Uncoupled Turbulent Duct Flows

Abstract

The calculation of the momentum and heat-transfer properties of turbulent internal flows is similar to that for the laminar flows of Chapter 5, with the obvious differences implied by the addition of turbulent stresses. Again we concentrate our attention on three different conditions in which momentum and heat transfer may occur in duct flows. Section 7.1 deals with fully developed velocity and temperature fields in ducts with smooth and rough surfaces. Section 7.2 considers heat transfer starting far downstream of the duct entry, so that the velocity field is fully developed (∂u/∂x=0,v=0), and the temperature field is developing. In this case, the energy equation can be written in a form like Eq. (5.3), using the eddy-viscosity and turbulent-Prandtl-number concepts, as

$$ u\frac{{\partial T}}{{\partial x}} = \frac{v}{{\Pr }}\frac{1}{{{{r}^{K}}}}\frac{\partial }{{\partial y}}\left[ {{{r}^{K}}\left( {1 + \frac{{\Pr }}{{{{{\Pr }}_{t}}}}\varepsilon _{m}^{ + }} \right)\frac{{\partial T}}{{\partial y}}} \right], $$

((7.1))