Eur. Phys. J. Plus (2020) 135: 231
https://doi.org/10.1140/epjp/s13360-020-00256-4

Regular Article

Non-similar heat transfer phenomenon over non-isothermal rotating disk

¹ Department of Basic Science, Swedish College of Engineering and Technology Wah Cantt, Wah Cantt, 47000, Pakistan
² Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, 44000, Pakistan

^* e-mail: usman725.iiui@gmail.com

Received: 27 August 2019
Accepted: 30 January 2020
Published online: 7 February 2020

Abstract

Heat transfer phenomenon from a free rotating flat disk has been analyzed with the consideration of variable surface temperature cases. A new class of variable surface temperature of the disk has been considered for which the heat transfer phenomenon becomes non-similar in nature whereby the momentum transport continues to remain of self-similar nature. In view of the available literature, only those variable disk temperatures have so far been considered for which the self-similarity of the associated heat transport phenomenon does not break down; such a collection of variable disk temperature functions, in general, belongs to the power-law family. In this study, consideration has been given to those forms of variable disk temperature functions which do not belong to this family. Specifically, the sinusoidal, the exponentially increasing/decreasing and the polynomial-type (increasing/decreasing) surface temperatures of the rotating disk have been considered for which the self-similar solution is impossible and these have never been studied so far to the best of our knowledge. The motivation behind this study is twofold: first, to extend the study of heat transfer phenomenon in the rotating disk boundary layer from self-similar to non-similar nature, and second, to sort out the best possible situations for which an enhanced heat transfer process is guaranteed. Our analysis reveals the achievement of significant heat transfer enhancement for the cases of exponential and polynomial-type (increasing) specifications of the variable disk temperature function. For example, exponentially increasing disk temperature of a free rotating disk in the quiescent air yields 27% augmentation in heat transfer rate in comparison with the isothermal case. Similarly, an enhancement of 15% in the heat transfer rate is obtained for the case of (increasing) polynomial-type disk temperature when compared with the isothermal case whereby the other specifications show a reverse trend with some interesting findings highlighting the insulating role of rotating disk under certain circumstances. In addition to these conclusions, the considered cases have been investigated in detail and the results have been reported in several tables which would serve as a reference for the future experimental and theoretical studies in this direction.