Izzati ah Khalid

Uniform Solution on the Combined Effect of Magnetic Field and Internal Heat Generation on Rayleigh–Bénard Convection in Micropolar Fluid

Combined effect of magnetic field and internal heat generation on the onset of Rayleigh― Benard convection in a horizontal micropolar fluid layer is studied. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid, and free-free with combination isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. The influence of various parameters on the onset of convection has been analyzed. It is shown that the presence of magnetic field always has a stability effect on the Rayleigh―Benard convection in micropolar fluid.

Effect of Internal Heat Generation on Benard-Marangoni Convection in Micropolar Fluid with Feedback Control

The effect of uniform distribution of internal heat generation on the linear stability analysis of the Benard-Marangoni convection in an Eringens micropolar fluids with feedback control is investigated theoretically. The upper free surface is assumed to be non-deformable and the lower boundary is taken to be rigid and isothermal with fixed temperature and span-vanishing boundaries. The eigenvalue is solved numerically using the Galerkin method. The influence of the internal heat generation; Q and feedback control; K in micropolar fluids with various parameters on the onset of stationary convection has been analysed.

Control strategy on the double-diffusive convection in a nanofluid layer with internal heat generation

The influences of feedback control and internal heat source on the onset of Rayleigh–Benard convection in a horizontal nanofluid layer is studied analytically due to Soret and Dufour parameters. The confining boundaries of the nanofluid layer (bottom boundary–top boundary) are assumed to be free–free, rigid–free, and rigid–rigid, with a source of heat from below. Linear stability theory is applied, and the eigenvalue solution is obtained numerically using the Galerkin technique. Focusing on the stationary convection, it is shown that there is a positive thermal resistance in the presence of feedback control on the onset of double-diffusive convection, while there is a positive thermal efficiency in the existence of internal heat generation. The possibilities of suppress or augment of the Rayleigh–Benard convection in a nanofluid layer are also discussed in detail.

Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy

A linear stability analysis has been carried out to examine the effect of internal heat source on the onset of Rayleigh–Benard convection in a rotating nanofluid layer with double diffusive coefficients, namely, Soret and Dufour, in the presence of feedback control. The system is heated from below and the model used for the nanofluid layer incorporates the effects of thermophoresis and Brownian motion. Three types of bounding systems of the model have been considered which are as follows: both the lower and upper bounding surfaces are free, the lower is rigid and the upper is free, and both of them are rigid. The eigenvalue equations of the perturbed state were obtained from a normal mode analysis and solved using the Galerkin method. It is found that the effect of internal heat source and Soret parameter destabilizes the nanofluid layer system while increasing the Coriolis force, feedback control, and Dufour parameter helps to postpone the onset of convection. Elevating the modified density ratio hastens the instability in the system and there is no significant effect of modified particle density in a nanofluid system.

Coriolis force in a nanofluid layer in the presence of Soret effect

The influence of coriolis force on the onset of steady Rayleigh-Benard convection subjected to Soret parameter in a horizontal nanofluid layer is considered analytically. The confined lower and upper boundary conditions of the nanofluid layer are considered to be free-free, rigid-free and rigid-rigid respectively. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis diffusion. Following the usual linear stability theory, the eigenvalue solution is obtained numerically by using Galerkin technique. From the investigation, the presence of coriolis force due to the rotation inhibits the onset of convection in nanofluid layer and have a stabilizing effect. Further, the instability of the system get advanced with the increased values of the Soret parameter.

Effects of internal heat source and soret on the onset of Rayleigh–Bénard convection in a nanofluid layer

The influences of internal heat source and Soret on the steady Rayleigh–Benard convection in an infinitely horizontal nanofluid layer is studied. The lower and upper boundary conditions of the nanofluid layer are considered to be free–free, rigid–free and rigid–rigid respectively. The nanofluid model used includes both effects of Brownian motion together with thermophoresis diffusion respectively. Using linear stability theory, the eigenvalue problem is obtained through the use of Galerkin technique. It is observed that the greater the intensity of internal heat source and the greater values of Soret parameter, the more rapid the onset of thermal instability in a nanofluid layer system.The influences of internal heat source and Soret on the steady Rayleigh–Benard convection in an infinitely horizontal nanofluid layer is studied. The lower and upper boundary conditions of the nanofluid layer are considered to be free–free, rigid–free and rigid–rigid respectively. The nanofluid model used includes both effects of Brownian motion together with thermophoresis diffusion respectively. Using linear stability theory, the eigenvalue problem is obtained through the use of Galerkin technique. It is observed that the greater the intensity of internal heat source and the greater values of Soret parameter, the more rapid the onset of thermal instability in a nanofluid layer system.

On oscillatory magnetoconvection in a nanofluid layer in the presence of internal heat source and Soret effect

The onset of oscillatory magnetoconvection for an infinite horizontal nanofluid layer subjected to Soret effect and internal heat source heated from below is examined theoretically with the implementation of linear stability theory. Two important properties that are thermophoresis and Brownian motion are included in the model and three types of lower-upper bounding systems of the model: rigid–rigid, rigid–free as well as free–free boundaries are examined. Eigenvalue equations are gained from a normal mode analysis and executed using Galerkin technique. Magnetic field effect, internal heat source effect, Soret effect and other nanofluid parameters on the oscillatory convection are presented graphically. For oscillatory mode, it is found that the effect of internal heat source is quite significant for small values of the non-dimensional parameter and elevating the internal heat source speed up the onset of convection. Meanwhile, the increasing of the strength of magnetic field in a nanofluid layer reduced t...

The effect of magnetic field on Marangoni convection in a nanofluid layer with internal heat source

Magnetic field in Marangoni thermal instability in an infinite parallel plane of nanofluid layer together with internal heat source is investigated using linear stability theory. Two important properties of thermophoresis and Brownian motion are included in the model and two types of lower free–upper free and lower rigid–upper free bounding systems of the model are considered. The system is assumed to be heated from below and the eigenvalue equations are gained from a normal mode analysis and executed numerically by using Galerkin technique. Influences of magnetic field within nanofluid layer always stabilize the system and the initiation of thermocapillary instability in an infinite parallel plane of nanofluid layer gets advanced with the increased in internal heat source.