The effect of feedback control on the criterion for the onset of Marangoni convection in a horizontal micropolar fluid layer is studied 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. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is found that the onset of instability can be delayed through the use of feedback control.

Abstract:The onset of Marangoni convection in a horizontal fluid layer with a free surface overlying a solid layer heated from below is studied. Problem is focused on the effect of the solid layer depth or its conductivity. The viscosity group, R v , Biot number, Bi, depth ratio, d r and conductivity ratio, k r , are significant on determining the critical Marangoni number M c with the corresponding critical wavenumber α c . The characteristics problem is solved numerically. Results show that the temperaturedependent viscosity destabilizes the fluid system but it behaves oppositely when a higher relative thermal conductivity ratio or higher depth ratio is taken.

An anisotropic porous layer saturated with a viscoelastic double diffusive binary fluid is examined numerically for the onset of Darcy-Rayleigh convection. From below, the system is heated, while from above, it is cooled. The temperature-dependent viscosity was added to the double diffusive binary fluid, and the Galerkin expansion method was used to determine the critical Darcy-Rayleigh number. When their values are raised, the impacts of strain retardation, thermal anisotropy parameter and Dufour number slow the production of heat transfer and stabilise the system. When the values are increased, the stress relaxation, Darcy-Prandtl, mechanical anisotropy parameters, temperature dependent viscosity and Soret number accelerate the heat transfer process in convection, which destabilises the system

Mathematics is a fundamental subject for all courses especially in engineering, business and economics. A good understanding of mathematics will help in daily activities and in many other situation either in simplified or complex forms. However, some students may have difficulties learning this subject and often felt that they need extra help from different resources. One of the learning methods that commonly used is through visualization where students view video in order to understand the topic. This study aimed to identify the technical criterion in producing an effective video to assist the process of teaching and learning. The main instrument implemented is by conducting a survey and follow-up by assessment questions with the respondents. The response and comments from the student's perspective are taken as a guide to help educators to improve video making in learning mathematics.

The effect of feedback control on the onset of double-diffusive convection in a horizontal binary fluid layer is studied analytically subjected to cross diffusion coefficients which are the Soret and Dufour parameters. The confined boundaries of the binary fluid layer are considered to be free-free, rigid-free and rigid-rigid which described the lower and upper surfaces respectively. The linear stability theory is applied, and the eigenvalue solution is obtained numerically using 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 doublediffusive convection in binary fluid mixture.