant panels calculations of heat output in heating and cooling application
Ceiling mounted radiant panels calculations of heat output in heating and cooling application Lawrence Drojetzki 1,*, and Janusz Wojtkowiak 1 1 Poznan University of Technology, Institute of Environmental
More informationLaminar Mixed Convection in the Entrance Region of Horizontal Quarter Circle Ducts
Proceedings of the 5th IASME/WSEAS Int. Conference on Heat Transfer Thermal Engineering and Environment Athens Greece August 5-7 007 49 Laminar Mixed Convection in the Entrance Region of Horizontal Quarter
More informationAnalytical solutions of heat transfer for laminar flow in rectangular channels
archives of thermodynamics Vol. 35(2014), No. 4, 29 42 DOI: 10.2478/aoter-2014-0031 Analytical solutions of heat transfer for laminar flow in rectangular channels WITOLD RYBIŃSKI 1 JAROSŁAW MIKIELEWICZ
More informationChapter 6 Fundamental Concepts of Convection
Chapter 6 Fundamental Concepts of Convection 6.1 The Convection Boundary Layers Velocity boundary layer: τ surface shear stress: s = μ u local friction coeff.: C f y y=0 τ s ρu / (6.) (6.1) Thermal boundary
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 informationCOMPUTATIONAL ANALYSIS OF LAMINAR FORCED CONVECTION IN RECTANGULAR ENCLOSURES OF DIFFERENT ASPECT RATIOS
HEFAT214 1 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 14 16 July 214 Orlando, Florida COMPUTATIONAL ANALYSIS OF LAMINAR FORCED CONVECTION IN RECTANGULAR ENCLOSURES
More informationHEAT TRANSFER THERMAL MANAGEMENT OF ELECTRONICS YOUNES SHABANY. C\ CRC Press W / Taylor Si Francis Group Boca Raton London New York
HEAT TRANSFER THERMAL MANAGEMENT OF ELECTRONICS YOUNES SHABANY C\ CRC Press W / Taylor Si Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business
More informationWITPRESS WIT Press publishes leading books in Science and Technology. Visit our website for the current list of titles.
Introduction to Heat Transfer WITPRESS WIT Press publishes leading books in Science and Technology. Visit our website for the current list of titles. www.witpress.com WITeLibrary Home of the Transactions
More informationFin Convection Experiment
Fin Convection Experiment Thermal Network Solution with TNSolver Bob Cochran Applied Computational Heat Transfer Seattle, WA TNSolver@heattransfer.org ME 331 Introduction to Heat Transfer University of
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 informationCOMPARISON OF THERMAL CHARACTERISTICS BETWEEN THE PLATE-FIN AND PIN-FIN HEAT SINKS IN NATURAL CONVECTION
HEFAT014 10 th International Conerence on Heat Transer, Fluid Mechanics and Thermodynamics 14 6 July 014 Orlando, Florida COMPARISON OF THERMA CHARACTERISTICS BETWEEN THE PATE-FIN AND PIN-FIN HEAT SINKS
More informationChapter 8: Flow in Pipes
8-1 Introduction 8-2 Laminar and Turbulent Flows 8-3 The Entrance Region 8-4 Laminar Flow in Pipes 8-5 Turbulent Flow in Pipes 8-6 Fully Developed Pipe Flow 8-7 Minor Losses 8-8 Piping Networks and Pump
More informationNumerical study of forced convection around heated horizontal triangular ducts
Advanced Computational Methods and Experiments in Heat Transfer XI 0 Numerical study of forced convection around heated horizontal triangular ducts O. Zeitoun, M. E. Ali & A. Nuhait King Saud University,
More informationChapter 5 Time-Dependent Conduction
Chapter 5 Time-Dependent Conduction 5.1 The Lumped Capacitance Method This method assumes spatially uniform solid temperature at any instant during the transient process. It is valid if the temperature
More informationEntropy ISSN
344, 344 363 Entropy ISSN 1099-4300 www.mdpi.org/entropy/ Thermal Analysis in Pipe Flow: Influence of Variable Viscosity on Entropy Generation I. T. Al-Zaharnah 1 and B. S. Yilbas 1 Mechanical Engineering
More informationCHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW
CHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW 4.1 Introduction Boundary layer concept (Prandtl 1904): Eliminate selected terms in the governing equations Two key questions (1) What are the
More informationReview: Conduction. Breaking News
CH EN 3453 Heat Transfer Review: Conduction Breaking News No more homework (yay!) Final project reports due today by 8:00 PM Email PDF version to report@chen3453.com Review grading rubric on Project page
More informationTime-Dependent Conduction :
Time-Dependent Conduction : The Lumped Capacitance Method Chapter Five Sections 5.1 thru 5.3 Transient Conduction A heat transfer process for which the temperature varies with time, as well as location
More informationExergy Losses Relation with Driving Forces for Heat Transfer Process on Hot Plates Using Mathematical Programming
Proceedings of the 3 rd International Conference on Fluid Flow, Heat and Mass Transfer (FFHMT 16) Ottawa, Canada May 2 3, 2016 Paper No. 103 Exergy Losses Relation with Driving Forces for Heat Transfer
More informationNatural Convection from a Long Horizontal Cylinder
Natural Convection from a Long Horizontal Cylinder Hussein Awad Kurdi Saad Engineering Technical College of Al Najaf, Al-Furat Al-Awsat Technical University, Iraq ABSTRACT: Natural convection from a Long
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 6 th Edition, John Wiley and Sons Chapter 7 External
More informationIntroduction to Heat Transfer
FIFTH EDITION Introduction to Heat Transfer FRANK P. INCROPERA College of Engineering University ofnotre Dame DAVID P. DEWITT School of Mechanical Purdue University Engineering THEODORE L. BERGMAN Department
More informationNUMERICAL HEAT TRANSFER ENHANCEMENT IN SQUARE DUCT WITH INTERNAL RIB
NUMERICAL HEAT TRANSFER ENHANCEMENT IN SQUARE DUCT WITH INTERNAL RIB University of Technology Department Mechanical engineering Baghdad, Iraq ABSTRACT - This paper presents numerical investigation of heat
More informationME 331 Homework Assignment #6
ME 33 Homework Assignment #6 Problem Statement: ater at 30 o C flows through a long.85 cm diameter tube at a mass flow rate of 0.020 kg/s. Find: The mean velocity (u m ), maximum velocity (u MAX ), and
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 informationConvective Heat and Mass Transfer Prof. A. W. Date Department of Mechanical Engineering Indian Institute of Technology, Bombay
Convective Heat and Mass Transfer Prof. A. W. Date Department of Mechanical Engineering Indian Institute of Technology, Bombay Module No.# 01 Lecture No. # 41 Natural Convection BLs So far we have considered
More informationName: ME 315: Heat and Mass Transfer Spring 2008 EXAM 2 Tuesday, 18 March :00 to 8:00 PM
Name: ME 315: Heat and Mass Transfer Spring 2008 EXAM 2 Tuesday, 18 March 2008 7:00 to 8:00 PM Instructions: This is an open-book eam. You may refer to your course tetbook, your class notes and your graded
More informationChapter 8: Flow in Pipes
Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks
More informationThermal and Fluids in Architectural Engineering
hermal and Fluids in Architectural Engineering 12. Convection heat transfer Jun-Seo Par, Dr. Eng., Prof. Dept. of Architectural Engineering Hanyang Univ. Where do we learn in this chaper 1. Introduction
More information