# Flow of thin liquid film over a rough rotating disk in the presence of a transverse magnetic field

TL;DR: In this paper, the development of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field has been analyzed for different patterns of surface roughness of the disk and different initial distributions of the height of the liquid lubricant.

Abstract: The development of a flow of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field has been analysed for different patterns of surface roughness of the disk and different initial distributions of the height of the liquid lubricant. The numerical solution of the governing equation of motion subject to initial and boundary conditions has been obtained by a finite-difference method. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid lubricant on the spinning disk have been obtained for different values of the two parameters M , the Hartmann number and Nratio, the ratio of the surface tension effect to the centrifugation effect. In the absence of the magnetic field, the results have been observed to agree with those of [6]. It has been observed that the effect of surface roughness is to enhance the relative volume of the fluid retained on the spinning disk and this is further enhanced by the presence of the magnetic field.

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653 citations

### "Flow of thin liquid film over a rou..." refers background or result in this paper

...Several theoretical and experimental investigations have been considered by taking into account different aspects of this process ([3], [5], [6], [8], [9], [11], [12], [14], [15]) and these have been sparked by the importance of the study of the detailed mechanism that retains the lubricant onto the surface of the rotating disk....

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...When the initial height of the lubricant is constant, it is observed from Figure 2 that the uniform distribution of lubricant height remains uniform with time for different values of M and when M = 0 the results agree with those of [3]....

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...Case i: smooth disk surface (h(r) = 0) and negligible liquid surface tension (γ = 0) This case addresses the effect of magnetic field on the retention of conducting fluid on the smooth spinning disk and hence is an extension of the work done by [3]....

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...Different initial distributions of the height of the lubricant [3] lead to different relative volume ( Q/Q0 ) of the conducting fluid retained on the spinning disk (Figure 4), where Q0 is the initial fluid volume on the disk....

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108 citations

### "Flow of thin liquid film over a rou..." refers background in this paper

...Several theoretical and experimental investigations have been considered by taking into account different aspects of this process ([3], [5], [6], [8], [9], [11], [12], [14], [15]) and these have been sparked by the importance of the study of the detailed mechanism that retains the lubricant onto the surface of the rotating disk....

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...The radius of the disk is large compared with the thickness of the film so that the edge effect is neglected ([5], [6], [11], [14])....

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99 citations

### "Flow of thin liquid film over a rou..." refers background in this paper

...Several theoretical and experimental investigations have been considered by taking into account different aspects of this process ([3], [5], [6], [8], [9], [11], [12], [14], [15]) and these have been sparked by the importance of the study of the detailed mechanism that retains the lubricant onto the surface of the rotating disk....

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53 citations

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### "Flow of thin liquid film over a rou..." refers background or methods or result in this paper

...As has been pointed out by Tu [ 14 ] and Hwang and Ma [6], the boundary conditions at the edge of a flnite disk cannot be prescribed in a simple mathematical form due to the complicated edge efiect known as ‘tea-pot efiect’....

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...This case is an extension of the results presented by [6] and [ 14 ] and considers the magnetic efiects on the rate of retention of the liquid lubricant....

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...It is of interest to compute the total volume Q(T) of the lubricant that remains on the rough rotating disk and it is given by [ 14 ]...

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...Using Laplace formula that relates the ∞uid pressure „ p , the surface tension ∞ and the mean curvature 1 according to ([7] and [ 14 ]) „ p = ∞...

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...Several theoretical and experimental investigations have been considered by taking into account difierent aspects of this process ([3], [5], [6], [8], [9], [11], [12], [ 14 ], [15]) and these have been sparked by the importance of the study of the detailed mechanism that retains the lubricant onto the surface of the rotating disk....

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