Chapter 9 Convection in Turbulent Channel Flw9章在槽道湍流对流.docVIP

Chapter 9: Convection in Turbulent Channel Flow 9.1 Introduction Laminar channel flow was discussed in Chapter 6; many features of turbulent flow are similar Chapter begins with the criteria for fully developed velocity and temperature profiles Chapter Focus: Analysis of fully developed flows Analysis is limited to the following general boundary conditions: (i) uniform surface temperature (ii) uniform surface heat flux 9.2 Entry Length Criteria for entry length was discussed in Chapter 6 As a rule of thumb, fully developed velocity and temperature profiles exist for (6.7) where is the hydraulic or equivalent diameter where is the flow area and P is the wetted perimeter Eq. (6.7) is recommended for Pr = 1 fluids More elaborate correlations exist, especially for hydrodymanic entry length; the following approximations are recommended: From White (9.1) From Latzko (9.2) Thermal entry length doesn’t lend itself to a simple, universally-applicable equation since the flow is influenced by fluid properties and boundary conditions Hydrodynamic entry length is much shorter for turbulent flow than for laminar, so much so that sometimes it’s neglected from analysis Thermal entry length is often important Analysis of heat transfer in the thermal entry length is complicated and is not covered in the text 9.3 Governing Equations Figure 9.1 shows a circular pipe with the velocity in the x-direction is labeled as Assumptions: Two-dimensional Axisymmetric Incompressible flow 9.3.1 Conservation Equations After Reynolds-averaging, conservation of mass reduces to: (9.3) Using the same conditions, the Reynolds-averaged x-momentum equation reduces to: (9.4) Conservation of energy becomes: (9.5) 9.3.2 Apparent Shear Stress and Heat Flux The apparent shear stress and heat flux are defined similarly to that of the flat plate development: (9.6) (9.7) 9.3.3 Mean Velocity and Temperature Mean velocity and bulk, or mean, temperature are used in correlations for predicting friction and