Question

1- Hydrodynamic and thermally developing and developed regions (what does it mean? how does it happen? and what are implications on hydrodynamics and thermal characteristics of the flow?)

This is from a heat transfer course.

Answer 1

Entry Flow In A Duct - e Growth of boundary layer has a remarkable influence on flow through a constant area duct or pipe Consider a flow entering a pipe with uniform velocity 1. The boundary layer starts growing on the wall at the entrance of the pipe 2. Gradually it becomes thicker in the downstream. 3. The flow becomes fully developed when the boundary layers from the wall meetat the axis of the pipe The velocity profile is nearly rectangular at the entrance and it gradually changes to a parabolic profile at the fully developed region. . Before the boundary layers from the periphery meet at the axis, there prevails a core region which is uninfluenced by viscosity . Since the volume-flow mustbe same for every section and the boundary-layer thickness increases in the flow direction, the inviscid core accelerates, and there is a corresponding fall in pressure Entrance length: It can be shown that for laminar incompressible flows, the veloci ty profle approaches the parabolic profile through a distance Le from the entry of the pipe. This is known as entrance length and is given by Le 0.05Re where Re For a Reynolds number of 2000, this distance, the entrance length is about 100 pipe-diameters. For turbulent flows, the entrance region is shorter, since the turbulent bound ary layer grows faster . At the entrance region, 1. The velocity gradient is steeper at the wall, causing a higher value of shear stress as compared to a developed flow 2. Momentum flux across any section is higher than that typically at the inlet due to the change in shape of the velocity profile 3. Arising out of these, an additional pressure drop is brought aboutat the entrance region as compared to the pressure drop in the fully developed region. Developed Region Entrance Region Fig. 31.1 Development of boundary layer in the entrance region of a duct

Thermal Considerations during Internal Flows Tw>T(r,0) T (r,o Tw T (r,o) T (r,o T (r,0) Thermal entrance region Fully devloped Figure 3.4 Thermally developing flow in a duct Tube surface condition: either a uniform wall temperature (UWT) condition or a uniform wall heat ux condition (UWH). A fully developed temperature prole diers according to the surface conditions. For both surface conditions, however, the amount by which the fluid temperature exceeds the entrance temperature increases with increasing (x) (Figure3.4). In order to study the evelopment of thermal boundary layer,a hydrodynamically fully developed dow may be considered. (figure3.5) 1. For laminar flow, the thermal entrance length may be expressed as (3.20) we can say eD e0.05 Rep Pr Comparing this with hydrodynamics boundary layer, it can be said that if Pr >1hydrodynamic boundary layer grows more rapidly Pr > 1, zch < Zed δ > δΤ at any section; even otherwise Therefore, for Pr > 1, δ has to be > ST