Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Effect of Slip on the Convective Instability Characteristics of the Stagnation Point Flow Over a Rough Rotating Disk

  • Mukherjee, Dip (Department of Mathematics, National Institute of Technology Rourkela) ;
  • Sahoo, Bikash (Department of Mathematics, National Institute of Technology Rourkela)
  • Received : 2020.04.22
  • Accepted : 2020.11.30
  • Published : 2021.12.31
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Abstract

In this paper we look at the three dimensional stagnation point flow problem over a rough rotating disk. We study the theoretical behaviour of the stagnation point flow, or forced flow, in the presence of a slip factor in which convective instability stationary modes appear. We make a numerical investigation of the effects of slip on the behaviour of the flow components of the stagnation point flow where the disk is rough. We provide, for the first time in the literature, a complete convective instability analysis and an energy analysis. Suitable similarity transformations are used to reduce the Navier-Stokes equations and the continuity equation into a system of highly non-linear coupled ordinary differential equations, and these are solved numerically subject to suitable boundary conditions using the bvp4c function of MATLAB. The convective instability analysis and the energy analysis are performed using the Chebyshev spectral method in order to obtain the neutral curves and the energy bars. We observe that the roughness of the disk has a destabilising effect on both Type-I and Type-II instability modes. The results obtained will be prominently treated as benchmarks for our future studies on stagnation flow.

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Acknowledgement

The first author would like to thank the second author for his guidance and support, and the institute for financial support.

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