Stability of Marangoni convection in a composite porous-fluid with a boundary slab of finite conductivity

A linear stability analysis is used to investigate the onset of Marangoni convection in a three-layer system comprising an incompressible fluid saturated porous layer over which lies a layer of the same fluid and below which lies a solid layer. The lower boundary is subjected to a fixed heat flux, while the upper free surface of the fluid is non-deformable. At the interface between the fluid and the porous layer, the Beavers-Joseph slip condition is used and the Darcy law is employed to describe the flow in the porous medium. The asymptotic analysis of the long-wavelength is performed and the results are compared with those for the case of porous-fluid layer system. The effects of the thermal conductivity and the thickness of the solid plate on the onset of convective instability are studied. It is found that the solid plate with a higher relative thermal conductivity or higher thickness ratio tends to stabilize the system

Synchronization of two different fractional order chaotic systems with unknown parameters using a robust adaptive nonlinear controller

In this paper, a robust adaptive nonlinear feedback controller scheme is proposed to realize the synchronization between two different fractional-order chaotic systems with fully unknown parameters, external disturbance and uncertainties. Bounds of the uncertainties and external disturbance assumed to be unknown. A new theorem is presented to satisfy Lyapunov stability condition in fractional-order systems when their parameters are fully unknown with external disturbance and uncertainties. Numerical simulations are applied using MATLAB software to show the effectiveness of the proposed schemes

Feedback control of the Marangoni-Bénard convection in a horizontal fluid layer with internal heat generation

Feedback control is applied to the steady Marangoni-Bénard convection in a horizontal layer of fluid with internal heat generation heated from below and cooled from above. The analytical technique is used to obtain the close form analytical expression for the onset of Marangoni-Bénard convection when the lower boundary is conducting. The effects of feedback control are studied by examining the critical Marangoni numbers and wave numbers. It is shown that the critical Marangoni number decreases as the value of internal heat generation but the critical Marangoni number can be increased through the use of feedback control

Feedback Control of the Marangoni–Bénard Instability in a Fluid Layer with a Free-Slip Bottom

Feedback control was applied to the steady Marangoni–Bénard convection in a horizontal layer of fluid with a free-slip bottom heated from below and cooled from above. The critical values of the Marangoni numbers for the onset of steady convection are calculated and the latter is found to be critically dependent on the Crispation and Bond numbers. It is shown that the onset of instability can be delayed and the critical Marangoni number can be increased through the use of feedback control

Modelling of Marangoni convection using proper orthogonal decomposition

Proper orthogonal decomposition (POD) is applied to Marangoni convection in a horizontal fluid layer heated from below and cooled from above with non-deformable free surface. We investigate two-dimensional Marangoni convection for the case of free-slip bottom in the limit of small Prandtl number. The POD technique is then used to the velocity and temperature data to obtain basis functions for both velocity and temperature fields. When these basis functions are used in a Galerkin procedure, the low-dimensional of Marangoni convection are constructed with the smallest possible degree of freedom. The results based on this low-dimensional model are discussed

Marangoni convection in a variable viscosity fluid layer with feedback control.

Feedback control was applied to the steady Marangoni convection in a horizontal layer of fluid with variable viscosity and free-slip at the lower boundary heated from below and cooled from above. Prediction for the onset of convection are obtained from the analysis by numerical technique. The effects of feedback control are studied by examining the critical Marangoni numbers and wave numbers. It is shown that the onset of Marangoni convection with variable viscosity can be delayed and the critical Marangoni number can be increased through the use of feedback control

Stability of Marangoni convection in a fluid layer with variable viscosity and deformable free surface under free-slip condition

The steady marangoni convection is investigated in a horizontal layer of fluid with a free-slip bottom heated from below and cooled from above. Since the viscosity is temperature dependentthe consequences of relaxing oberbeck-boussinesq approximation and free surface deformability are theoretically examined by means of small disturbance analysis. Prediction forthe onset of convection are obtained from the analysis by numerical technique. The effect of variable viscosity and surface deformation on the onset of fluid motion is investigated in detail.It is shown that the critical values of marangoni and wave number depend strongly on the viscosity variation and surface deformation

Similarity solution of marangoni convection boundary layer flow over a flat surface in a nanofluid

The problem of steady Marangoni boundary layer flow and heat transfer over a flat plate in a nanofluid is studied using different types of nanoparticles. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta-Fehlberg (RKF) method. Three different types of nanoparticles are considered, namely, Cu, Al2O3, and TiO2, by using water as a base fluid with Prandtl number Pr=6.2. The effects of the nanoparticle volume fraction φ and the constant exponent m on the flow and heat transfer characteristics are obtained and discussed

MHD viscous flow and heat transfer induced by a permeable shrinking sheet with prescribed surface heat flux

The problem of magnetohydrodynamic (MHD) boundary layer flow and heat transfer due to a permeable shrinking sheet with prescribed surface heat flux is studied. The viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected. The transformed nonlinear ordinary differential equations are solved numerically via the implicit finite-difference scheme known as the Keller-box method. Both two-dimensional and axisymmetric cases are considered. The results for the skin friction coefficient and the wall temperature, as well as the velocity and temperature profiles are presented and discussed for various parameters. Dual solutions exist for certain range of the suction parameter and Hartmann number. It is found that the boundary layer separation is delayed with Hartmann number

Numerical solutions of Wang's stretching/shrinking sheet problem for nanofluids

The steady stagnation-point flow of a viscous and incompressible fluid over a continuously stretching or shrinking sheet in its own plane in a water-based copper (Cu) nanofluid is studied theoretically. The formulation of the present problem in a nanofluid follows that of Wang's stretching/shrinking sheet problem in a viscous fluid. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. The numerical solutions are obtained and discussed for the skin friction coefficient and the velocity profiles for various values of the governing parameters, namely the nanoparticle volume fraction and stretching/shrinking parameters. It is found that dual solutions exist for the shrinking sheet case