Classification of Flow Regimes
The flow regime can be also classified according to the geometry of a conduit or flow area. From this point of view, we distinguish:
Internal flow is a flow for which the fluid is confined by a surface. Detailed knowledge of behaviour of internal flow regimes is of importance in engineering, because circular pipes can withstand high pressures and hence are used to convey liquids. On the other hand, external flow is such a flow in which boundary layers develop freely, without constraints imposed by adjacent surfaces. Detailed knowledge of behaviour of external flow regimes is of importance especially in aeronautics and aerodynamics.
In fluid dynamics, external flow is such a flow in which boundary layers develop freely, without constraints imposed by adjacent surfaces. In comparison to internal flow, external flows feature highly viscous effects confined to rapidly growing “boundary layers” in the entrance region, or to thin shear layers along the solid surface. Accordingly, there will always exist a region of the flow outside the boundary layer. In this region velocity, temperature, and/or concentration does not change in and their gradients may be neglected.
This effect causes the boundary layer to be expanding and the boundary-layer thickness relates to the fluid’s kinematic viscosity.
This is demonstrated on the following picture. Far from the body the flow is nearly inviscid, it can be defined as the flow of a fluid around a body that is completely submerged in it.
External Flow – Flat Plate
The average Nusselt number over the entire plate is determined by:
This relation gives the average heat transfer coefficient for the entire plate only when the flow is turbulent over the entire plate, or when the laminar flow region of the plate is too small relative to the turbulent flow region.
In fluid dynamics, internal flow is a flow for which the fluid is confined by a surface. Detailed knowledge of behaviour of internal flow regimes is of importance in engineering, because circular pipes can withstand high pressures and hence are used to convey liquids. Non-circular ducts are used to transport low-pressure gases, such as air in cooling and heating systems. The internal flow configuration is a convenient geometry for heating and cooling fluids used in energy conversion technologies such as nuclear power plants.
For internal flow regime an entrance region is typical. In this region a nearly inviscid upstream flow converges and enters the tube. To characterize this region the hydrodynamic entrance length is introduced and is approximately equal to:
The maximum hydrodynamic entrance length, at ReD,crit = 2300 (laminar flow), is Le = 138d, where D is the diameter of the pipe. This is the longest development length possible. In turbulent flow, the boundary layers grow faster, and Le is relatively shorter. For any given problem, Le / D has to be checked to see if Le is negligible when compared to the pipe length. At a finite distance from the entrance, the entrance effects may be neglected, because the boundary layers merge and the inviscid core disappears. The tube flow is then fully developed.
Internal Laminar Flow – Nusselt Number
Constant Surface Temperature
Constant Surface Heat Flux
Therefore, for fully developed laminar flow in a circular tube subjected to constant surface heat flux, the Nusselt number is a constant. There is no dependence on the Reynolds or the Prandtl numbers.
Internal Turbulent Flow – Nusselt Number
See also: Dittus-Boelter Equation
For fully developed (hydrodynamically and thermally) turbulent flow in a smooth circular tube, the local Nusselt number may be obtained from the well-known Dittus-Boelter equation. The DittusBoelter equation is easy to solve but is less accurate when there is a large temperature difference across the fluid and is less accurate for rough tubes (many commercial applications), since it is tailored to smooth tubes.
The Dittus-Boelter correlation may be used for small to moderate temperature differences, Twall – Tavg, with all properties evaluated at an averaged temperature Tavg.
For flows characterized by large property variations, the corrections (e.g. a viscosity correction factor μ/μwall) must be taken into account, for example, as Sieder and Tate recommend.
Calculation of the Nusselt number using Dittus-Boelter equation
For fully developed (hydrodynamically and thermally) turbulent flow in a smooth circular tube, the local Nusselt number may be obtained from the well-known DittusBoelter equation.
To calculate the Nusselt number, we have to know:
The Nusselt number for the forced convection inside the fuel channel is then equal to: