Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 67
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The most common are two-dimensional objects inuniform flow, which are used in basic research and teaching.BOOKCOMP, Inc. — John Wiley & Sons / Page 441 / 2nd Proofs / Heat Transfer Handbook / Bejan———0.097pt PgVar———Normal PagePgEnds: TEX[441], (3)442123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWSltwdl(a) Flat plate(b) Cylinderdlhw(c) Rectangular block(d ) Sphere[442], (4)Figure 6.2 Basic configurations of objects.Lines: 167 to 190A flat plate of large width (w ) and small thickness (t ) is often usedto introduce the concept of boundary layer flow and heat transfer. An infinitelylong cylinder ( d) in cross flow is also a geometrically simple object, but theflow develops complexity at high velocities due to separation on the curved surface.Flow passing an infinitely long rectangular body (w h, w ) also involvescomplexities caused by flow separation at the sharp corners.
A sphere in uniformflow is also one of the basic configurations, where axisymmetric flow prevails at lowvelocities.The orientation of the heated object relative to the fluid flow has a significantinfluence on heat transfer. Well-studied configurations are parallel flow along a flatplate as in Fig.
6.3a, flows impinging on a plane (Fig. 6.3b), a wedge and a cone(Fig. 6.3c), and the side of a cylinder (Fig. 6.3d). In many studies the impingingflow is assumed to be parallel to the symmetry axis of the object as illustrated bythe sketches in Fig. 6.3. The study of impinging heat transfer has as one objective theunderstanding of heat transfer near the symmetry axis. For the plane and the cylinder,the point on the symmetry axis is called the stagnation point.Figure 6.4 illustrates flows through heated objects placed in regular geometricpatterns.
These arrays are commonly found in heat exchangers that transmit heatfrom the external surfaces of tubes or flat plates (strips) to the fluid. In heat exchangerapplications, the array of cylinders (Fig. 6.4a and b) is called a tube bank. When therow of objects is deep, the fluid flow develops a repeating pattern after a few rows,that is, a fully developed pattern.
The fluid temperature increases toward the end of therow as the fluid absorbs heat from the objects in the upstream rows and the thermalenvironment for an individual object bears the characteristics of internal flow. Thecase of a stack of parallel plates (Fig. 6.4c and d) involves an extra feature; that is,the fluid can bypass the plates in the stack. Such a situation is commonly found in thecooling of electronics.BOOKCOMP, Inc. — John Wiley & Sons / Page 442 / 2nd Proofs / Heat Transfer Handbook / Bejan———0.097pt PgVar———Normal PagePgEnds: TEX[442], (4)MORPHOLOGY OF EXTERNAL FLOW HEAT TRANSFER123456789101112131415161718192021222324252627282930313233343536373839404142434445(a) Parallel flow over a flat plate443(b) Flow impinging on a plate[443], (5)Lines: 190 to 192———(c) Flow impinging on a wedge or a cone(d ) Flow impinging on a cylinderFigure 6.3 Flow configurations.If the heated object is in contact with the bounding surface, the heat and fluidflow patterns become more complex.
Figure 6.5 shows some configurations that arefound in industrial equipment, particularly in electronic equipment. A rectangularblock on a flat substrate simulates an integrated-circuit (IC) package on a printedwiring board (PWB) in Fig. 6.5a. If a certain number of rectangular packages aremounted on a PWB, with their longer sides extending laterally and leaving narrowedge-to-edge gaps between the packages on the same row, such a package array ismodeled by an array of two-dimensional blocks (Fig. 6.5b). Two-dimensional blocks(frequently referred to as ribs) are also provided on a surface to enhance heat transfer.Longitudinal planar fins on a substrate are commonly used as a heat sink for the ICpackage (Fig.
6.5c). The pin fin array is a common heat sink device for electroniccomponents (Fig. 6.5d).In most of the examples illustrated in Fig. 6.5, the flow and the temperature field arethree-dimensional. In addition, flow separation and vortex shedding from the objectsare common features in the velocity range of practical interest. The contributionmade by the substrate is another complicating factor because heat conduction in thesubstrate is coupled with surface heat transfer on the object as well as the substrate.This coupled process is called conjugate heat transfer.
