tailieunhanh - Ebook Schaum's outline of theory and problems of heat transfer (2nd edition): Part 2

(BQ) This Schaum's Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. | Chapter 7 Forced Convection: Turbulent Flow Turbulent flow is characterized by random motion of fluid particles, disrupting the fluid’s movement in lamina as discussed in the preceding chapters. It is the most common type of motion, however, because of the minimal disturbances which might cause it to occur. The time-average equation (), written for velocity, is valid for any quantity 4 which has a time-average value c$ and a fluctuating component 4’, ., 4 = c$ + +’. Thus where At = t - to. Properties of the time average are: 41 + +2 ds = 6 1 +6 2 ds where C is independent of t and s is any spatial coordinate. In addition, it is almost always the case that 4; +$# 0 if (bl and & are turbulent flow properties. 71 EQUATIONS OF MOTION . By use of the boundary layer concept the general equations of motion, called the Nuvier-Stokes equations after their formulators, can be simplified to the point of being solved. The x-direction momentum equation for incompressible, laminar, boundary layer flow over a flat plate was derived in Problem . Since it is a simplified form of the more general x-direction Navier-Stokes equation, we shall extend it to the case of turbulent flow, ., d a dX turbulent: dY (U + U’)- (U + U ’ ) + (U + U’) -(G + U’) The instantaneous quantities in the laminar equation have been replaced by the sum of their average and fluctuating components in the turbulent equation. Inherent in this move is the assumption that the Navier-Stokes equations are valid for turbulent flow. 184 CHAP 71 185 FORCED CONVECTION: TURBULENT FLOW Along with the momentum equations, we may consider the two-dimensional incompressible continuity equation: -au - =h, + o laminar: ax rjry a a -(ii + U') + -(6 + U') dX JY turbulent: () =0 Combining the turbulent equations () and (), taking the time average of the resultant equation, and applying the rules (), we obtain which is the x-direction equation of motion for a viscous .

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