cen58933_ch08 - cen58933_ch08.qxd 11:29 AM Page 419 CHAPTER...

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INTERNAL FORCED CONVECTION L iquid or gas flow through pipes or ducts is commonly used in heating and cooling applications. The fluid in such applications is forced to flow by a fan or pump through a tube that is sufficiently long to accomplish the desired heat transfer. In this chapter we will pay particular attention to the de- termination of the friction factor and convection coefficient since they are di- rectly related to the pressure drop and heat transfer rate, respectively. These quantities are then used to determine the pumping power requirement and the required tube length. There is a fundamental difference between external and internal flows. In external flow, considered in Chapter 7, the fluid has a free surface, and thus the boundary layer over the surface is free to grow indefinitely. In internal flow, however, the fluid is completely confined by the inner surfaces of the tube, and thus there is a limit on how much the boundary layer can grow. We start this chapter with a general physical description of internal flow, and the mean velocity and mean temperature. We continue with the discussion of the hydrodynamic and thermal entry lengths, developing flow, and fully developed flow. We then obtain the velocity and temperature profiles for fully developed laminar flow, and develop relations for the friction factor and Nusselt number. Finally we present empirical relations for developing and fully developed flows, and demonstrate their use. 419 CHAPTER 8 CONTENTS 8–1 Introduction 420 8–2 Mean Velocity and Mean Temperature 420 8–3 The Entrance Region 423 8–4 General Thermal Analysis 426 8–5 Laminar Flow in Tubes 431 8–6 Turbulent Flow in Tubes 441 cen58933_ch08.qxd 9/4/2002 11:29 AM Page 419
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8–1 INTRODUCTION You have probably noticed that most fluids, especially liquids, are transported in circular pipes. This is because pipes with a circular cross section can with- stand large pressure differences between the inside and the outside without undergoing any distortion. Noncircular pipes are usually used in applications such as the heating and cooling systems of buildings where the pressure dif- ference is relatively small and the manufacturing and installation costs are lower (Fig. 8–1). For a fixed surface area, the circular tube gives the most heat transfer for the least pressure drop, which explains the overwhelming popu- larity of circular tubes in heat transfer equipment. The terms pipe, duct, tube, and conduit are usually used interchangeably for flow sections. In general, flow sections of circular cross section are referred to as pipes (especially when the fluid is a liquid), and the flow sections of non- circular cross section as ducts (especially when the fluid is a gas). Small di- ameter pipes are usually referred to as tubes. Given this uncertainty, we will use more descriptive phrases (such as a circular pipe or a rectangular duct ) whenever necessary to avoid any misunderstandings.
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