Rotationally symmetric flow of Reiner-Rivlin fluid over a heated porous wall using numerical approach

2021 ◽  
pp. 095440622110342
Author(s):  
Talat Rafiq ◽  
M Mustafa ◽  
Junaid Ahmad Khan
Keyword(s):  
Boundary Layer ◽  
Layer Structure ◽  
Full Range ◽  
Porous Wall ◽  
Symmetric Flow ◽  
Axial Velocity Component ◽  
Suction Velocity ◽  
Rotationally Symmetric ◽  
Non Linear System ◽  
Rotationally Symmetric Flow

This research features one parameter family of solutions representing rotationally symmetric flow of non-Newtonian fluid obeying Reiner-Rivlin model. Such flows take place over a revolving plane permeable surface through origin such that fluid at infinity also undergoes uniform rotation about the vertical axis. Heat transfer accompanied with viscous heating effect is also analyzed. A similarity solution is proposed that results into a coupled non-linear system with four unknowns. Boundary layer structure is characterized by a parameter [Formula: see text] that compares angular velocity of external flow with that of the rotating surface. Solutions are developed by a well-known package bvp4c of MATLAB for full range of [Formula: see text]. Flow pattern for different choices of [Formula: see text] is scrutinized by computing both 2 D and 3 D streamlines. It is further noted that value of suction velocity is important with regards to the sign of axial velocity component. Boundary layer suppresses considerably whenever the surface is permeable. For sufficiently high suction velocity with [Formula: see text], entire fluid undergoes rigid body rotation. In no suction case, axially upward flow accelerates for increasing values of parameter [Formula: see text] in the range [Formula: see text], whereas opposite trend is apparent in the case [Formula: see text]. Results for normalized wall shear and Nusselt number are scrutinized for various choices of embedded parameters.

scholarly journals Unsteady flow in a rotating torus after a sudden change in rotation rate

2011 ◽  
Vol 688 ◽  
pp. 88-119 ◽  
Author(s):  
R. E. Hewitt ◽  
A. L. Hazel ◽  
R. J. Clarke ◽  
J. P. Denier
Keyword(s):  
Boundary Layer ◽  
Rotation Rate ◽  
Transient Flow ◽  
Rotational Symmetry ◽  
Sudden Change ◽  
Navier Stokes ◽  
Ekman Number ◽  
Rotationally Symmetric ◽  
Rotationally Symmetric Flow ◽  
Final Rotation

AbstractWe consider the temporal evolution of a viscous incompressible fluid in a torus of finite curvature; a problem first investigated by Madden & Mullin (J. Fluid Mech., vol. 265, 1994, pp. 265–217). The system is initially in a state of rigid-body rotation (about the axis of rotational symmetry) and the container’s rotation rate is then changed impulsively. We describe the transient flow that is induced at small values of the Ekman number, over a time scale that is comparable to one complete rotation of the container. We show that (rotationally symmetric) eruptive singularities (of the boundary layer) occur at the inner or outer bend of the pipe for a decrease or an increase in rotation rate respectively. Moreover, on allowing for a change in direction of rotation, there is a (negative) ratio of initial-to-final rotation frequencies for which eruptive singularities can occur at both the inner and outer bend simultaneously. We also demonstrate that the flow is susceptible to a combination of axisymmetric centrifugal and non-axisymmetric inflectional instabilities. The inflectional instability arises as a consequence of the developing eruption and is shown to be in qualitative agreement with the experimental observations of Madden & Mullin (1994). Throughout our work, detailed quantitative comparisons are made between asymptotic predictions and finite- (but small-) Ekman-number Navier–Stokes computations using a finite-element method. We find that the boundary-layer results correctly capture the (finite-Ekman-number) rotationally symmetric flow and its global stability to linearised perturbations.

The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disk

1960 ◽  
Vol 7 (4) ◽  
pp. 617-631 ◽  
Author(s):  
M. H. Rogers ◽  
G. N. Lance
Keyword(s):  
Viscous Fluid ◽  
Rotating Disk ◽  
Symmetric Flow ◽  
Uniform Suction ◽  
Rotationally Symmetric ◽  
Rotationally Symmetric Flow

The flow produced by an infinite rotating disk when the fluid at infinity is in a state of solid rotation is investigated numerically. When the fluid at infinity is rotating in the same sense as the disk, physically acceptable solutions exist in all cases. When the fluid at infinity is rotating in the opposite sense to that of the disk, the only physically acceptable solutions appear to be those in which there is a uniform suction present acting through the disk.

A Numerical Study of Rotationally Symmetric Flow of Second-Order Fluid

1973 ◽  
Vol 40 (3) ◽  
pp. 685-687 ◽  
Author(s):  
M. Balaram ◽  
B. R. Luthra
Keyword(s):  
Angular Velocity ◽  
Flow Parameter ◽  
Numerical Study ◽  
Wall Stress ◽  
Rotating Disk ◽  
Second Order ◽  
Symmetric Flow ◽  
Rotationally Symmetric ◽  
Tangential Wall ◽  
Rotationally Symmetric Flow

This is a numerical investigation of the steady flow produced by an infinite rotating disk when the second-order fluid at infinity is in a state of solid rotation. The flow field is determined when the fluid at infinity is rotating in the same sense as that of the disk. The use of this viscometric representation limits the result to weakly viscoelastic fluids. The numerical computations obtained indicate that the question of increased or decreased total (radial plus tangential) wall stresses due to the presence of elasticity depends on the flow parameter S(S > 1 or S < 1, indicate that the fluid at infinity having a faster or slower angular velocity compared with that of the disk). We found that the total wall stress is higher or lower when compared with a Newtonian fluid depending on S > 1 or S < 1, respectively. With increasing |α| (as the fluid becomes more non-Newtonian), the total wall stress is increased or decreased when S < 1 or S > 1.

On rotationally symmetric flow above an infinite rotating disk

1975 ◽  
Vol 67 (4) ◽  
pp. 657-666 ◽  
Author(s):  
R. J. Bodonyi
Keyword(s):  
Transition Layer ◽  
Numerical Solutions ◽  
Outer Boundary ◽  
Rotating Disk ◽  
Angular Speed ◽  
Wall Region ◽  
Rotating Fluid ◽  
Symmetric Flow ◽  
Rotationally Symmetric ◽  
Rotationally Symmetric Flow

The similarity equations for rotationally symmetric flow above an infinite counter–rotating disk are investigated both numerically and analytically. Numerical solutions are found when α, the ratio of the disk's angular speed to that of the rigidly rotating fluid far from it, is greater than −0.68795. It is deduced that there exists a critical value αcr, of α above which finite solutions are possible. The value of α and the limiting structure as α → αcrare found using the method of matched asymptotic expansions. The flow structure is found to consist of a thin viscous wall region above which lies a thick inviscid layer and yet another viscous transition layer. Furthermore, this structure is not unique: there can be any number of thick inviscid layers, each separated from the next by a viscous transition layer, before the outer boundary conditions on the solution are satisfied. However, comparison with the numerical solutions indicates that a single inviscid layer is preferred.

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