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Unlike hydrodynamic developed flow, a constant profile shape is used to define thermally fully developed flow because temperature continually approaches ambient temperature. [2] Dimensionless analysis of change in profile shape defines when a flow is thermally fully developed. Requirement for thermally fully developed flow:
A Graetz number of approximately 1000 or less is the point at which flow would be considered thermally fully developed. [ 2 ] When used in connection with mass transfer the Prandtl number is replaced by the Schmidt number , Sc, which expresses the ratio of the momentum diffusivity to the mass diffusivity.
For fully developed internal laminar flow, the Nusselt numbers tend towards a constant value for long pipes. For internal flow: = where: D h = Hydraulic diameter k f = thermal conductivity of the fluid h = convective heat transfer coefficient
The moment method was developed from the observation that the plot of the second derivative of the thermal profile for laminar flow over a plate looks very much like a Gaussian distribution curve. [9] It is straightforward to cast the properly scaled thermal profile into a suitable integral kernel. The thermal profile central moments are ...
For flow in a pipe of diameter D, experimental observations show that for "fully developed" flow, [n 2] laminar flow occurs when Re D < 2300 and turbulent flow occurs when Re D > 2900. [13] [14] At the lower end of this range, a continuous turbulent-flow will form, but only at a very long distance from the inlet of the pipe. The flow in between ...
Assume that the flow is steady, two-dimensional, and fully developed (i.e., the velocity profile does not change along the streamwise direction). [45] Note that this widely-used fully-developed assumption can be inadequate in some instances, such as some compressible, microchannel flows, in which case it can be supplanted by a locally fully ...
Simple modelling will enable many properties of fully developed, turbulent plumes to be investigated. [6] Many of the classic scaling arguments were developed in a combined analytic and laboratory study described in an influential paper by Bruce Morton , G.I. Taylor and Stewart Turner [ 7 ] and this and subsequent work is described in the ...
In engineering, the Moody chart or Moody diagram (also Stanton diagram) is a graph in non-dimensional form that relates the Darcy–Weisbach friction factor f D, Reynolds number Re, and surface roughness for fully developed flow in a circular pipe. It can be used to predict pressure drop or flow rate down such a pipe.