Finite-length cylinders

Dimensionless Temperature and Heat Loss Fraction for Finite-Length Cylinders. The finite-length circular cylinder of radius R and length 2X, shown in Fig. 3.9, has constant properties and is cooled through the sides and the two ends by uniform film coefficients hr and hx, respectively. The sys-... 

Perry, J. and Perl, M. (2008) The evaluation of the 3-D residual stress field due to hydraulic autofiettage in a finite length cylinder incorporating the Bauschinger effect factor based on the zero offtet yield stress . ASME Pressure Vessel and Piping Division Conference, July 27-31, 2008, Chicago, IL, Paper No. PVP 2008-61032. 

Fig. 9.3 Wall correction factors K for a rigid sphere on the axis of a cylinder of finite length in creeping flow (S7) (1) L /D = 1 (2) LJD = f (3) LJD = i.

FIGURE 7.18 Sphere-to-rod transition in DMDBPMA, ra-dodecane solution. 0.54 M (+) of DMDBPMA is fitted with sticky hard-sphere (Magg = 4 and U/kBT = -1.92) and 1.25 M (o) of DMDBPMA is fitted by monodisperse cylinders of finite length, L = 87 A, and radius, R = 5 A. The presence of cylinders is also confirmed by the q 1 dependence in the spectra. 

C.8.a. Circular disk or rod of finite length, with axis parallel to infinitely long cylinder, pairwise-summation form... 

In a manner similar to that described above, the solution for a three-dimensional block may be expressed as a product of three infinite-plate solutions for plates having the thickness of the three sides of the block. Similarly, a solution for a cylinder of finite length could be expressed as a product of solutions of the infinite cylinder and an infinite plate having a thickness equal to the length of the cylinder. Combinations could also be made with the infinite-cylinder and infinite-plate solutions to obtain temperature distributions in semi-infinite bars and cylinders. Some of the combinations are summarized in Fig. 4-18, where... 

Two finite-length concentric cylinders are placed in a large room maintained at 20°C. The inner cylinder has a diameter of 5.0 cm and the outer cylinder has a diameter of 10 cm. The length of the cylinders is 10 cm. The inner cylinder is newly turned cast iron and maintained at a temperature of 400°C. The outer cylinder is Monel metal oxidized at 1110°F. Calculate the heat lost by the inner cylinder. 

View factors for two concentric cylinders of finite length (a) outer cylinder to inner cylinder b) outer cylinder to itself. 

A cylinder of a finite length is formed by the perpendicular penetration of an infinitely long cylinder with a plate. In the same manner, a very long prism... 

The temperature distribution in a cylinder of finite length is given by (2.192). In order to explicitly calculate the cooling time tk, we will limit ourselves to the first term in each infinite series and then later we will check whether this simplification was correct. We therefore put... 

In a rheological experiment, one of the two cylinders is typically rotated with a known angular velocity, and the torque required to produce this motion is measured. Let us suppose that the torque is measured on the inner cylinder. Now, if we ignore the finite length of the Couette device, we have seen that there is a single nonzero component of the velocity ug(r). Hence, if we examine the various components of the rate-of-strain tensor E,... 

Now let us consider heat exchange for a cylinder of finite length. Let a be the radius and L the length of the cylinder. By solving problem (4.2.1)-(4.2.3), we obtain the following expression for bulk temperature [277] ... 

The one-dimensional charts for a flat plate and an infinitely long cylinder can be used to determine the temperature of a cylinder of finite length. It can be shown that the dimensionless unsteady temperature of a solid cylinder of height 2H and diameter 2R may be expressed as the product of the dimensionless temperature of a flat plate of thickness 2H and the temperature of an infinitely long cylinder of diameter 2R,... 

Problems involving unsteady diffusion in more then one coordinete direction, such as a cylinder or finite length or a long slab of comparable width and depth dimensions, cun usually be solvnd by separation of variables. For example, for a cylinder of radius R and length L the governing equation and boundary conditions for an ideal gas mixture and constant surface conditions would be... 

Finite Circular Cylinder. The dimensionless shape factor for an isothermal right circular cylinder of length L and diameter d (Fig. 3.4c) was obtained from the analytical solution for the capacitance [96,97], Using the square root of the total surface area, the result is recast as... 

Finite Square Cylinder. The dimensionless shape factors for finite square cylinders of length L and side dimension W (Fig. 3.4d) can be calculated using the finite circular expression by means of the equivalent aspect ratio... 

Element on plane to exterior of right circular cylinder of finite length. Plane does not intersect cylinder... 

Equations 7.42-7.44 show that the value of S has high order with respect to small parameter a/L or a/lj, a/ o, and therefore the geometric factor of a cylinder of finite length for a two-coil induction probe H > L) slightly differs from that of an infinitely long one, i.e. G. In the case of symmetric location of the probe (e = 0) this fact was demonstrated in Chapter 5. 

To calculate viscosity, shear stress, and shear gradient, it is usually necessary to make a series of corrections for the finite length of the cylinder, the variation of the shear gradient with distance, etc. These corrections vary from instrument to instrument. 

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