^{1}Basic Engineering Sciences Department, College of Engineering Majmaah University, Majmaah, Saudi Arabia^{2}Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan^{3}College of Computer and Information Sciences, Majmaah University, Majmaah, Saudi Arabia^{4}Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Kelantan, Machang, Kelantan, Malaysia^{5}Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, UiTM Shah Alam, Malaysia

PLoS One, 2018;13(1):e0188656.

PMID: 29304161
DOI: 10.1371/journal.pone.0188656
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.

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