Natural convection heat transfer in an oscillating vertical cylinder

Ilyas Khan; Nehad Ali Shah; Asifa Tassaddiq; Norzieha Mustapha; Seripah Awang Kechil

doi:10.1371/journal.pone.0188656

Natural convection heat transfer in an oscillating vertical cylinder

PLoS One. 2018 Jan 5;13(1):e0188656. doi: 10.1371/journal.pone.0188656. eCollection 2018.

Authors

Ilyas Khan¹, Nehad Ali Shah², Asifa Tassaddiq³, Norzieha Mustapha⁴, Seripah Awang Kechil⁵

Affiliations

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.

Abstract

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Convection*
Energy Transfer
Hot Temperature*
Hydrodynamics
Mathematical Concepts
Models, Theoretical
Rheology
Temperature

Grants and funding

The first author acknowledges with thanks the Deanship of Scientific Research (DSR) at Majmaah University, Majmaah, Saudi Arabia, for technical and financial support through vote number 37/97 for this research project. The authors would like to thank the financial support received from the Ministry of Higher Education of Malaysia under the Fundamental Research Grant Scheme FRGS/1/2014/SG04/UiTM/02/1 and the Universiti Teknologi MARA. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.