In the case of heat sinks, thesubstrate is usually made from the same (highly conductive) material as the fins andis in good thermal contact with the fins. The heat source is bonded to the lower sideof the substrate, so that the heat flows from the substrate to the fins. These featuresBOOKCOMP, Inc. — John Wiley & Sons / Page 443 / 2nd Proofs / Heat Transfer Handbook / Bejan0.097pt PgVar———Normal PagePgEnds: TEX[443], (5)444123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWS(a) In-line arrangement of cylinders(b) Staggered arrangement of cylinders[444], (6)Lines: 192 to 192———*(c) Plate stack in free stream(d ) Staggered array of plates(offset strips)23.854pt PgVar———Normal PagePgEnds: TEXFigure 6.4 Arrays of objects.[444], (6)(a) Rectangular block on substrate(b) Two-dimensional block array(c) Planar fin array on substrate(plate fin heat sink)(d ) Pin array on substrate(pin fin heat sink)Figure 6.5 Objects on substrates.BOOKCOMP, Inc.
— John Wiley & Sons / Page 444 / 2nd Proofs / Heat Transfer Handbook / BejanANALYSIS OF EXTERNAL FLOW HEAT TRANSFER123456789101112131415161718192021222324252627282930313233343536373839404142434445445often justify the assumption of an isothermal condition over the substrate, and as aresult, conjugate heat transfer does not play a major role.This section concludes with the following observations:1. Classical analytical solutions are available for two-dimensional cases wherethe flow is laminar up to the point of transition to turbulent flow or flow separation.For turbulent flows in simple circumstances, approximate analytical solutions basedon phenomenological laws of turbulence kinetics are also available. Results for bothlaminar and turbulent flows are discussed in Sections 6.4 and 6.6.2.
The advent of computational fluid dynamics (CFD) codes has expanded thepossibility of finding detailed features of flow and heat transfer in many complex situations. Developments after flow separation (such as vortex shedding) can be studied indetail and three-dimensional situations can be considered, although the computationalresource is finite and the scope of analysis in a narrower zone must be limited whenthe flow involves more complex features. For processes occurring outside the analysiszone, assumptions or approximations are frequently employed.
These assumptions introduce inaccuracies in the solution, and experiments are required to justify solutionsfor a certain number of cases. Such experimental verification is called benchmarking,and only benchmarked CFD codes can be used as product design tools.3. There are many circumstances where experiments are the only means for obtaining useful heat transfer data.
In many instances empirical relationships still serveas invaluable tools to estimate heat transfer, particularly for the design of industrialequipment.[445], (7)Lines: 192 to 232———-2.75386pt PgVar———Normal PagePgEnds: TEX[445], (7)6.3ANALYSIS OF EXTERNAL FLOW HEAT TRANSFERFor a general three-dimensional flow (Fig.
6.1), the six unknowns at any instant at agiven location are the three velocity components and the pressure, temperature, anddensity. For constant fluid properties, the flow field is not coupled to the temperature field and can be obtained independently. With a known flow field, the energyequation subsequently provides the temperature variation. The determination of flowand temperature fields and gradients permits computation of the local heat transfercoefficient h:−kf (∂T /∂n)sh=(6.1a)Ts − Trefand its nondimensional representation, known as the Nusselt number:Nu =hLkf(6.1b)The surface heat flux can be obtained fromq = h(Ts − Tref )BOOKCOMP, Inc. — John Wiley & Sons / Page 445 / 2nd Proofs / Heat Transfer Handbook / Bejan(6.1c)446123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWSHere Ts is the local surface temperature and Tref is the fluid reference temperature.For external flow, this is typically the local ambient environment temperature.Experimental Determination of Convection Transport The experimental technique has been employed extensively.
For a given geometrical configuration, it involves the simulation of thermal loads and flow conditions and the determinationof resulting thermal fields. Experimental techniques are often used for validation ofnumerical simulations of laminar flows in complex geometries and for transport characterization for turbulent flow.Analytical Solutions The key nondimensional flow parameter in convection analysis is the Reynolds number, Re, which is defined later. For Re 1, the nonlinearadvection terms in the momentum equations can be neglected, and the resulting linearized set of equations can then be solved analytically for a limited set of conditions.Numerical Simulations of Transport With the advent of high-speed digital computers, it has become possible to carry out numerical simulations with great accuracyfor virtually any geometrical configuration in laminar flow.
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