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

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

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

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

Marangoni driven boundary layer flow past a flat plate in nanofluid with suction/injection

The problem of Marangoni convection boundary layer flow past a flat plate in a nanofluid when the wall is permeable, where there is suction or injection effect, 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, namely Cu, Al2O3 and TiO2 are considered by using water as a base fluid with Prandtl number Pr = 6.2. The effects of the suction or injection parameter on the flow and heat transfer characteristics are discussed

Stagnation-point flow past a shrinking sheet in a nanofluid.

In this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It was found that nanoparticles of low thermal conductivity, TiO2, have better enhancement on heat transfer compared to nanoparticles Al2O3 and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0

Radiation effects on Marangoni convection over a flat surface with suction and injection

The radiation effect on a steady two-dimensional Marangoni convection flow over a permeable flat surface is studied numerically. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations by using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the shooting method. Numerical results are obtained for the interface velocity and the surface temperature gradient as well as the velocity and temperature profiles for some values of the governing parameters. The results indicate that the heat transfer rate at the surface decreases as the radiation parameter increases. The effects of suction or injection parameter on the flow and heat transfer characteristics are discussed

Effects of radiation, joule heating and viscous dissipation on MHD Marangoni convection over a flat surface with suction and injection

In this paper, we studied the effects of thermal radiation, Joule heating and viscous dissipation on magnetohydrodynamics (MHD) Marangoni convection boundary layer over a flat surface. We also investigated the influence of suction and injection on the boundary layer. Numerical results were obtained using the shooting method along with the Runge-Kutta-Fehlberg method. The influences of the interest parameters on the reduced velocity along the interface, velocity profiles as well as the reduced heat transfer at the interface and temperature profiles were presented in tables and figures. From the results, we discovered that thermal radiation, magnetic parameter, Joule heating, viscous dissipation and suction parameter can reduce the velocity and heat transfer at the interface

MHD stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet

The steady magnetohydrodynamic (MHD) two-dimensional stagnation-point boundary layer flow and heat transfer of a viscous, incompressible and electrically conducting fluid over a permeable flat stretching/shrinking sheet in the presence of an externally applied magnetic field of constant strength is studied. The governing partial differential equations are first transformed into a system of ordinary differential equations, which is then been solved numerically using a shooting method built in Maple software. It is found that the heat transfer rate at the surface reduces with the Eckert number and it is also found that dual solutions exist for certain values of the mass flux parameter and the stretching/shrinking parameter

Effects of Joule Heating and Viscous Dissipation on MHD Marangoni Convection Boundary Layer Flow

An analysis is performed to study the effects of the Joule heating and viscous dissipation on the magnetohydrodynamics (MHD) Marangoni convection boundary layer flow. The governing partial differential equations are reduced to a system of ordinary differential equations via the similarity transformations. Numerical results of the similarity equations are obtained using the Runge-Kutta-Fehlberg method. Effects of the magnetic field parameter, and the combined effects of the Joule heating and the viscous dissipation are investigated and the numerical results are tabulated in tables and figures. It is found that the magnetic field reduces the fluid velocity but increases the fluid temperature. On the other hand, the combined effects of the Joule heating and viscous dissipation have significantly influenced the surface temperature gradient