Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source

Chaotic convection in a viscoelastic fluid saturated porous layer, heated from below, is studied by using Oldroyd’s type constituting relation and in the presence of an internal heat source. A modified Darcy law is used in the momentum equation, and a heat source term has been considered in energy equation. An autonomous system of fourth-order differential equations has been deduced by using a truncated Fourier series. Effect of internal heat generation on chaotic convection has been investigated. The asymptotic behavior can be stationary, periodic, or chaotic, depending upon the flow parameters. Construction of four-scroll, or “two-butterfly,” and chaotic attractor has been examined

Qualitative Analysis of a Modified Leslie-Gower Predator-prey Model with Weak Allee Effect II

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for models with (without) Allee effect and the local existence and stability of the limit cycle emerging through Hopf bifurcation has also been studied. The phase portrait diagrams are sketched to validate analytical and numerical findings

Qualitative Analysis of a Modified Leslie-Gower Predator-prey Model with Weak Allee Effect II

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for models with (with- out) Allee effect and the local existence and stability of the limit cycle emerging through Hopf bifurcation has also been studied. The phase portrait diagrams are sketched to validate analytical and numerical findings

The Impact of Nonlinear Harvesting on a Ratio-dependent Holling-Tanner Predator-prey System and Optimum Harvesting

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using Pontryagin maximum principle. The numerical simulations have been presented in support of the analytical findings

Onset of Convection in Porous Medium Saturated by Viscoelastic Nanofluid: More Realistic Result

The present paper deals with the linear thermal instability analysis of viscoelastic nanofluid saturated porous layer. We consider a set of new boundary conditions for the nanoparticle fraction, which is physically more realistic. The new boundary condition is based on the assumption that the nanoparticle fraction adjusts itself so that the nanoparticle flux is zero on the boundaries. We use Oldroyd-B type viscoelastic fluid that incorporates the effects of Brownian motion and thermophoresis. Expressions for stationary and oscillatory modes of convection have been obtained in terms of the Rayleigh number, which are found to be functions of various parameters. The numerical results have been presented through graphs

Study of Heat and Mass Transport in Bénard-Darcy Convection with G-Jitter and Variable Viscosity Liquids in a Porous Layer with Internal Heat Source

In this research article, we investigated the weakly non-linear effect of gravity modulation for the temperature dependent viscous fluid in a horizontal porous layer in the presence of internal heat source. We use power series expansion in terms of the amplitude of gravity modulation, which is considered to be small for double-diffusive convection in porous media. We graphically show the effect of internal heat source, solute Rayleigh number, Lewis number, Vadász number, thermo-rheological parameter, the amplitude of gravity modulation, the frequency of modulation on the heat and mass transfer using Ginzburg-Landau equation. The effect of gravity modulation is found significant and is more effective for the low values of frequency of modulation

A Local Nonlinear Stability Analysis of Modulated Double Diffusive Stationary Convection in a Couple Stress Liquid

The non-autonomous Ginzburg-Landau equation with time-periodic coefficients is derived for two modulated double-diffusive stationary convection involving couple stress liquid. The heat and mass transports are quantified in terms of Nusselt and Sherwood numbers, which are obtained as functions of the slow time scale. Effects of Prandtl number, Lewis number, solute Rayleigh number and couple stress parameter have been discuused in detail

Nonlinear thermal instability in a horizontal porous layer with an internal heat source and mass flow

© 2016, Springer-Verlag Wien. Linear and nonlinear stability analyses of Hadley–Prats flow in a horizontal fluid-saturated porous medium with a heat source are performed. The results indicate that, in the linear case, an increase in the horizontal thermal Rayleigh number is stabilizing for both positive and negative values of mass flow. In the nonlinear case, a destabilizing effect is identified at higher mass flow rates. An increase in the heat source has a destabilizing effect. Qualitative changes appear in Rz as the mass flow moves from negative to positive for different internal heat sources