Internal flow laminar

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

Equation 2-25 is valid for calculating the head loss due to valves and fittings for all conditions of flows laminar, transition, and turbulent [3], The K values are a related function of the pipe system component internal diameter and the velocity of flow for v-/2g. The values in the standard tables are developed using standard ANSI pipe, valves, and fittings dimensions for each schedule or class [3]. The K value is for the size/type of pipe, fitting, or valve and not for the fluid, regardless of whether it is liquid or gas/vapor. 

In the case of internal flows extensive experimental data are available for turbulent pipe flow. The study of turbulent-friction coefficients in pipe flow has brought forth a number of effects displayed by flowing polymer solutions. Furthermore, many hydro-dynamic investigations in pipe flow have been made to elucidate the flow behavior (laminar and turbulent) of Newtonian fluids. Thus, the pipe is one of the most investigated and traditional pieces of test apparatus and one can easily compare the flow behavior of Newtonian fluids and polymer solutions under constant boundary conditions. 

Internal flows of the type here being considered occur in heat exchangers, for example, where the fluid may flow through pipes or between closely spaced plates that effectively form a duct Although laminar duct flows do not occur as extensively as turbulent duct flows, they do occur in a number of important situations in which the size of the duct involved is small or in which the fluid involved has a relatively high viscosity. For example, in an oil cooler the flow is usually laminar. Conventionally, it is usual to assume that a higher heat transfer rate is achieved with turbulent flow than with laminar flow. However, when the restraints on possible solutions to a particular problem are carefully considered, it often turns out that a design that involves laminar flow is the most efficient from a heat transfer viewpoint. 

This chapter has been concerned with flows in wb ch the buoyancy forces that arise due to the temperature difference have an influence on the flow and heat transfer values despite the presence of a forced velocity. In extemai flows it was shown that the deviation of the heat transfer rate from that which would exist in purely forced convection was dependent on the ratio of the Grashof number to the square of the Reynolds number. It was also shown that in such flows the Nusselt number can often be expressed in terms of the Nusselt numbers that would exist under the same conditions in purely forced and purely free convective flows. It was also shown that in turbulent flows, the buoyancy forces can affect the turbulence structure as well as the momentum balance and that in turbulent flows the heat transfer rate can be decreased by the buoyancy forces in assisting flows whereas in laminar flows the buoyancy forces essentially always increase the heat transfer rate in assisting flow. Some consideration was also given to the effect of buoyancy forces on internal flows. 

We start this chapter with a general physical description of internal flow, and the average velocity and average temperature. We continue with the discussion of the hydrodynamic, and thermal entry lengths, developing flow, and fully developed flow. We then obtain the velocity and temperature profiles for fully developed laminar flow, and develop relations for the friction factor and Nusselt nmnber. Hinally we present empirical relations for developing and full developed flows, and demonstrate their use. 

In practice, it is found convenient to express the pressure loss for all types of fully developed internal flosvs (laminar or turbulent flows, circular or noncLrcu-lar pipes, smooth or rough surfaces, horizontal or inclined pipes) as (Fig. 8-19)... 

The Chilton-Colburn analogy has been obserx ed to hold quite well in laminar or turbulent flow over plane surfaces. But this is not always the case for internal flow and flow over irregular geometries, and in such cases specific relations developed should be used. When dealing with flow over blunt bodies, it is important to note that/in these relations is the skin friction coefficient, not the total drag coefficient, which also includes tlie pressure drag. 

Equipment designs based on indirect conduction usually transfer the heat from the primary heat transfer fluid to the intermediate wall within some kind of internal duct or channel. Transfer coefficients for these cases depend on the nature of the flow (laminar or turbulent) and the geometry of the duct or channel (short or long). Expressions for evaluating the transfer coefficients for these cases are available in standard texts. An expression for the convective thermal resistance can be generated similar to that derived for the conductive resistance ... 

In this work, heat and fluid flow in some common micro geometries is analyzed analytically. At first, forced convection is examined for three different geometries microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant wall heat flux boundary condition is assumed. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. Steady, laminar flow having constant properties (i.e. the thermal conductivity and the thermal diffusivity of the fluid are considered to be independent of temperature) is considered. The axial heat conduction in the fluid and in the wall is assumed to be negligible. In this study, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. 

