Longitudinal flow between cylinders

FIGURE 5.42 Nusselt numbers for fully developed longitudinal flow between cylinders in a triangular array [263]. 

E.M. Sparrow and A.L. Loeffler Jr., Longitudinal laminar flow between cylinders arranged in regular array, AIChE J. 5(3) 325 (1959). 

In the study of Miyatake and Iwashita [256], the relationship of local Nusselt number and Graetz number is formulated for developing longitudinal flow between a triangular array of cylinders with a uniform heat flux and various pitch-to-diameter ratios. For PID = 1.01-1.1 ... 

Fully developed turbulent flow and heat transfer in triangular and square arrays have been analyzed by Deissler and Taylor [261, 262]. The friction factors for longitudinal flow between the cylinders in a triangular and a square array are given in Fig. 5.40. Correspondingly, the Nusselt numbers, in terms of the Stanton number, defined as Nu/(Re Pr), are given in Fig. 5.41, where the cylinders are considered to be uniformly heated. 

E. M. Sparrow, and A. L. Loeffler Jr., Longitudinal Laminar Flow between Cylinders Arranged in Regular Array, AlChE J., (5) 325-330,1959. 

In the case of an incompressible fluid, the first invariant is zero, I - div v = 0. For simple one- and two-dimensional flows (such as flows in thin films, longitudinal flow in a tube, and tangential flow between concentric cylinders), the third invariant h is identically zero. 

Miyatake and Iwashita [255] also investigated the developing longitudinal laminar flow between a square array of cylinders with uniform wall temperature. The local and logarithmic Nusselt number can be obtained using the following correlations ... 

It is convenient to consider the stable. flow in a clearance between two infinitely long cylinders with radii and R2, one of which is rotating with angular velocity Q in a cylindrical system of coordinates. Each particle of material describes a curve along the common axis of cylinders z with angular velocity to(r) and longitudinal velocity U(r). 

In the book [117], some data are given on the hydrodynamic characteristics of bodies of various shapes these data mainly pertain to the region of precrisis self-similarity. The influence of roughness of the cylinder surface and the turbulence level of the incoming flow on the drag coefficient is discussed in [522]. In [211], the relationship between hydrodynamic flow characteristics in turbulent boundary layers and the longitudinal pressure gradient is studied. Analysis of the transition to turbulence in the wake of circular cylinders is presented in [333]. 

Hutton et al fS llJ have studied many types of lubricants with several techniques ultrasonic technique in longitudinal or in shear mode, shear flow in concentric cylinders. Viscoelastic behaviour in shear but also in compression have been shown and the differences between Qy, (shear modulus at infinite frequency), G (apparent shear modulus deduced from traction curves) and G (mechanical shear modulus) have been clearly pointed out. 

The preliminary estimation of the anisotropic viscosity coefficients Tiii and for solutions of an aromatic polyamide was performed in [57, 58]. Flow cells combined with an IR spectrophotometer were used in these studies to determine the values of angles 0 and (p. Angle (p was small (2-3°), and it was thus assumed that the molecules lie in the shear plane, and angle 6 was estimated with the dichroism of one of the n bands of poly-p-benzamide (PBA). Measurements of the torque in the moving cylinder of a rotary viscometer conducted in parallel with measurements of the velocity of fall of a ball along the axis of the cylinders in the space between them demonstrated the differences in the values of the longitudinal and transverse Tij viscosities. 

The design of Sharpington et al. features a rectilinear wind tunnel longitudinally divided into four separate bioassay chambers. Each bioassay chamber is fitted on its upstream end with a 4 cm diameter glass cylinder that is closed with chick skin on its interior (bioassay chamber) end and connected to a constant-temperature water circulation system set to 34°C on its exterior end. Airflow is provided by a forced-air system that controls flow rate, temperature, and humidity. Notably, the airstream is purified by passing it through activated charcoal and zeolite filters, in addition. Glass partitions between the bioassay chambers separate the conditioned air into four separate odor... 

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