Be´nard-Marangoni Instability in an Open Vertical Cylinder With Lateral Heating

2005 ◽  
Author(s):  
B. Xu ◽  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Convective Flow ◽  
Marangoni Number ◽  
Vertical Cylinder ◽  
Base Flow ◽  
Matrix Structure ◽  
Governing Equations ◽  
Thermocapillary Effect ◽  
Lateral Heating ◽  
Banded Matrix ◽  
Critical Marangoni Number

A linear stability analysis of Rayleigh-Be´nard-Marangoni flow of low Prandtl number fluid contained in an open vertical cylinder is presented. The cylinder is heated laterally and is cooled at top surface by radiation. Governing equations of the flow are solved for axisymmetric base flow using higher order finite difference scheme. Small perturbation was applied to the obtained base flow to determine the critical Marangoni number and Grashof number at which the axisymmetry is broken. The eigenvalue matrix equation is solved using linear fractional transformation with banded matrix structure taken into account. It is found that the thermocapillary effect stabilizes the convective flow driven by buoyancy.

Thermocapillary Instabilities of Low Prandtl Number Fluid in a Laterally Heated Vertical Cylinder

2006 ◽  
Vol 128 (6) ◽  
pp. 1228-1235 ◽  
Author(s):  
B. Xu ◽  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Matrix Structure ◽  
Various Boundary Conditions ◽  
Banded Matrix ◽  
High Order Finite Difference

Stabilities of surface-tension-driven convection in an open cylinder are investigated numerically. The cylinder is heated laterally through its sidewall and is cooled at free surface by radiation. A seeding crystal at constant temperature is in contact with the free surface. Axisymmetric base flow is solved using the high-order finite difference method. Three-dimensional perturbation is applied to the obtained base flow to determine the critical Marangoni numbers at which the axisymmetry is broken. The eigenvalue matrix equation is solved using linear fractional transformation with banded matrix structure taken into account. Critical Marangoni-Reynolds numbers are obtained at various boundary conditions.

scholarly journals Transient free convective MHD flow past an infinite vertical cylinder

2013 ◽  
Vol 40 (3) ◽  
pp. 385-402 ◽  
Author(s):  
Rudra Deka ◽  
Ashish Paul
Keyword(s):  
Convective Flow ◽  
Magnetic Parameter ◽  
Vertical Cylinder ◽  
Mhd Flow ◽  
Governing Equations ◽  
One Dimensional ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Laplace Transform Technique ◽  
Transient Velocity

This paper presents an analytical solution of unsteady one-dimensional natural convective flow of a viscous incompressible and electrically conducting fluid past an infinite vertical cylinder with constant temperature and magnetic field, applied normal to the direction of flow. Exact solutions of dimensionless unsteady linear governing equations are obtained by using Laplace transform technique. Numerical computations for the transient velocity, temperature, skin-friction, Nusselt number are computed and presented in graphs for various set of physical parametric values viz; Grashof number, Prandtl number, magnetic parameter and time.

Stability of Axisymmetric Thermocapillary Flows in an Open Vertical Cylinder With Lateral Heating

2005 ◽  
Author(s):  
B. Xu ◽  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Stability Analysis ◽  
Finite Difference ◽  
Prandtl Number ◽  
Vertical Cylinder ◽  
Base Flow ◽  
Marangoni Flow ◽  
Lateral Heating ◽  
Thermocapillary Flows

Instability of Marangoni-Rayleigh-Be´nard convection of low Prandtl number fluid in an open vertical cylinder subjected to lateral heating is investigated using higher order finite difference scheme. Radiative boundary condition is applied to the free surface and bottom of the cylinder is adiabatic. The axisymmetric base flow is solved and then linear stability analysis is conducted to determine the critical points at which the flow becomes asymmetric. It is revealed that the Marangoni flow plays a stabilizing role to the Rayleigh-Be´nard convection.

