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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 [52 Lin -0 —— No PgE [52 CHAPTER 7 Natural Convection YOGESH JALURIA Mechanical and Aerospace Engineering Department Rutgers University New Brunswick, New Jersey 7.1 Introduction 7.2 Basic mechanisms and governing equations 7.2.1 Governing equations 7.2.2 Common approximations 7.2.3 Dimensionless parameters 7.3 Laminar natural convection flow over flat surfaces 7.3.1 Vertical surfaces 7.3.2 Inclined and horizontal surfaces 7.4 External laminar natural convection flow in other circumstances 7.4.1 Horizontal cylinder and sphere 7.4.2 Vertical cylinder 7.4.3 Transients 7.4.4 Plumes, wakes, and other free boundary flows 7.5 Internal natural convection 7.5.1 Rectangular enclosures 7.5.2 Other configurations 7.6 Turbulent flow 7.6.1 Transition from laminar flow to turbulent flow 7.6.2 Turbulence 7.7 Empirical correlations 7.7.1 Vertical flat surfaces 7.7.2 Inclined and horizontal flat surfaces 7.7.3 Cylinders and spheres 7.7.4 Enclosures 7.8 Summary Nomenclature References 7.1 INTRODUCTION The convective mode of heat transfer involves fluid flow along with conduction, or diffusion, and is generally divided into two basic processes. If the motion of the 525
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526 NATURAL CONVECTION 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 [526 Lin 0.0 —— Nor PgE [526 fluid arises from an external agent, for instance, a fan, a blower, the wind, or the motion of the heated object itself, which imparts the pressure to drive the flow, the process is termed forced convection. If, on the other hand, no such externally induced flow exists and the flow arises “naturally” from the effect of a density difference, resulting from a temperature or concentration difference in a body force field such as gravity, the process is termed natural convection. The density difference gives rise to buoyancy forces due to which the flow is generated. A heated body cooling in ambient air generates such a flow in the region surrounding it. The buoyant flow arising from heat or material rejection to the atmosphere, heating and cooling of rooms and buildings, recirculating flow driven by temperature and salinity differences in oceans, and flows generated by fires are other examples of natural convection. There has been growing interest in buoyancy-induced flows and the associated heat and mass transfer over the past three decades, because of the importance of these flows in many different areas, such as cooling of electronic equipment, pollution, materials processing, energy systems, and safety in thermal processes. Several books, reviews, and conference proceedings may be consulted for detailed presentations on this subject. See, for instance, the books by Turner (1973), Jaluria (1980), Kakac ¸ et al. (1985), and Gebhart et al. (1988).
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