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This paper studies the heat transfer analysis caused due to free convection in a vertically oscillating cylinder. Exact solutions are determined by applying the Laplace and finite Hankel transforms. Expressions for temperature distribution and velocity field corresponding to cosine and sine oscillations are obtained. The solutions that have been obtained for velocity are presented in the forms of transient and post-transient solutions. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. Numerical computations and graphical illustrations are used in order to study the effects of Prandtl and Grashof numbers on velocity and temperature for various times. The transient solutions for both cosine and sine oscillations are also computed in tables. It is found that, the transient solutions are of considerable interest up to the times t = 15 for cosine oscillations and t = 1.75 for sine oscillations. After these moments, the transient solutions can be neglected and, the fluid moves according with the post-transient solutions.
This article was published in the following journal.
Name: PloS one
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The length of the face determined by the distance of separation of jaws. Occlusal vertical dimension (OVD or VDO) or contact vertical dimension is the lower face height with the teeth in centric occlusion. Rest vertical dimension (VDR) is the lower face height measured from a chin point to a point just below the nose, with the mandible in rest position. (From Jablonski, Dictionary of Dentistry, 1992, p250)
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A condition caused by the failure of body to dissipate heat in an excessively hot environment or during PHYSICAL EXERTION in a hot environment. Contrast to HEAT EXHAUSTION, the body temperature in heat stroke patient is dangerously high with red, hot skin accompanied by DELUSIONS; CONVULSIONS; or COMA. It can be a life-threatening emergency and is most common in infants and the elderly.