Turbulent Flow in a Tube

The developed velocity profile for turbulent flow in a tube will appear as shown in Fig. 5-15. A laminar sublayer, or film, occupies the space near the surface, while the central core of the flow is turbulent. To determine the heat transfer analytically for this situation, we require, as usual, a knowledge of the temperature distribution in the flow. To obtain this temperature distribution, the 

The heat flow across a fluid element in laminar flow may be expressed by 

It will be recalled that a is the molecular diffusivity of heat. In turbulent flow one might assume that the heat transport could be represented by 

Equation (5-108) expresses the total heat conduction as a sum of the molecular conduction and the macroscopic eddy conduction. In a similar fashion, the shear stress in turbulent flow could be written 

An additional assumption is that the ratio of the heat transfer per unit area to the shear stress is constant across the flow field. This is consistent with the assumption that heat and momentum are transported at the same rate. Thus 

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Deviation from the ideal plug flow can be described by the dispersion model, which uses the axial eddy diffusivity (m s ) as an indicator of the degree of mixing in the flow direction. If the flow in a tube is plug flow, the axial dispersion is zero. On the other hand, if the fluid in a tube is perfectly mixed, the axial dispersion is infinity. For turbulent flow in a tube, the dimensionless Peclet number (Pe) deflned by the tube diameter (v dlE-Q is correlated as a function of the Reynolds number, as shown in Figure 10.3 [3] dz is the axial eddy diffusivity, d is the tube diameter, and v is the velocity of liquid averaged over the cross section of the flow channel. 

TURBULENT FLOW IN A TUBE OF CIRCULAR CROSS-SECTION... 

It turns out that Eq. (5-56) can also be applied to turbulent flow over a flat plate and in a modified way to turbulent flow in a tube. It does not apply to laminar tube flow. In general, a more rigorous treatment of the governing equations is necessary when embarking on new applications of the heat-trans-fer-fluid-friction analogy, and the results do not always take the simple form of Eq. (5-56). The interested reader may consult the references at the end of the chapter for more information on this important subject. At this point, the simple analogy developed above has served to amplify ouf understanding of the physical processes in convection and to reinforce the notion that heat-transfer and viscous-transport processes are related at both the microscopic and macroscopic levels. 

Hyperbolic Model for Describing Dispersion Effects in Turbulent flow in a Tube... 

C Someone claims that in fully developed turbulent flow in a tube, the shear stress is a maximum at the tube surface. Do you agree with this claim Explain. 

We now take up the problem of estimating the heat transfer coefficients and the energy flux E in turbulent flow in a tube. As in our analysis of the corresponding mass transfer problem (Chapter 10), we consider the transfer processes between a cylindrical wall and a turbulently flowing n-component fluid mixture. We examine the phenomena occurring at any axial position in the tube, assuming that fully developed flow conditions are attained. For steady-state conditions, the differential energy balance (Eqs. 11.1.1 and 11.1.2) takes the form... 

In 1883, Reynolds demonstrated that the transition from laminar to turbulent flow in a tube is associated with a dimensionless quantity called the Reynolds number, Re [1] ... 

Brosh, A., Winograd, Y., 1974. Experimental study of turbulent flow in a tube with wall suction. ASME J. 

Eroshenko, V.M., Ershov, A.V., Zaichik, L.I., 1981c. Calculation of fully developed turbulent flow in a tube with injection and suction. High Temp. Sci. 19, 80 85. 

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