The effects of Coriolis force and radial stretch on the convective instability characteristics of the Bödewadt flow

2021 ◽  
pp. 095440622110071
Author(s):  
Dip Mukherjee ◽  
Bikash Sahoo
Keyword(s):  
Boundary Layer ◽  
Coriolis Force ◽  
Boundary Layer Flow ◽  
Convective Instability ◽  
Type I ◽  
Similarity Transformations ◽  
Instability Modes ◽  
Neutral Curves ◽  
Lower Disk ◽  
Layer Flow

The Bödewadt boundary-layer flow is induced by the rotation of a viscous fluid rotating with a constant angular velocity over a stationary disk. In this paper, the Bödewadt boundary-layer flow has been studied in the presence of the Coriolis force to observe the effect of radial stretch of the lower disk on the flow. For the first time in the literature, a numerical investigation of the effects of both stretching mechanism and the Coriolis force on the flow behaviour and on the convective instability characteristics of the above flow has been carried out. In this paper, the Kármán similarity transformations have been considered in order to convert the system of PDEs representing the momentum equations of the flow into a system of highly non-linear coupled ODEs and solved numerically to obtain the velocity profiles of the Bödewadt flow. Then, a convective instability analysis has been performed by using the Chebyshev collocation method in order to obtain the neutral curves. From the neutral curves it is observed that radial stretch has a globally stabilising effect on both the inviscid Type-I and the viscous Type-II instability modes. This underlying physical phenomena has been verified by performing an energy analysis of the flow. The results obtained excellently supports the previous works and will be prominently treated as a benchmark for our future studies.

scholarly journals The Convective Instability of Boundary-Layer Flows Over Rotating Spheroids

2009 ◽  
Author(s):  
A. Samad ◽  
S. J. Garrett
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Convective Instability ◽  
Laminar Flows ◽  
Type I ◽  
Rotating Sphere ◽  
Flow Equations ◽  
Layer Flow

The continuous development of spinning projectiles and other industrial applications has led to the need to understand the laminar boundary-layer flow and subsequent onset of transition over the general family of rotating spheroids. We begin by finding the laminar boundary-layer flow over a general spheroid. In particular, we distinguish between prolate and oblate spheroids and use an appropriate spheroidal coordinate system in each case. The laminar-flow equations are established for each family of spheroid rotating in otherwise still fluid. An eccentricity parameter e is used to distinguish particular bodies within the oblate or prolate families. In each case, setting e = 0 reduces the equations to those already established by Howarth [2] and Banks [4] for the rotating sphere. In this preliminary study the laminar-flow equations at each latitude are solved by extending the original series solutions due to Howarth and Banks for the rotating sphere. The laminar flows obtained are consistent with established results for the rotating sphere as e tends to zero, and tend to the von Ka´rma´n [5] solution for the rotating disk as the latitude is reduced close to the nose. Analyses of the convective instability are performed on the rotating prolate family. These extend the linear analyses previously published by Malik, Lingwood and Garrett & Peake [6–10] on related geometries. An investigation into the relative importance of type I (crossflow) and type II (streamline curvature) modes is also presented. At low latitudes increasing eccentricity has negligible effects on the stability characteristics of the flow. However as the latitude increases, eccentricity is seen to lower the upper (type I) branch of the neutral curve, reducing the region of instability.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

scholarly journals On the non-parallel instability of the rotating-sphere boundary layer

2017 ◽  
Vol 818 ◽  
pp. 288-318 ◽  
Author(s):  
Antonio Segalini ◽  
Stephen J. Garrett
Keyword(s):  
Boundary Layer ◽  
Type I ◽  
Type Ii ◽  
Local Surface ◽  
Viscous Effects ◽  
Rotating Sphere ◽  
Local Type ◽  
Instability Modes ◽  
Layer Flow ◽  
Remarkable Agreement

We present a new solution for the steady boundary-layer flow over the rotating sphere that also accounts for the eruption of the boundary layer at the equator and other higher-order viscous effects. Non-parallel corrections to the local type I and type II convective instability modes of this flow are also computed as a function of spin rate. Our instability results are associated with the previously observed spiral vortices and remarkable agreement between our predictions of the number of vortices and experimental observations is found. Vortices travelling at 70 %–80 % of the local surface speed are found to be the most amplified for sufficient spin rates, also consistent with prior experimental observations.

scholarly journals Series Solutions of Boundary Layer Flow of a Micropolar Fluid Near the Stagnation Point Towards a Shrinking Sheet

2009 ◽  
Vol 64 (9-10) ◽  
pp. 575-582 ◽  
Author(s):  
Sohail Nadeem ◽  
Saeid Abbasbandy ◽  
Majid Hussain
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Local Skin ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Local Skin Friction ◽  
Layer Flow

