Chapters authored
Thickness and Thermal Conductivities of the Walls and Fluid Layer Effects on the Onset of Thermal Convection in a Horizontal Fluid Layer Heated from Below
The thermal boundary conditions have important effects on the hydrodynamics of a thermo‐convective fluid layer. These effects are introduced through the Biot number under the Robin type boundary conditions. The thermal conductivity and thicknesses of the walls are key properties to bridge two known ideal situations widely studied: the fluid layer bounded by two insulating walls and the fluid layer bounded by two perfect thermal conducting walls. This chapter is devoted to the physical mechanisms involved in the thermal boundary conditions, its influence on the linear stability of the fluid layer and its implications with the pattern formation. A review of very important investigations on the subject is also given. The role of the thermal conductivities and thicknesses of the walls is explained with help of curves of criticality for the thermoconvection in a horizontal Newtonian fluid layer.
Part of the book: Vortex Structures in Fluid Dynamic Problems
Applications of Viscoelastic Fluids Involving Hydrodynamic Stability and Heat Transfer
Rayleigh and Marangoni convection and rheology are linked in the thermal convection of viscoelastic fluids to some recent technological applications. Such technology developments as the ones presented here undoubtedly shall be based on interdisciplinary projects involving not only rheology or fluid mechanics but several other disciplines. Three practical applications which use Rayleigh or Marangoni convection in their working principle are presented along with some technical details. This contribution focus mainly on the physical mechanism and the involved hydrodynamics of some lab and industrial applications. Finally, a short discussion on the role play by the convective mechanisms is given in order to provide integration of the exposed ideas.
Part of the book: Polymer Rheology
Bioconvective Linear Stability of Gravitactic Microorganisms
Interesting results on the linear bioconvective instability of a suspension of gravitactic microorganisms have been calculated. The hydrodynamic stability is characterized by dimensionless parameters such as the bioconvection Rayleigh number R, the gyrotaxis number G, the motility of microorganisms d, and the wavenumber k of the perturbation. Analytical and numerical solutions are calculated. The analytical one is an asymptotic solution for small wavenumbers (and for any motility number) which agrees very well with the numerical solutions. Two numerical methods are used for the sake of comparison. They are a shooting method and a Galerkin method. Marginal curves of R against k for fixed values of d and G are presented along with curves corresponding to the variation of the critical values of Rc and kc. Moreover, those critical values are compared with the experimental data reported in the literature, where the gyrotactic algae Chlamydomonas nivalis is the suspended microorganism. It is shown that the agreement between the present theoretical results and the experiments is very good.
Part of the book: Heat and Mass Transfer
Feedback Control of Rayleigh Convection in Viscoelastic Maxwell Fluids
Control of Rayleigh convection in a viscoelastic Maxwell fluid is addressed here by considering a feedback from shadowgraphic visualizations. Here, a theoretical approach is made to the problem of the onset of convective motion through a source term in the lower thermal boundary condition. A numerical Galerkin technique is then used to study the linear hydrodynamic stability. Small relaxation times are considered for Prandtl numbers 1 and 10. Interesting results for the Rayleigh, the wavenumber, and the frequency of oscillations are presented along with discussion on the physical mechanism. In short, the linear hydrodynamic stability analysis states that suppression of convection may be favored.
Part of the book: Heat and Mass Transfer