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In this paper, the classic coupled thermoelasticity model of hollow and solid spheres under radial-symmetric loading condition (r, t) is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, and the heat source are considered in the most general forms, where no limiting assumption is used. This generality allows to simulate a variety of applicable problems. [DOI: 10.1115/1.4001198] Keywords: coupled thermoelasticity, hollow sphere, exact solution

This paper presents a new approach to using virtual reality (VR) to design spherical mechanisms. VR provides a three-dimensional (3-D) design space where a designer can input design positions using a combination of hand gestures and motions and view the resultant mechanism in stereo using natural head movement to change the viewpoint. Because of the three-dimensional nature of the design and verification of spherical mechanisms, VR is examined as a new design interface in this research. In addition to providing a VR environment for design, the research presented in this paper has focused on developing a 'design in context' approach to spherical mechanism design. Previous design methods have involved placing coordinate frames along the surface of a constraint sphere. The new 'design in context' approach allows a designer to freely place geometric models of movable objects inside an environment consisting of fixed objects. The fixed objects could either act as a base for a mechanism or be potential sources of interference with the motion of the mechanism. This approach allows a designer to perform kinematic synthesis of a mechanism while giving consideration to the interaction of that mechanism with its application environment.

Spherical 4R mechanisms are studied for which the crank is relatively smaller than the remaining links. The theory of small-crank mechanisms is applied to obtain approximate descriptions for the follower angular displacement in terms of the input crank angle. The follower angle is presumed to comprise a mean and a perturbational motion. This results in an approximate expression in which the follower displacement is given as a linear combination of simple harmonic functions of the first and second harmonics of the crank angle. The approximate equations are utilized for synthesis of spherical 4R mechanisms for function generation. In contrast to the conventional design procedures, the use of the approximate equations allows the synthesis of spherical mechanisms in which a prescribed function is satisfied for the entire motion of the mechanism. In addition to design examples, sample error charts are provided to assist the designer in ascertaining feasible ranges for design and corresponding orders of error.

The axial pressure distribution in the entrance area of a randomly packed bed of spheres at Reynolds numbers 1036-2749 was measured for expansion angles 0, 30, 60 and 90 degrees. For the 0 and 30 inlet geometries, a necessary constant pressure gradient was achieved within about one and one half sphere diameters. Thus, it is determined that the entrance length is of the same measurement for these cases. For the 60 and 90 geometry angles, non-constant pressure gradients were obtained.

Little is known about the rotational motion of spheres falling through viscous fluids in inclined tubes. Most studies have investigated translational and rotational motions in vertical tubes. These works show that in creeping flow a sphere's translational and rotational velocities are independent. Rotation is predicted and observed for eccentric spheres while concentric spheres fall without rotation. Experiments were performed by us with steel spheres of radius r falling through glycerine in a tube of variable inclination angle and of radius R such that r/R = 0.882, 0.757, 0.442. For the cases involving two or three spheres falling together various modes of motion were observed. Especially interesting was the finding that the rotation direction of a sphere gradually changes from positive (opposite to downhill rolling) to negative (in the sense of downhill rolling) as the tube inclination angle is increased. This is allowed by the inertia-induced lift force which maintains a sphere at a very small but finite distance from the inclined tube wall. However, by further increasing the inclination angle the lift force eventually becomes smaller than the apparent weight of the sphere which, upon finally contacting the tube wall, descends by rolling along it. Examination of our findings in the light of earlier results for vertical and inclined tubes suggests that, through its effect on sphere eccentricity, inertia indirectly affects the rotational motion of a falling sphere when [Re.sub.p] > [10.sup.-3] but it does not significantly affect the translational motion when [Re.sub.p] < 1. None of the inclined tube studies performed to date has been completely devoid of inertia-induced lift effects.

Heat transfer is obtained for a sphere in low Peclet number movement across a radiatively participating, gray, continuous medium. The discrete ordinates method is used to solve the radiative transfer equations. Solutions for the coupled energy and radiation transfer equations were also obtained. Formulations are expressed in the form of Planck and Peclet numbers and are also applicable to higher Peclet flows.

A study on the problem of heat conduction from spheres was conducted to obtain the analytical solutions of the issue of conduction heat transfer from oblate and prolate spheroids. Two special cases can be derived from the general solution, namely, the sphere and the flat circular disk. The experiment has relevance in a number of research areas, such as, for example, heat transfer in stationary packed beds. Results are discussed.

A new method developed for the reduction of the fluid drag of a circular cylinder may also be used to reduce the drag of a sphere, a very common axially symmetric bluff body. The method's applicability to drag reduction of a sphere was tested using a model consisting of a flat surface and a spherical surface. Conclusions were drawn after measurement of the drag coefficient C(sub D) of models consisting of a normal surface to the flow direction and a curved spherical surface.

A study was conducted, using the theoretical approach of the elementary cell for two-phase systems, to evaluate the upper and lower bounds of the effective thermal conductivity of packed beds of rough spheres. The result shows the effects of the surface roughness on the effective thermal conductivity of the bed.

A study was conducted to investigate the problem of unsteady mass transfer from a sphere that impulsively moves from rest to a finite velocity in a non-uniform concentration distribution. The relative importance of the concentration boundary layer development, velocity field development, and time dependent free stream concentration field is illustrated with the results.

S. HOSSEIN CHERAGHI [*] Several methods for the evaluation of sphericity error exist. The Minimum Radial Separation (MRS) spheres method is a method that has been studied by several researchers. [...]

Researchers at Massachusetts Institute of Technology, Cambridge, and University of Central Florida, Orlando, developed a versatile fabrication technique for making large quantities of uniform spheres from a wide variety of [...]