in this work, the steady and laminar mixed convection of nanofluid in horizontal concentric annulus withrotating inner cylinder is investigated numerically. the inner and outer cylinders are kept at constanttemperature ti and to respectively, where ti>to. the annular space is filled with alumina-water nanofluid.the governing equations with the corresponded boundary conditions in the polar coord...

It is well recognized that the intervertebral disc is composed of a nucleus pulposus, an annulus fibrosus, and a cartilage plate and may play a very important role in spinal stability and kinetics. Degeneration by aging of the lumbar intervertebral disc has been implicated as an important causal factor in the development of low back pain. This study has been undertaken to evaluate the ultrastru...

In this paper we study the duality of the harmonic spaces on the annulus Ω = Ω1 \Ω − between two pseudoconvex domains with Ω− ⊂⊂ Ω1 in Cn and the Bergman spaces on Ω−. We show that on the annulus Ω, the space of harmonic forms for the critical case on (0, n−1)-forms is infinite dimensional and it is dual to the the Bergman space on the pseudoconvex domain Ω−. The duality is further identified e...

BACKGROUND CONTEXT The annulus-endplate anchorage system performs a critical role in the disc, creating a strong structural link between the compliant annulus and the rigid vertebrae. Endplate failure is thought to be associated with disc herniation, a recent study indicating that this failure mode occurs more frequently than annular rupture. PURPOSE The aim was to investigate the structural ...

This note is a sequel to the paper On rings on rings by Anatole Beck [ l ] . The problem we consider (originally proposed by Paul Rosenbloom) is that of characterizing the parameter p for the annulus Q = {1< | s| <p} in terms of the ring R of bounded analytic functions nn this annulus. Beck's solution involves properties of univalent functions, and although the subset of univalent functions in ...