SECTION E 



CONVECTIVE HEAT TRANSFER AND 

 FRICTION IN FLOW OF LIQUIDS 



CHAPTER 1. TURBULENT HEAT TRANSFER 

 AND FRICTION IN SMOOTH PASSAGES 



ROBERT G. DEISSLER 



E,l. Introduction. When turbulent flow occurs in a passage, macro- 

 scopic portions of fluid move about in an apparently random fashion. 

 Inasmuch as the mean velocity varies with distance from the wall, some 

 of the portions of fluid move into regions of different mean velocities. 

 Momentum is then transferred from one portion to another, and a shear 

 stress in addition to that caused by molecular action is produced. 



If heat transfer takes place between the passage wall and the fluid, 

 a temperature (or enthalpy) gradient occurs across the passage, and some 

 of the portions of fluid move into regions of different mean temperature. 

 This motion produces heat transfer in addition to that caused by molecu- 

 lar conduction. 



E,2. Basic Equations. Using the method of Reynolds, the instan- 

 taneous velocities, temperatures (or enthalpies), and fluid properties in 

 the equations of momentum, energy, and continuity [1, pp. 49, 50, 55] 

 can be divided into mean and fluctuating components. If time averages 

 are taken, the following equations for shear stress r and heat transfer q, 

 applicable to flow in a passage or boundary layer, are obtained: 



r = ^i^ - pW (2-1) 



ay 



q=-k^ + pW (2-2) 



In these equations u is the mean velocity in the x direction, u' and v' the 

 fluctuation in velocity in the x and y directions respectively, while p, ju, 

 and k are the density, the viscosity, and the thermal conductivity of the 

 fluid. The enthalpy fluctuation h' rather than the temperature fluctuation 



( 288 ) 



