Viscoelastic Fluid Saturated Porous Layer Research Articles

Cross Diffusion Effect on Linear and Nonlinear Double Diffusive Convection in a Viscoelastic Fluid Saturated Porous Layer with Internal Heat Source

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theory is based on the normal mode technique, while the nonlinear theory is based on a minimal representation of truncated double Fourier series. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is considered to model the momentum equation. The onset criterion for stationary and oscillatory convection and steady heat and mass transfer have been obtained analytically using linear and nonlinear theory, respectively. The combined effect of an internal heat source and cross diffusion is investigated. The effects of Dufour, Soret, internal heat, relaxation and retardation time, Lewis number and concentration Rayleigh number on stationary, oscillatory, and heat and mass transport are depicted graphically. Heat and mass transfer are presented graphically in terms of Nusselt and Sherwood numbers, respectively. It is reported that the stationary and oscillatory convection are significantly influenced with variation of Soret and Defour parameters. An increment of the internal heat parameter has a destabilizing effect as well as enhancing the heat transfer process. On the other hand, an increment of internal heat parameter has a variable effect on mass transfer. It is found that there is a critical value for the thermal Rayleigh number, below which increasing internal heat decreases the Sherwood number, while above it increasing the internal heat increases the Sherwood number.

The Onset of Double-Diffusive Convection in a Two-Layer System With a Viscoelastic Fluid-Saturated Porous Medium Under High-Frequency Vibration

Abstract The effect of high frequency vibration in the gravity field on the double-diffusive convection in a two-layer system with a viscoelastic fluid-saturated porous layer is studied. The averaging method is employed to split the unknown functions into a periodic rapidly varying part and a slower mean part. Then, the governing equation of perturbations is numerically solved by the Chebyshev tau method and QZ decomposition method. The influence of physical parameters on the stability of system is investigated. It is shown that the neutral stability curves are bimodal under high frequency vibration. The parameter of the high frequency vibration mainly stabilizes the pure fluid layer for greater wave numbers and has a weak impact on the whole system for smaller wave numbers.

The effects of double-diffusion and viscous dissipation on the oscillatory convection in a viscoelastic fluid saturated porous layer

The effects of the double-diffusion and viscous dissipation on the convective instability in a horizontal porous layer are investigated. The porous medium is saturated with a binary viscoelastic fluid. The Oldroyd-B model of viscoelastic fluid is considered. Constant temperature and concentration differences are maintained between the boundaries. A basic flow is present in the horizontal direction. The governing parameters are the thermal Rayleigh number (RaT), solutal Rayleigh number (RaS), Gebhart number (Ge), Lewis number (Le), Péclet number (Pe), dimensionless relaxation time (λ1), and dimensionless retardation time (λ2). A small perturbation to the basic flow is assumed, and a linear stability analysis is performed. A detailed discussion is carried out considering RaT as the eigenvalue. The critical wave number and frequency are also derived for a wide range of Lewis numbers and solutal Rayleigh numbers. The oscillatory modes are analyzed. It is found that transverse rolls are the preferred mode for the onset of oscillatory convection, except for some special cases. Moreover, a negative solutal Rayleigh number stabilizes the flow. An opposite effect is seen in the presence of a positive solutal Rayleigh number.

Stability of triple diffusive convection in a viscoelastic fluid-saturated porous layer

The triple diffusive convection in an Oldroyd-B fluid-saturated porous layer is investigated by performing linear and weakly nonlinear stability analyses. The condition for the onset of stationary and oscillatory is derived analytically. Contrary to the observed phenomenon in Newtonian fluids, the presence of viscoelasticity of the fluid is to degenerate the quasiperiodic bifurcation from the steady quiescent state. Under certain conditions, it is found that disconnected closed convex oscillatory neutral curves occur, indicating the requirement of three critical values of the thermal Darcy-Rayleigh number to identify the linear instability criteria instead of the usual single value, which is a novel result enunciated from the present study for an Oldroyd-B fluid saturating a porous medium. The similarities and differences of linear instability characteristics of Oldroyd-B, Maxwell, and Newtonian fluids are also highlighted. The stability of oscillatory finite amplitude convection is discussed by deriving a cubic Landau equation, and the convective heat and mass transfer are analyzed for different values of physical parameters.

