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• Chaotic convection in Oldroyd-B fluid saturated porous medium is studied. • The effect of temperature modulation is included. • The research is on the basis of Darcy-Brinkman model. • The exchange of chaotic motion from steady convection is found. The analysis of chaotic convection of Oldroyd-B fluid in porous medium under temperature modulation is presented on the basis of Darcy-Brinkman model. A four-dimensional nonlinear system resulting from a truncated Galerkin expansion of the conservation and constitutive equations is set up to deal with the stability of convection with different Darcy number and Darcy-Rayleigh number. The chaotic behavior is controlled by Darcy-Rayleigh number while Darcy number has a great influence on the stability of system. With the lower boundary which is heated in a time-periodic manner, the system will change over to a state of periodic or chaotic motion from steady convection. [ABSTRACT FROM AUTHOR]

• 3-D falling film flow simulations calculated with VOF method are performed. • The influence of tilt and sloshing conditions on falling film flow are examined. • The tilt conditions make the column flow much easier convert to sheet flow. • Under roll motion, a secondary crest zone nearby the main crest zone emerges. The shell-side flow patterns and liquid film thickness (δ) distribution of the falling film are extremely important for the comprehensive performance of the spiral-wound heat exchangers. In this paper, 3-D simulations calculated with volume of fluid (VOF) method are performed to study the inter-tube flow modes and the distribution characteristics of δ around the tube. At first, the effects of different spray densities, longitudinal inter-tube spacings (S t) and spray holes arrangements (S h) on the δ distribution are studied to determine the appropriate values. After that, the influence of tilt and sloshing conditions are examined based on the selected geometric parameters. The results show that although the value of S t has a significant influence on the fluctuation range of δ in stable zone, the average δ in stable zone could remain in the same level. For the spray holes arrangement, the decrease of S h does not thicken the δ in stable zone but promotes a 46% axial length expansion for the crest zone with a thicker δ. The tilt conditions significantly deteriorate the inter-tube flow modes transitions, which makes the column flow much easier convert to sheet flow. Under roll motion, a secondary crest zone emerges nearby the original main crest zone and its δ is 30%–40% thinner than that of the original main crest zone. [ABSTRACT FROM AUTHOR]

• Instabilities with the surface tension and the buoyancy for a non-Newtonian fluid in a fluid-porous system are studied with a deformable surface. • The influences of different key parameters on Rayleigh and Marangoni instabilities in short- and long-wave branches are investigated. • It is found that there is an interval of the Marangoni number in short-wave branches for which the critical Rayleigh number is absent. • Opposite effects between long- and short-wave branches in the coupling mode are observed. This paper describes the linear stability analysis of Rayleigh–Marangoni–Bénard convection with a deformable surface in a fluid overlying a highly porous layer. Using the Chebyshev tau-QZ method, we investigate the oscillatory mode of both the Rayleigh and Marangoni instabilities for non-Newtonian fluids. The numerical results indicate that a deformable upper surface destabilizes the system. Moreover, the Marangoni instabilities in long-wave branches first decrease and then increase with increasing depth ratio, while the opposite effects are observed in short-wave branches. The Rayleigh instabilities decrease monotonically as the depth ratio increases. For certain reference parameters, the system becomes more stable as the Biot number and Galileo number increase. A greater strain retardation time and a smaller stress relaxation time lead to more stable Marangoni convection in long-wave branches, whereas these viscoelastic times have the opposite effects in short-wave branches. The influence of viscoelasticity on the Rayleigh instability is also investigated. Finally, the coupling mode of the two instabilities is studied in detail. Variations in the Marangoni number influence long- and short-wave branches differently. Interestingly, there is an interval of the Marangoni number in short-wave branches for which no critical Rayleigh number exists. [ABSTRACT FROM AUTHOR]

By utilizing a randomly swimming model, a linear stability analysis is applied to investigate the stability of bioconvection in a horizontal suspension layer of motile gyrotactic micro-organisms with heated from below. The micro-organisms under consideration are orientated by a balance between a gravitational torque, due to them being bottom heavy, and viscous torque arising from local fluid velocity gradients. The obtained eigenvalue problem containing thermal Rayleigh number and bioconvection Rayleigh number is solved numerically using one-term Galerkin method. The case of non-oscillatory instability is analyzed, the relationship among thermal Rayleigh number, bioconvection Rayleigh number, Lewis number, critical wavenumber and the shape of microorganisms are discussed. We point out that the heating from below makes the layer more unstable. When increasing the value of thermal Rayleigh number to 1750, the suspension becomes unstable itself, which imply that bioconvection Rayleigh number has nothing to do with the stability of this system. We also find that Lewis number has no effect on critical value of thermal Rayleigh number, but has a great influence on critical bioconvection Rayleigh number. The increasing cell eccentricity enlarges the critical value of bioconvection Rayleigh number, which means that the suspension is more stable. [ABSTRACT FROM AUTHOR]

The qualitative effect of variable internal heat source and variable gravity on the onset of convection in a horizontal fluid saturated sparsely packed porous layer is investigated using linear stability analysis. The single term Galerkin technique is used to compute the value of the critical Rayleigh number and the corresponding wave number. Three different sets of variable gravity and heat source functions are chosen and their influence on the onset of convection is discussed. The eigenvalues are obtained for free-free velocity boundary conditions with isothermal temperature conditions on the boundaries. The influence of porous parameter on the onset of convection is brought out. It is found that the variable heat source and variable gravity does not affect the shape and size of the convective cell at the onset of convection. However the porous parameter do so. [ABSTRACT FROM AUTHOR]