Transient Free Convective Flow of CNT Water Nanofluid with Heat Transfer from a Moving Cylinder

2020 ◽  
Vol 10 ◽  
Author(s):  
C. Sridevi ◽  
A. Sailakumari
Keyword(s):  
Carbon Nanotubes ◽  
Heat Generation ◽  
Convective Flow ◽  
Volume Fraction ◽  
Vertical Cylinder ◽  
Single Wall Carbon Nanotubes ◽  
Free Convective Flow ◽  
Multi Wall Carbon Nanotubes ◽  
Moving Cylinder ◽  
Variable Surface

Background: In this paper, transient two-dimensional laminar boundary layer viscous incompressible free convective flow of water based nanofluid with carbon nanotubes (CNTs) past a moving vertical cylinder with variable surface temperature is studied numerically in the presence of thermal radiation and heat generation. Methods: The prevailing partial differential equations which model the flow with initial and boundary conditions are solved by implicit finite difference method of Crank Nicolson type which is unconditionally stable and convergent. Results: Influence of Grashof number (Gr), nanoparticle volume fraction ( ), heat generation parameter (Q), temperature exponent (m), radiation parameter (N) and time (t) on velocity and temperature profiles are sketched graphically and elaborated comprehensively. Conclusion: Analysis of Nusselt number and Skin friction coefficient are also discussed numerically for both single wall carbon nanotubes (SWCNTs) and multi wall carbon nanotubes (MWCNTs).

scholarly journals Linear Stability of a Steady Convective Flow between Permeable Cylinders

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 342
Author(s):  
Maksims Zigunovs ◽  
Andrei Kolyshkin ◽  
Ilmars Iltins
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Chemical Reaction ◽  
Linear Stability Analysis ◽  
Convective Flow ◽  
Base Flow ◽  
Marginal Stability ◽  
Heat Sources ◽  
Rate Of Increase

Linear stability analysis of a steady convective flow in a tall vertical annulus caused by nonlinear heat sources is conducted in the paper. Heat sources are generated as a result of a chemical reaction. The effect of radial cross-flow through permeable porous walls of the annulus is analyzed. The problem is relevant to biomass thermal conversion. The base flow solution is obtained by solving nonlinear boundary value problem. Linear stability analysis is performed, using collocation method. The calculations show that radial inward or outward flow has a stabilizing effect on the flow, while the increase in the Frank–Kamenetskii parameter (proportional to the intensity of the chemical reaction) destabilizes the flow. The increase in the Reynolds number based on the radial velocity leads to the appearance of the second minimum on the marginal stability curves. The rate of increase in the critical Grashof number with respect to the Reynolds number is different for inward and outward radial flows.

Nonlinear Marangoni convection in bounded layers. Part 1. Circular cylindrical containers

1982 ◽  
Vol 120 ◽  
pp. 91-122 ◽  
Author(s):  
S. Rosenblat ◽  
S. H. Davis ◽  
G. M. Homsy
Keyword(s):  
Marangoni Number ◽  
Finite Amplitude ◽  
Surface Cooling ◽  
Aspect Ratios ◽  
Linearized Stability ◽  
Double Eigenvalues ◽  
Critical Marangoni Number ◽  
Side Walls ◽  
Convective State ◽  
The Stability

We consider liquid in a circular cylinder that undergoes nonlinear Marangoni insta- bility. The upper free surface of the liquid is taken to have large-enough surface tension that surface deflections are neglected. The side walls are adiabatic and impenetrable, and for mathematical simplicity the liquid is allowed to slip on the side walls. The linearized stability theory for heating from below gives the critical Marangoni number Mc as a function of cylinder dimensions, surface-cooling condition and Rayleigh number. The steady nonlinear convective states near Mc are calculated using an asymptotic theory, and the stability of these states is examined. At simple eigenvalues Mc the finite-amplitude states are determined. We find th at the Prandtl number of the liquid influences the stability of axisymmetric states, distinguishing upflow at the centre from downflow. Near those aspect ratios corresponding to double eigenvalues Me, where two convective states of linear theory are equally likely, the nonlinear theory predicts sequences of transitions from one steady convective state to another as the Marangoni number is increased. These transitions are determined and discussed in detail. Time-periodic convection is possible in certain cases.

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