Internal Flow. Internally finned circular tubes are commercially available in aluminum and copper (or copper alloys). For laminar flow, the following correlations are available [113] Spiral-Fin Tubes. 

Discrepancy between the conventional theory and the microchannel measurements of friction factor/ in gaseous flow has been attributed to compressibility [6]. In general it appears that/Re for compressible slip flow is less than that for the incompressible case [3]. In a comprehensive study of results of microscale single-phase internal flows [1], it has been found that the only definitive conclusion that can be reached from the currently available data is that gaseous slip flow data indicate an approximate 60% reduction in / compared to macroscale theory at the same Re (while for laminar non-slip water flow/ appears to be approximately 20% higher than the theoretical predictions). The finding for compressible slip flow seems to be supported by a simple analytical correlation with the factor c 0.6 0.05 [3] ... 

Where H is the charmel height (the smaller dimension in a rectangular channel), tw,av the average wall shear stress, V the kinematic viscosity, and p the density of the fluid. In internal flows, the laminar to turbulent transition in abrupt entrance rectangular ducts was found to occur at a transition Reynolds number Ret = 2200 for an aspect ratio ac = I (square ducts), to Ret = 2500 for flow between parallel planes with = 0 [4]. For intermediate channel aspect ratios, a linear interpolation is recommended. For circular tubes. Ret = 2300 is suggested. These transition Reynolds number values are obtained from experimental observations in smooth channels in macroscale applications of 3 mm or larger hydraulic diameters. Their applicability to microchannel flows is still an open question. 

EXTERNAL FLOW - Kolmogoroff Inertial Sub Range, Laminar Flow, etc. INTERNAL FLOW - Deformable or Rigid Sphere, Parallel Interface, etc. 

This workbook computes the Nusselt number for forced convection in a circular pipe as a function of the Reynolds (based on diameter) and Prandtl numbers (and where appropriate one or two other parameters). It includes subroutines for laminar, transition, and turbulent flows and for liquid metals. Results for a range of Reynolds and Prandtl numbers are shown in this plot. This spreadsheet was developed to aid in verifying our internal-flow module (Ribando, 1998). 

Due to the fact that the physical dimensions of the flow structures in microfluidic systems are in the micro-scale, the Reynolds numbers characterizing fluid-flow in microfluidic systems are well below the critical value for turbulence and the flow regime is, consequently, laminar (Pohar Plazl, 2008). Therefore, micromixers in microfluidic systems rely on molecular diffusion. In general, micromixers used for ionic liquid synthesis are designed in such a way that their internal flow geometries reduce diffusion distances. Some examples of micromixers used for ionic liquid synthesis are shown in Figure 3. 

Modelling plasma chemical systems is a complex task, because these system are far from thennodynamical equilibrium. A complete model includes the external electric circuit, the various physical volume and surface reactions, the space charges and the internal electric fields, the electron kinetics, the homogeneous chemical reactions in the plasma volume as well as the heterogeneous reactions at the walls or electrodes. These reactions are initiated primarily by the electrons. In most cases, plasma chemical reactors work with a flowing gas so that the flow conditions, laminar or turbulent, must be taken into account. As discussed before, the electron gas is not in thennodynamic equilibrium... 

Friction Coefficient. In the design of a heat exchanger, the pumping requirement is an important consideration. For a fully developed laminar flow, the pressure drop inside a tube is inversely proportional to the fourth power of the inside tube diameter. For a turbulent flow, the pressure drop is inversely proportional to D where n Hes between 4.8 and 5. In general, the internal tube diameter, plays the most important role in the deterrnination of the pumping requirement. It can be calculated using the Darcy friction coefficient,, defined as... 

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

Class HA in a Class IIA BSC, an internal blower (Fig. 10.9,St draws sui-ficient room air into the front grill to maintain a minimum calculated measured average velocity of at least 0.37 m s at the opening of the cabinet. The supply air flows through a HEPA filter and provides particulate-free air to the work surface. Laminar airflow reduces turbulence m the work zone and niim-mizes the potential for cross-contamination. 

Flow through the plates must be laminar, and the critical internal areas are [25,54,61] ... 

Fauske, H. K., Turbulent and Laminar Flashing Flow Considerations, Paper Presented at the 4th International Symposium on Multi-phase Flow, Miami Beach, FL, December 15-17, 1986. 

---