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## Internal Flow

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**Internal Flow**Chapter 8 Section 8.1 through 8.9 Lecture 13**1. Flow in Tubes**Hydrodynamics Entrance & Fully Developed Regions**Hydrodynamic Entrance**ReD,c< 2300, Laminar Flow**Friction Factor & Pressure Drop**Moody Factor: ReD≤2300 2300≤ReD≤20000 ReD>20000**Friction Factor & Pressure Drop**3000 ≤ ReD< 5x106**Energy Balance**For constant heat flux:**Energy Balance**For constant Ts:**3. Laminar Flow in Circular Tubes**For fully developed conditions**Laminar Flow in Circular Tubes**For the entry region: Ts=Constant 0.48 < Pr <16,700 0.0044 < ( ) < 9.75 [ReDPr/(L/D)]1/3 (μ/μs)0.14 ≥2 All properties at average Tm**4. Turbulent Flow in Circular Tubes**Colburn Equation**Turbulent Flow in Circular Tubes**Dittus-Boelter Equation n = 0.4 for heating, Ts > Tm n = 0.3 for cooling, Ts < Tm 0.7 < Pr <160 ReD≥10,000 L/D ≥ 10**5. Flow in Noncircular Tubes**Effective Diameter For turbulent flow, correlations for circular tubes can be used. For laminar flow, Nu values can be found in Table 8.1, page519**Fully Developed Conditions**Laminar Flow: Turbulent Flow: Correlations for Nu can be used for Sh by replacing Pr with Sc**7. Methodology for Convection Calculation**• Identify the flow geometry, calculate Dh • Specify reference T for fluid properties • Calculate Re, laminar or turbulent ? • Flow entrance or fully developed region? • Select appropriate correlation**Example 1**Steam condensing on the outer surface of a thin-walled circular tube of 50-mm diameter and 6-m length maintains a uniform surface temperature of 100C. Water flows through the tube at a rate of =0.25 kg/s, and its inlet and outlet temperatures are Tm,i=15C and Tm,o=57C. What is the average convection coefficient associated with the water flow?**Example 1**Known:Flow rate and inlet and outlet T of water flowing through a tube of 100 C Find: Average convection heat transfer coefficient Schematic:**Example 1**Assumptions: 1. Negligible outer surface resistance and tube wall conduction; 2. Negligible kinetic and potential energy and flow work change; 3. Constant properties. Properties: Table A.6, for water at (15+57)/2=36 C, cp = 4178 J/kgC Analysis: For constant Ts, Eqn. 8.42b**= 756 W/m2K**Example 1 Analysis: P = D**Example 2**Freon is being transported at 0.1 kg/s through a Teflon tube of inside diameter Di=25mm and outside diameter Do=28 mm, while atmospheric air at V=25 m/s and 300K is in cross flow over the tube. What is the heat transfer per unit of length of tube to Freon at 240K?**Example 2**Known:Flow rate and temperature of Freon passing through a Teflon tube of prescribed inner and outer diameter. Velocity and temperature of air in cross flow over tube. Find: Heat transfer per unit length of tube Schematic:**Example 2**Assumptions: (1) Steady-state conditions, (2) One-dimensional radial conduction, (3) Constant properties, (4) Fully developed flow. Properties:**Example 2**Analysis:**Example 2**Analysis: Lecture 13