Reynolds number laminar flow

Experimental evidence from a porous sphere burning rate measurement in a low Reynolds number laminar flow condition confirms that the mass burning rate per unit area can be represented by... 

Clearly, in the absence of a radial temperature or velocity gradient, no radial mass transfer can exist unless, of course, a reaction occurs at the bed wall. When a system is adiabatic, a radial temperature and concentration gradient cannot exist unless a severe radial velocity variation is encountered (Carberry, 1976). Radial variations in fluid velocity can be due to the nature of flow, e.g. in laminar flow, and in the case of radial variations in void fraction. In general, an average radial velocity independent of radial position can be assumed, except from pathological cases such as in very low Reynolds numbers (laminar flow), where a parabolic profile might be anticipated. 

Time resolution can also be limited by the parabolic flow profile of a confined fluid in the low Reynolds number (laminar flow) regime. The fluid velocity at the walls approaches zero. If the probe beam sample molecules spread over the entire width of a channel, their differing velocities must be considered. Those in close proximity to the walls travel very slowly, whereas those at the center of the channel flow most rapidly. To compensate for this effect, we flow an extra layer of buffer against the walls... 

For DG / p < 2100 Reynolds number, laminar flow zone, apply the following equation for inside tube wall h, value ... 

Laminar flow ceases to be stable when a small perturbation or disturbance in the flow tends to increase in magnitude rather than decay. For flow in a pipe of circular cross-section, the critical condition occurs at a Reynolds number of about 2100. Thus although laminar flow can take place at much higher values of Reynolds number, that flow is no longer stable and a small disturbance to the flow will lead to the growth of the disturbance and the onset of turbulence. Similarly, if turbulence is artificially promoted at a Reynolds number of less than 2100 the flow will ultimately revert to a laminar condition in the absence of any further disturbance. 

The quantity a, which is the ratio of the velocity at the edge of the laminar sub-layer to the stream velocity, was evaluated in Chapter 11 in terms of the Reynolds number for flow over the surface. For flow over a plane surface, from Chapter 11 ... 

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

As noted in Section 6.1.3 of Volume 2, the Carman-Kozeny equation applies only to conditions of laminar flow and hence to low values of the Reynolds number for flow in the bed. In practice, this restricts its application to fine particles. Approaches based on both the Carman-Kozeny and the Ergun equations are very sensitive to the value of the voidage and it seems likely that both equations overpredict the pressure drop for fluidised systems. 

Flows can be classified into two major categories (a) incompressible and (b) compressible flow. Most hqnids fall into the incompressible-flow category, while most gases are compressible in nature. A perfect fluid can be defined as a flnid that is nonviscous and nonconducting. Fluid flow, compressible or incompressible, can be classified by the ratio of the inertial forces to the viscons forces. This ratio is represented by the Reynolds nnmber (Nji,). At a low Reynolds number, the flow is considered to be laminar, and at high Reynolds numbers, the... 

Dimensionless equations - some empirical and some with theoretical bases - are often used in chemical engineering calculations. Most dimensionless numbers are usually called by the names of person(s) who first proposed or used such numbers. They are also often expressed by the first two letters of a name, beginning with a capital letter for example, the well-known Reynolds number, the values of which determine conditions of flow (laminar or turbulent) is usually designated as Re, or sometimes as The Reynolds number for flow inside a round straight tube is defined as dvp p, in which d is the inside tube diameter (L), V is the fluid velocity averaged over the tube cross section (LT ), p is the fluid density (ML" ), and p is the fluid viscosity (ML T" ) (this is defined... 

It is well known in fluid flow studies that below a certain critical value of the Reynolds number the flow will be mainly laminar in nature, while above this value, turbulence plays an increasingly important part. The same is true of film flow, though it must be remembered that in thin films a large part of the total film thickness continues to be occupied by the relatively nonturbulent laminar sublayer, even at large flow rates (N e ARecr J- Hence, the transition from laminar to turbulent flow cannot be expected to be so sharply marked as in the case of pipe flow (D12). Nevertheless, it is of value to subdivide film flow into laminar and turbulent regimes depending on whether (Ar6 5 Ar u). 