An analysis has been carried out to obtain the series solution of boundary layer flow of a micropolar fluid towards a shrinking sheet. The governing equations of micropolar fluid are simplified using suitable similarity transformations and then solved by homotopy analysis method (HAM). The convergence of the HAM solutions has been obtained by using homotopy-pade approximation. The effects of various parameters such as porosity parameter R, the ratio λ and the microinertia K on the velocity and microinertia profiles as well as local skin friction coefficient are presented graphically and in tabulated form.

scholarly journals The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
D. R. V. S. R. K. Sastry ◽  
A. S. N. Murti ◽  
T. Poorna Kantha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Similarity Transformations ◽  
Layer Flow

The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.

scholarly journals Radiative Boundary Layer Flow in Porous Medium due to Exponentially Shrinking Permeable Sheet

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Paresh Vyas ◽  
Nupur Srivastava
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Layer Flow ◽  
Radiative Heat ◽  
Saturated Porous Medium ◽  
Similarity Transformations ◽  
Layer Flow ◽  
Rosseland Approximation

This communication pertains to the study of radiative heat transfer in boundary layer flow over an exponentially shrinking permeable sheet placed at the bottom of fluid saturated porous medium. The porous medium has permeability of specified form. The fluid considered here is Newtonian, without phase change, optically dense, absorbing-emitting radiation but a nonscattering medium. The setup is subjected to suction to contain the vorticity in the boundary layer. The radiative heat flux in the energy equation is accounted by Rosseland approximation. The thermal conductivity is presumed to vary with temperature in a linear fashion. The governing partial differential equations are reduced to ordinary differential equations by similarity transformations. The resulting system of nonlinear ordinary differential equations is solved numerically by fourth-order Runge-Kutta scheme together with shooting method. The pertinent findings displayed through figures and tables are discussed.

scholarly journals New similarity solution of boundary layer flow along a continuously moving convectively heated horizontal plate by deductive group method

2015 ◽  
Vol 19 (3) ◽  
pp. 1017-1024 ◽  
Author(s):  
Mohammed Uddin ◽  
Waqar Khan ◽  
Ahmad Ismail ◽  
M.A.A. Hamad
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Factor ◽  
Boundary Layer Flow ◽  
Group Method ◽  
Horizontal Plate ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Convective Parameter ◽  
Layer Flow

A mathematical model is presented and analyzed for steady two-dimensional non-isothermal laminar free convective boundary layer flow along a convectively heated moving horizontal plate. New similarity transformations are developed using one parameter deductive group transformations and hence the governing transport equations are reduced to a system of coupled, nonlinear ordinary differential equations with associated boundary conditions. The reduced equations are then solved numerically by an implicit finite difference numerical method. The effects of pertinent parameters on the non-dimensional velocity, temperature, friction factor and heat transfer rates are investigated and presented graphically. It is found that friction factor decreases with the free convective parameter and rate of heat transfer increases with the convection-conduction parameter.

Unsteady Boundary Layer Flow of Nanofluid Past an Impulsively Stretching Sheet

2013 ◽  
Vol 29 (3) ◽  
pp. 423-432 ◽  
Author(s):  
M. Mustafa ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Similarity Transformations ◽  
Nanoparticles Concentration ◽  
Motion Effect ◽  
Nanoparticles Volume Fraction ◽  
Layer Flow

AbstractThe unsteady laminar boundary layer flow of nanofluid caused by a linearly stretching sheet is considered. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into similar forms by using appropriate similarity transformations. The uniformly valid explicit expressions of velocity, temperature and nanoparticles volume fraction are derived. Convergence of the series solutions is carefully analyzed. It is observed that an increase in the strength of Brownian motion effect rises the temperature appreciably. However rate of heat transfer and nanoparticles concentration at the sheet is reduced when Brownian motion effect intensifies. It is also found that the temperature and nanoparticles concentration are increasing functions of the unsteady parameter.

An Exact Solution of Oscillatory Couette Flow in a Rotating System

1991 ◽  
Vol 58 (4) ◽  
pp. 1104-1107 ◽  
Author(s):  
B. S. Mazumder
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Unsteady Flow ◽  
Couette Flow ◽  
Coriolis Force ◽  
Boundary Layer Flow ◽  
Shear Stresses ◽  
Flat Plates ◽  
Rotating System ◽  
Layer Flow

An exact solution of oscillatory Ekman boundary layer flow bounded by two horizontal flat plates, one of which is oscillating in its own plane and other at rest, is obtained. The effect of coriolis force on the resultant velocities and shear stresses for steady and unsteady flow has been studied.

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