The Effect of Slip on the Convective Instability Characteris tics of the Stagnation Point Flow Over a Rough Rotating Disk
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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 en ergy 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 con ditions 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 adestabilising 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.
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 en ergy 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 con ditions 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 adestabilising 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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