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.

The Onset of Double Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer with Non-Equilibrium Model

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

Onset of Darcy–Brinkman convection in a binary viscoelastic fluid saturated porous layer

The onset of Darcy–Brinkman double-diffusive convection in a binary viscoelastic fluid-saturated porous layer is studied using both linear and weakly nonlinear stability analyses. The Oldroyd-B model is employed to describe the rheological behavior of the fluid. An extended form of Darcy–Oldroyd law incorporating the Brinkman’s correction and time derivative is used to describe the fluid flow and the Oberbeck–Boussinesq approximation is invoked. The onset criterion for stationary and oscillatory convection is derived analytically. The effects of rheological parameters, Darcy number, normalized porosity, Lewis number, solute Rayleigh number, and Darcy–Prandtl number on the stability of the system is investigated. The results indicated that there is a competition among the processes of thermal, solute diffusions and viscoelasticity that causes the convection to set in through the oscillatory modes rather than the stationary. The Darcy–Prandtl number has a dual effect on the threshold of oscillatory convection. The nonlinear theory based on the method of truncated representation of Fourier series is used to find the transient heat and mass transfer. Some existing results are reproduced as the particular cases of present study.

Double diffusive convection in a viscoelastic fluid-saturated porous layer using a thermal non-equilibrium model

The stability of a binary viscoelastic fluid-saturated porous layer which is heated from below is studied, where the fluid and solid phases are not in local thermal equilibrium. The modified Darcy-Oldroyd model is employed as a momentum equation, with the fluid and solid phase temperature fields modelled separately. It is found that the inter-phase heat transfer coefficient has a significant effect on the stability of the system. Competition between the processes of viscous relaxation and thermal diffusion cause the convection to set in through oscillatory rather than stationary instability, with the viscoelastic parameters inhibiting the onset of convection. In the case of weakly non-linear theory, both steady and unsteady cases are considered. In the unsteady case the transient behaviour of the Nusselt and Sherwood numbers is investigated. The effect of thermal non-equilibrium on heat and mass transfer is also discussed.

Thermal convection in a rotating viscoelastic fluid saturated porous layer

Linear and nonlinear stability of a rotating viscoelastic fluid saturated porous layer heated from below is studied analytically. The modified Darcy–Oldroyd model that includes the time derivative and Coriolis terms is employed as a momentum equation. The onset criterion for both stationary and oscillatory convection is derived as a function of Taylor number, Darcy–Prandtl number and viscoelastic parameters. There is a competition between the processes of rotation, viscous relaxation and thermal diffusion that causes the convection to set in through oscillatory mode rather than stationary. The rotation inhibits the onset of convection in both stationary and oscillatory modes. The stress relaxation parameter destabilizes the system towards the oscillatory mode, while the strain retardation parameter enhances the stability. The effect of Darcy–Prandtl number on the stability of the system is also investigated. The nonlinear theory is based on the truncated representation of Fourier series method. The effect of rotation, stress relaxation and strain-retardation time and also the Darcy–Prandtl number on the transient heat transfer is presented graphically.

The onset of convection in a binary viscoelastic fluid saturated porous layer

AbstractThe onset of convection in a binary viscoelastic fluid‐saturated porous layer is studied using a linear and a weak nonlinear stability analyses. The modified Darcy‐Oldroyd model is employed as a momentum equation. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. There is a competition between the processes of thermal, solute diffusions, and viscoelasticity that causes the convection to set in through oscillatory rather than stationary. The effect of solute Rayleigh number, Prandtl number, diffusivity ratio, relaxation, and retardation parameters on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method is used to find the heat and mass transfer. The effect of various parameters on heat and mass transfer is also brought out. The transient behaviour of the Nusselt number and Sherwood number is investigated by solving the finite amplitude equations using Runge‐Kutta method.