Steady magnetohydrodynamic Poiseuille flow of two immiscible non‐Newtonian and Newtonian fluids in a horizontal channel with Ohmic heating

Heat Transfer ◽  
2021 ◽  
Author(s):  
Abiodun J. Gbadeyan ◽  
Lukman O. Ahmed
Keyword(s):  
Poiseuille Flow ◽  
Ohmic Heating ◽  
Newtonian Fluids ◽  
Horizontal Channel

Convective and absolute instabilities in Rayleigh–Bénard–Poiseuille mixed convection for viscoelastic fluids

2015 ◽  
Vol 765 ◽  
pp. 167-210 ◽  
Author(s):  
S. C. Hirata ◽  
L. S. de B. Alves ◽  
N. Delenda ◽  
M. N. Ouarzazi
Keyword(s):  
Rayleigh Number ◽  
Mixed Convection ◽  
Poiseuille Flow ◽  
Flow Direction ◽  
Viscoelastic Fluids ◽  
Newtonian Fluids ◽  
Absolute Instability ◽  
Elastic Regime ◽  
Elasticity Number ◽  
Rayleigh Benard

AbstractThe convective and absolute nature of instabilities in Rayleigh–Bénard–Poiseuille (RBP) mixed convection for viscoelastic fluids is examined numerically with a shooting method as well as analytically with a one-mode Galerkin expansion. The viscoelastic fluid is modelled by means of a general constitutive equation that encompasses the Maxwell model and the Oldroyd-B model. In comparison to Newtonian fluids, two more dimensionless parameters are introduced, namely the elasticity number${\it\lambda}_{1}$and the ratio${\it\Gamma}$between retardation and relaxation times. Temporal stability analysis of the basic state showed that the three-dimensional thermoconvective problem can be Squire-transformed. Therefore, one must distinguish mainly between two principal roll orientations: transverse rolls TRs (rolls with axes perpendicular to the Poiseuille flow direction) and longitudinal rolls LRs (rolls with axes parallel to the Poiseuille flow direction). The critical Rayleigh number for the appearance of LRs is found to be independent of the Reynolds number ($\mathit{Re}$). Depending on${\it\lambda}_{1}$and${\it\Gamma}$, two different regimes can be distinguished. In the weakly elastic regime, the emerging LRs are stationary, while they are oscillatory in the strongly elastic regime. For TRs, it is found that in the weakly elastic regime, the stabilization effect of$\mathit{Re}$is more important than in Newtonian fluids. Moreover, for sufficiently elastic fluids a jump is observed in the oscillation frequencies and wavenumbers for moderate$\mathit{Re}$. In the strongly elastic regime, the effect of the imposed throughflow is to promote the appearance of the upstream moving TRs for low values of$\mathit{Re}$, which are replaced by downstream moving TRs for higher values of $\mathit{Re}$. Moreover, the results proved that, contrary to the case where$\mathit{Re}=0$, the elasticity number${\it\lambda}_{1}$(the ratio${\it\Gamma}$) has a strongly stabilizing (destabilizing) effect when the throughflow is added. The influence of the rheological parameters on the transition curves from convective to absolute instability in the Reynolds–Rayleigh number plane is also determined. We show that the viscoelastic character of the fluid hastens the transition to absolute instability and even may suppress the convective/absolute transition. Throughout this paper, similarities and differences with the corresponding problem for Newtonian fluids are highlighted.

Vorticity generation and conservation for two-dimensional interfaces and boundaries

2014 ◽  
Vol 758 ◽  
pp. 63-93 ◽  
Author(s):  
M. Brøns ◽  
M. C. Thompson ◽  
T. Leweke ◽  
K. Hourigan
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Vortex Sheet ◽  
Newtonian Fluids ◽  
Two Dimensional ◽  
Two Fluids ◽  
Vorticity Generation ◽  
Planar Couette Flow

AbstractThe generation, redistribution and, importantly, conservation of vorticity and circulation is studied for incompressible Newtonian fluids in planar and axisymmetric geometries. A generalised formulation of the vorticity at the interface between two fluids for both no-slip and stress-free conditions is presented. Illustrative examples are provided for planar Couette flow, Poiseuille flow, the spin-up of a circular cylinder, and a cylinder below a free surface. For the last example, it is shown that, although large imbalances between positive and negative vorticity appear in the wake, the balance is found in the vortex sheet representing the stress-free surface.

Finite amplitude instability of second-order fluids in plane Poiseuille flow

1972 ◽  
Vol 52 (2) ◽  
pp. 273-285 ◽  
Author(s):  
Larry V. McIntire ◽  
C. H. Lin
Keyword(s):  
Hydrodynamic Stability ◽  
Poiseuille Flow ◽  
Finite Amplitude ◽  
Second Order ◽  
Equilibrium States ◽  
Newtonian Fluids ◽  
Plane Poiseuille Flow ◽  
Entire Spectrum ◽  
Second Order Fluids

The hydrodynamic stability of plane Poiseuille flow of second—order fluids to finite amplitude disturbances is examined using the method of Stuart, and Watson as extended by Reynolds & Potter. For slightly non-Newtonian fluids subcritical instabilities are predicted. No supercritical equilibrium states are expected if the entire spectrum of disturbance wavelengths is present. Possible implications with respect to the Toms phenomenon are discussed.

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