Equation (5.2a) is valid for any DG/ i value, Reynolds number, turbulent flow zone, or laminar flow zone. First calculate a Reynolds number from DG/[i. Then use Kern s Fig. 24, which appears in App. A as Fig. A.l. You may also derive this value by using Eq. (5.2a) for Jh. This equation is simply a curve-fit to Kern s figure. 

Monophasic fluid flow in capillary-scale ducts is characterized by a low Reynolds number, the flow in capillary-scale microreactors is generally laminar and transport... 

The characteristic length for a circular cylinder or sphere is taken to be the external diameter D. Thus, the Reynolds number is defined as Re = VD/v where V is Ihe uniform velocity of Ihe fluid as it approaches the cylinder or splicre. The critical Reynolds number for flow across a circular cylinder or sphere is about Re s 2 X 10. That is, the boundar) layer remains laminar for about Re < 2 X K) and becomes turbulent forRc 2 X l(y. ... 

Due to the shapes of channel cross sections, pressure losses can reach values of several bars for usual lengths. This leads to small flow velocities (some mm/s or cm/s) and low Reynolds numbers. The flow is then generally laminar or transitional. For very low Reynolds numbers (Re 1) the flow is said to be creeping and, neglecting the inertia term, the momentum equation becomes... 

Modeling Concepts We shall model the axial flow in the annular region as being laminar. This assumption is reasonable because a typical Reynolds number for flow in a LPCVD reactor is less than 1. As the reactant gases flow through the annulus, the reactants diffuse from the annulus radially inward between the wafers to eoat them. 

In fluid mechanics, the physical implication of a Reynolds number is the ratio of inertial forces (up) to viscous forces (ju/L). It is, therefore, used to illustrate the relative importance and dominance of these two types of forces for a given flow. Depending on the magnitude of the Reynolds number, the flow regimes can be classified as either laminar or turbulent flow. If a flow has a low Reynolds number, a laminar flow occurs, where viscous forces are dominant. The flow is therefore smooth. When the Reynolds number for a flow is greater than a critical value, the flow becomes turbulent flow and is dominated by inertial forces, resulting in random eddies, vortices and other flow fluctuations. Some of the examples are illustrated in Table 2.7. 

Based on the value of the critical Reynolds number or flow regime, different heat transfer correlations are applied. For laminar flow with Re < Re nt, the Nusselt number is correlated to ... 

Boundary Layer Theory. The Reynolds number for flow-through hollow fibers during our experiments was at most about 0.02 cm (diameter) x 4 cm/sec (velocity) x 1.0 g/cm (density)/ 0.007 poise (viscosity) 11 therefore, a boundary layer theory is needed for laminar flow in tubes. Because of its simplicity, the most attractive available theory is an approximate result of thln-film theory. This theory is restricted to a description of boundary layers that are thin in comparison to the tube radius. Furthermore, the ultrafiltrate velocity, J, must not vary along the tube length (uniform-wall-flux theory). At the centerline or axis of the fiber, the impermeable solute concentration C = C... 

Problem 10-9. Translating Flat Plate. Consider the high-Reynolds-number laminar boundary-layer flow over a semi-infinite flat plate that is moving parallel to its surface at a constant speed (7 in an otherwise quiescent fluid. Obtain the boundary-layer equations and the similarity transformation for f (r ). Is the solution the same as for uniform flow past a semi-infinite stationary plate Why or why not Obtain the solution for f (this must be done numerically). If the plate were truly semi-infinite, would there be a steady solution at any finite time (Hint. If you go far downstream from the leading edge of the flat plate, the problem looks like the Rayleigh problem from Chap. 3). For an arbitrarily chosen time T, what is the regime of validity of the boundary-layer solution ... 

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