Homogeneous–Heterogeneous Reactions in Boundary-Layer Flow of a Maxwell Nanofluid Over a Stretching Surface

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Nai-Li Xu ◽  
Hang Xu
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Shooting Method ◽  
Flow Direction ◽  
Equations Of Motion ◽  
Maxwell Fluid ◽  
Heterogeneous Reactions ◽  
Physical Parameters ◽  
Layer Flow ◽  
The Stability

Based on Buongiorno's theory and Cauchy equations of motion, a model is developed to examine homogeneous–heterogeneous reactions in boundary layer flow of a nanofluid over a stretching sheet in which a uniform magnetic field is added perpendicular to the flow direction. We apply the shooting method and the fourth-order Runge–Kutta integration to obtain multiple solutions of nonlinear ordinary differential equations with various physical parameters. Results show that nanofluids play significant roles in the procedures of homogeneous and heterogeneous reactions, which may help maintain the stability of chemical reactions. In addition, the terms related to Maxwell fluid either have effect on stability of the system; furthermore, the increasing elastic and magnetic parameters delay the appearance of bifurcation points.

NATURAL CONVECTION BOUNDARY LAYER FLOW ALONG A SPHERE EMBEDDED IN A POROUS MEDIUM FILLED WITH A NANOFLUID

2014 ◽  
Vol 44 (2) ◽  
pp. 149-157
Author(s):  
A. M. RASHAD
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Extended Model ◽  
Local Skin ◽  
Layer Flow

 A boundary-layer analysis is presented for the natural convec tion boundary layer flow about a sphere embedded in a porous medium filled with a nanofluid using Brinkman-ForchheimerDarcy extended model. The model used for the nanofluid incorporates the ef fects of Brownian motion and thermophoresis. The governing partial differential equa tions are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticles volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.

The stability of boundary-layer flow over single-and multi-layer viscoelastic walls

1988 ◽  
Vol 196 ◽  
pp. 359-408 ◽  
Author(s):  
K. S. Yeo
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Single Layer ◽  
Viscous Sublayer ◽  
Rigid Base ◽  
Theoretical Treatment ◽  
Dynamical Condition ◽  
Compliant Walls ◽  
Layer Flow ◽  
The Stability

In this paper, we are concerned with the linear stability of zero pressure-gradient laminar boundary-layer flow over compliant walls which are composed of one or more layers of isotropic viscoelastic materials and backed by a rigid base. Wall compliance supports a whole host of new instabilities in addition to the Tollmien-Schlichting mode of instability, which originally exists even when the wall is rigid. The perturbations in the flow and the compliant wall are coupled at their common interface through the kinematic condition of velocity continuity and the dynamical condition of stress continuity. The disturbance modes in the flow are governed by the Orr-Sommerfeld equation using the locally-parallel flow assumption, and the response of the compliant layers is described using a displacement-stress formalism. The theoretical treatment provides a unified formulation of the stability eigenvalue problem that is applicable to compliant walls having any finite number of uniform layers; inclusive of viscous sublayer. The formulation is well suited to systematic numerical implementation. Results for single- and multi-layer walls are presented. Analyses of the eigenfunctions give an insight into some of the physics involved. Multi-layering gives a measure of control over the stability characteristics of compliant walls not available to single-layer walls. The present study provides evidence which suggests that substantial suppression of disturbance growth may be possible for suitably tailored compliant walls.

scholarly journals The centrifugal instability of the boundary-layer flow over slender rotating cones

2014 ◽  
Vol 755 ◽  
pp. 274-293 ◽  
Author(s):  
Z. Hussain ◽  
S. J. Garrett ◽  
S. O. Stephen
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Rotating Disk ◽  
Alternative Formulation ◽  
Centrifugal Instability ◽  
Half Angle ◽  
Layer Flow ◽  
The Stability ◽  
Experimental And Theoretical Studies ◽  
Numerical Approaches

AbstractExisting experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as Görtler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode.

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