Circular cylinder laminar flow

Long Inclined Circular Cylinder, Laminar Flow. See Fig. 4.16c for nomenclature. The cylinder axis is inclined from the horizontal at an angle 0. The heat transfer from the ends is ignored, which will be valid for insulated ends or for LID 5. The analysis of Raithby and Hollands [225, 226] led to the following correlation ... 

Probstein et al (10) Investigated the use of detached strip type turbulence promoters in the ultrafiltration of bovine serum albumin in laminar flow. His apparatus is shown in Figure 27 the detached strip type promoters tested were circular cylinders with a diameter (D) approximately one-half (0.46) of the channel height and were across the center of the channel cross-section, transverse to the flow. 

The circular Couette flow between concentric cylinders is in the 0-direction only, and satisfies vr = vz = 0, ve = Vfl(r), and T = T(r). The inner cylinder is stationary while the outer cylinder rotates with an angular velocity w. Assuming a steady and laminar flow without end effects, the velocity distribution is... 

Let us imagine a long cylindrical capillary tube, of length L and radius r. Let x denote the distance outward radially from the axis of the tube and z denote the distance along the axis. Under conditions of laminar flow, the laminar surfaces are a family of right circular cylinders coaxial with the tube. 

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. ... 

FIGURE 716 Laminar boundary layer separation witli a turbulent wake flow over a circular cylinder at Re = 7.000. 

C Consider laminar flow of air across a hot circular cylinder. At what point on the cylinder will the heat liansfer be highest What would your answer be if the flow were turbulent 7-38C In flow over cylinders, why does ihe drag cocfTicient suddenly drop when the flow becomes turbulent Isn t turbulence supposed to increase the drag coefficient instead of decreasing it ... 

J. Schmid, Longitudinal laminar flow in an array of circular cylinders, nt. J. Heat Mass Transfer 9 925 (1966). 

J. H. Kim, Heat transfer in longitudinal laminar flow along circular cylinders in a square array. Fluid Flow and Heat Transfer over Rod or Tube Bundles (S.C. Yao and P.A. Pfund, eds.), Winter annual meeting of the American Society of Mechanical Engineers, December 2-7, New York, 1979, p. 155. 

The cause of large drag in the case of a body like a circular cylinder is the asymmetry in the velocity and pressure distributions at the cylinder surface that results from separation. All bodies in laminar streaming flow at large Reynolds number are subjected to viscous stresses that boundary-layer analysis shows must be... 

In what follows we consider the laminar boundary layer in a cross flow past a circular cylinder. This problem is also of practical importance, since tube elements are widely used in industrial equipment. 

Film condensation on a horizontal tube. For a curvilinear surface, in particular, for a horizontal circular cylinder along which a condensate film flows, the angle 6 is a nonconstant variable. By taking into account the fact that 6(6) d, where d is the diameter of a circular cylinder, and proceeding by analogy with (5.7.7), one can readily obtain the following formula for the heat transfer coefficient averaged over the external surface of the tube provided that the flow in the condensate film is laminar [200] ... 

It consists of a cylinder through which a liquid is pumped upwards (cf. Fig. 5.24). In order to ensure a laminar flow field, the liquid first passes through a conical tube having a small slope. After the liquid has reached the cylinder, it is allowed to flow over the top rim. This flow causes the circular liquid surface to be expanded continuously in a radial way. After a steady... 

Validation of the Simplified Equations. Steady-state laminar solutions to the simplified equations for flow around a long horizontal circular cylinder immersed in air with both T and T constant have been obtained by Kuehn and Goldstein [165] and Fujii et al. [101], using numerical methods. Their results, in terms of the Nusselt number, are plotted in Fig. 4.2,... 

Stratified Medium. For a long horizontal circular cylinder in a thermally stratified environment in which the temperature increases linearly with height (see Fig. 4.16h for nomenclature), AT is the temperature difference at the mid-height of the cylinder. First calculate the laminar isothermal Nusselt number Nu, from Eq. 4.45 with AT = AT and rename it NUf iS0 the corresponding calculated heat flow is qis0. The laminar Nusselt number Nu, corrected to account for the stratification is then estimated from... 

Calculation of the pressure drop from the prescribed field v on 5 , A, and is thus reduced to a quadrature whenever the classical solution for laminar flow through the cylinder is already known. A relationship comparable to the above was previously given for the special case of a circular cylinder by Brenner (B13) along with an example of its utility in applications. 

The simplest model of steady laminar flow in a uniform circular cylinder is known as the Hagen-Poiseuille flow. For axisymmetric flow in a circular tube of internal radius Rq and length I, the boundary conditions are... 

James, D.F. and A.J. Acosta, The Laminar Flow of Dilute Polymer Solutions Around Circular Cylinders, J. Fluid Mech., 42, 269 (1970)... 

James, D.F. Acosta, A.J. The laminar flow of dilute solutions around circular cylinders. J. Fluid Mech. Vol. 42, (1970) 269. 

In the range of Reynolds number Re = 103 to 107 (based on cyhnder diameter and free stream velocity), the flow aronnd a solid circular cylinder is periodic and transitional in character. The range of interest of the present work is located in a sub-critical flow regime (103 < Re < 105, corresponding to air velocities of - 0.1-10 m/s around a typically sized 0.1m diameter limb), in which, dne to the vortex shedding at the cylinder surface, the flow is highly unstable. The boundary layer remains fidly laminar up to the separation point and transition to turbulence... 

An increase in Be indicates a competition between the irreversibilities caused by heat transfer and friction. At high Reynolds numbers, the distribution of Be is relatively more uniform than at lower Re. For a circular Couette device, the Reynolds number (Re = wr2lv) at the transition from laminar to turbulent flow is strongly dependent on the ratio of the gap to the radius of the outer cylinder, 1 — n. The critical Re reaches a value 50,000 at 1 n 0.05. We may control the distribution of the irreversibility by manipulating various operational conditions such as the gap of the Couette device, the Brinkman number, and the boundary conditions. 

Couette flow is a laminar circular flow occurring between a rotating (inner) cylinder and a static one, and the extension via increased speed of rotation to centrifugally-driven instabilities leads to laminar Taylor vortex flow, tending to turbulent flow as speed increases. Poiseuille flow is axial. 

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