Universiti Teknologi Malaysia Institutional Repository

Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation

Mohamad, A.Q. and Khan, I. and Ismail, Z. and Shafie, S. (2016) Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation. SpringerPlus, 5 (1). ISSN 2193-1801

[img]
Preview
PDF
2MB

Official URL: https://www.scopus.com/inward/record.uri?eid=2-s2....

Abstract

Background: Non-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature. Methods: The governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time (t), the Grashof number (Gr), the Prandtl number (Pr), and the phase angle (ωt). Skin friction and the Nusselt number are also evaluated. Results: The exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver–Stehfest algorithm. Conclusion: The interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time (t), the Grashof number (Gr), the Prandtl number (Pr), and the phase angle (ωt).

Item Type:Article
Uncontrolled Keywords:Laplace transform technique, Non-coaxial rotation, Oscillating
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:71855
Deposited By: Fazli Masari
Deposited On:22 Nov 2017 20:07
Last Modified:22 Nov 2017 20:07

Repository Staff Only: item control page