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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 r s [39 5 Lin e -0 . 6 —— No r m PgE [39 5 CHAPTER 5 Forced Convection: Internal Flows ADRIAN BEJAN Department of Mechanical Engineering and Materials Science Duke University Durham, North Carolina 5.1 Introduction 5.2 Laminar flow and pressure drop 5.2.1 Flow entrance region 5.2.2 Fully developed flow region 5.2.3 Hydraulic diameter and pressure drop 5.3 Heat transfer in fully developed flow 5.3.1 Mean temperature 5.3.2 Thermally fully developed flow 5.4 Heat transfer in developing flow 5.4.1 Thermal entrance region 5.4.2 Thermally developing Hagen–Poiseuille flow 5.4.3 Thermally and hydraulically developing flow 5.5 Optimal channel sizes for laminar flow 5.6 Turbulent duct flow 5.6.1 Time-averaged equations 5.6.2 Fully developed flow 5.6.3 Heat transfer in fully developed flow 5.7 Total heat transfer rate 5.7.1 Isothermal wall 5.7.2 Wall heated uniformly 5.8 Optimal channel sizes for turbulent flow 5.9 Summary of forced convection relationships Nomenclature References 5.1 INTRODUCTION An internal flow is a flow con±guration where the flowing material is surrounded by solid walls. Streams that flow through ducts are primary examples of internal flows. Heat exchangers are conglomerates of internal flows. This class of fluid flow and 395
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396 FORCED CONVECTION: INTERNAL 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 [396 Lin e -1. 9 —— Nor m PgE n [396 convection phenomena distinguishes itself from the class of an external flow, which is treated in Chapters 6 (forced-convection external) and 7 (natural convection). In an external flow conFguration, a solid object is surrounded by the flow. There are two basic questions for the engineer who contemplates using an internal flow conFguration. One is the heat transfer rate, or the thermal resistance between the stream and the conFning walls. The other is the friction between the stream and the walls. The fluid friction part of the problem is the same as calculation of the pressure drop experienced by the stream over a Fnite length in the flow direction. The fluid friction question is the more basic, because friction is present as soon as there is flow, that is, even in the absence of heat transfer. This is why we begin this chapter with the calculation of velocity and pressure drop in duct flow. The heat transfer question is supplementary, as the duct flow will convect energy if a temperature difference exits between its inlet and the wall. To calculate the heat transfer rate and the temperature distribution through the flow, one must know the flow, or the velocity distribution. When the variation of temperature over the flow Feld is sufFciently weak so that the fluid density and viscosity are adequately represented by two constants, calculation of the velocity Feld and pressure drop is independent of that of the temperature Feld. This is the case in all the conFgurations and results reviewed in this chapter. When this approximation
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This note was uploaded on 12/03/2010 for the course ECON 089907 taught by Professor Mikey during the Spring '10 term at Nashville State Community College.

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