The prediction of turbulent Prandtl and Schmidt numbers

Heat transfer in annular passages—hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux

Publisher Summary This chapter focuses on heat transfer behavior of viscoelastic fluid in turbulent pipe flow Although the asymptotic values of the heat transfer and friction factor can be calculated, there exist no firm criteria for determining whether asymptotic conditions exist Predictions of the intermediate values of the friction and heat transfer are not yet possible, even if the rheology and the thermal properties of the aqueous polymer solution are known To deals with the problems, the Weissenberg or Deborah number has to be taken into account The behavior of viscoelastic fluids flowing turbulently in noncircular channels or over external surfaces represents a relatively unexplored area of fluid mechanics Open channel flow of viscoelastic fluid is another interesting field currently being investigated The chapter concludes that to approach turbulent heat transfer behavior analytically, the usual and simplest method is to solve the uncoupled energy equation using the empirically determined velocity profile Hence, it is essential to understand the fluid mechanics of non-Newtonian fluids as well as the rheology

Non-Newtonian Fluids in Circular Pipe Flow

An analysis has been performed using a method similar to Graetz’s formulation for the laminar thermal entry region. The fluid is assumed to have a fully developed turbulent velocity profile throughout the length of the pipe. Local and fully developed Nusselt numbers are presented for fluids with Prandtl numbers ranging from 0.7 to 100 for Reynolds numbers between 50000 and 500000. A thermal entrance length is defined as the heated length required to bring the local Nusselt number to within 5 percent of the fully developed value. This length is found to decrease with increasing Prandtl number, dropping from about 10 diameters for a Prandtl number of 0.7 to less than one diameter for a Prandtl number of 100. Comparison is made with the results of Deissler, who used an integral method-boundary layer approach, and also with available experimental data. The effect of the thermal boundary conditions was studied by comparing the present uniform heat flux results with those of previous investigators who considered uniform wall temperature.

Turbulent heat transfer in the thermal entrance region of a pipe with uniform heat flux

Turbulent heat transfer in a circular tube with variable circumferential heat flux


 The first three eigenvalues and constants for the problem of heat flow to a constant property fluid in established turbulent flow in a round pipe are presented for all important values of Reynolds and Prandtl Moduli. These results permit one to compute heat transfer from nonisothermal pipe walls. Comparisons with experiment are good for all fluids from oils to liquid metals. The thermal entry length and rate of heat transfer for low Prandtl Moduli are shown to depend markedly on the wall-temperature profile.

Charles Albert Sleicher

Papers

Heat transfer in a pipe with turbulent flow and arbitrary wall-temperature distribution