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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [Fi [43 Lin 2.7 —— No PgE [43 CHAPTER 6 Forced Convection: External Flows YOGENDRA JOSHI George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia WATARU NAKAYAMA Therm Tech International Kanagawa, Japan 6.1 Introduction 6.2 Morphology of external flow heat transfer 6.3 Analysis of external flow heat transfer 6.4 Heat transfer from single objects in uniform flow 6.4.1 High Reynolds number flow over a wedge 6.4.2 Similarity transformation technique for laminar boundary layer flow 6.4.3 Similarity solutions for the flat plate at uniform temperature 6.4.4 Similarity solutions for a wedge Wedge flow limits 6.4.5 Prandtl number effect 6.4.6 Incompressible flow past a flat plate with viscous dissipation 6.4.7 Integral solutions for a flat plate boundary layer with unheated starting length Arbitrarily varying surface temperature 6.4.8 Two-dimensional nonsimilar flows 6.4.9 Smith–Spalding integral method 6.4.10 Axisymmetric nonsimilar flows 6.4.11 Heat transfer in a turbulent boundary layer Axisymmetric flows Analogy solutions 6.4.12 Algebraic turbulence models 6.4.13 Near-wall region in turbulent flow 6.4.14 Analogy solutions for boundary layer flow Mixed boundary conditions Three-layer model for a “physical situation” Flat plate with an unheated starting length in turbulent flow Arbitrarily varying heat flux Turbulent Prandtl number 6.4.15 Surface roughness effect 6.4.16 Some empirical transport correlations Cylinder in crossflow Flow over an isothermal sphere 439
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440 FORCED CONVECTION: EXTERNAL FLOWS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [440 Lin -2. —— Nor PgE [440 6.5 Heat transfer from arrays of objects 6.5.1 Crossflow across tube banks 6.5.2 Flat plates Stack of parallel plates Offset strips 6.6 Heat transfer from objects on a substrate 6.6.1 Flush-mounted heat sources 6.6.2 Two-dimensional block array 6.6.3 Isolated blocks 6.6.4 Block arrays 6.6.5 Plate fin heat sinks 6.6.6 Pin fin heat sinks 6.7 Turbulent jets 6.7.1 Thermal transport in jet impingement 6.7.2 Submerged jets Average Nusselt number for single jets Average Nusselt number for an array of jets Free surface jets 6.8 Summary of heat transfer correlations Nomenclature References 6.1 INTRODUCTION This chapter is concerned with the characterization of heat transfer and flow under forced convection, where the fluid movement past a heated object is induced by an ex- ternal agent such as a fan, blower, or pump. The set of governing equations presented in Chapter 1 is nonlinear in general, due to the momentum advection terms, vari- able thermophysical properties (e.g., with temperature) and nonuniform volumetric heat generation. Solution methodologies for the governing equations are based on the nondimensional groups discussed in Section 6.3. Solutions can be obtained through analytical means only for a limited number of cases. Otherwise, experimental or nu- merical solution procedures must be employed.
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