All Outputs (84)

Discontinuity waves in temperature and diffusion models (2024)
Journal Article
Ciarletta, M., Straughan, B., & Tibullo, V. (2024). Discontinuity waves in temperature and diffusion models. Mechanics Research Communications, 137, Article 104274. https://doi.org/10.1016/j.mechrescom.2024.104274

We analyse shock wave behaviour in a hyperbolic diffusion system with a general forcing term which is qualitatively not dissimilar to a logistic growth term. The amplitude behaviour is interesting and depends critically on a parameter in the forcing... Read More about Discontinuity waves in temperature and diffusion models.

Asymptotic behaviour for convection with anomalous diffusion (2024)
Journal Article
Straughan, B., & Barletta, A. (2024). Asymptotic behaviour for convection with anomalous diffusion. Continuum Mechanics and Thermodynamics, 36(4), 737-743. https://doi.org/10.1007/s00161-024-01291-7

We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or penetrative conve... Read More about Asymptotic behaviour for convection with anomalous diffusion.

Thermal convection with a Cattaneo heat flux model (2024)
Journal Article
Gentile, M., & Straughan, B. (2024). Thermal convection with a Cattaneo heat flux model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2282), Article 20230771. https://doi.org/10.1098/rspa.2023.0771

The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective deriv... Read More about Thermal convection with a Cattaneo heat flux model.

Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium (2023)
Journal Article
Franchi, F., Nibbi, R., & Straughan, B. (2024). Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium. Transport in Porous Media, 151(1), 193-211. https://doi.org/10.1007/s11242-023-02038-9

We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double... Read More about Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium.

Stabilization estimates for the Brinkman–Forchheimer–Kelvin–Voigt equation backward in time (2023)
Journal Article
Gentile, M., & Straughan, B. (2023). Stabilization estimates for the Brinkman–Forchheimer–Kelvin–Voigt equation backward in time. Acta Mechanica, 234(9), 4001-4009. https://doi.org/10.1007/s00707-023-03592-5

The final value value problem for the Brinkman–Forchheimer–Kelvin–Voigt equations is analysed for quadratic and cubic types of Forchheimer nonlinearity. The main term in the Forchheimer equations is allowed to be fully anisotropic. It is shown that t... Read More about Stabilization estimates for the Brinkman–Forchheimer–Kelvin–Voigt equation backward in time.

Effect of Temperature Upon Double Diffusive Instability in Navier–Stokes–Voigt Models with Kazhikhov–Smagulov and Korteweg Terms (2023)
Journal Article
Straughan, B. (2023). Effect of Temperature Upon Double Diffusive Instability in Navier–Stokes–Voigt Models with Kazhikhov–Smagulov and Korteweg Terms. Applied Mathematics and Optimization, 87(54), Article 54. https://doi.org/10.1007/s00245-023-09964-6

We present models for convection in a mixture of viscous fluids when the layer is heated from below and simultaneously the pointwise volume concentration of one of the fluids is heavier below. This configuration produces a problem of competitive doub... Read More about Effect of Temperature Upon Double Diffusive Instability in Navier–Stokes–Voigt Models with Kazhikhov–Smagulov and Korteweg Terms.

Thermal convection in a higher-gradient Navier–Stokes fluid (2023)
Journal Article
Straughan, B. (2023). Thermal convection in a higher-gradient Navier–Stokes fluid. European Physical Journal Plus, 138(60), https://doi.org/10.1140/epjp/s13360-023-03658-2

We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing models for thermal convection, analysing these in detail, and deriving critical Rayleigh and wave numbers for the onset of convective flu... Read More about Thermal convection in a higher-gradient Navier–Stokes fluid.

Thermal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a generalized Maxwell–Cattaneo law (2022)
Journal Article
Straughan, B. (2023). Thermal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a generalized Maxwell–Cattaneo law. Annali dell'Universita di Ferrara, 69, 521–540. https://doi.org/10.1007/s11565-022-00448-z

We investigate thoroughly a model for thermal convection of a class of viscoelastic fluids in a porous medium of Brinkman–Darcy type. The saturating fluids are of Kelvin–Voigt nature. The equations governing the temperature field arise from Maxwell–C... Read More about Thermal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a generalized Maxwell–Cattaneo law.

Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection (2022)
Journal Article
Straughan, B. (2022). Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection. Environmental Fluid Mechanics, https://doi.org/10.1007/s10652-022-09888-9

We investigate the effects of anisotropic permeability and changing boundary conditions upon the onset of penetrative convection in a porous medium of Darcy type and of Brinkman type. Attention is focussed on the critical eigenfunctions which show ho... Read More about Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection.

Thermal convection with generalized friction (2021)
Journal Article
Straughan, B. (2022). Thermal convection with generalized friction. Annali dell'Universita di Ferrara, 68(1), 63-68. https://doi.org/10.1007/s11565-021-00382-6

A model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the L2 norm is shown for the perturbation velocit... Read More about Thermal convection with generalized friction.

Continuous dependence and convergence for a Kelvin–Voigt fluid of order one (2021)
Journal Article
Straughan, B. (2022). Continuous dependence and convergence for a Kelvin–Voigt fluid of order one. Annali dell'Universita di Ferrara, 68(1), 49-61. https://doi.org/10.1007/s11565-021-00381-7

It is shown that the solution to the boundary - initial value problem for a Kelvin–Voigt fluid of order one depends continuously upon the Kelvin–Voigt parameters, the viscosity, and the viscoelastic coefficients. Convergence of a solution is also sho... Read More about Continuous dependence and convergence for a Kelvin–Voigt fluid of order one.

Competitive Double Diffusive Convection in a Kelvin–Voigt Fluid of Order One (2021)
Journal Article
Straughan, B. (2021). Competitive Double Diffusive Convection in a Kelvin–Voigt Fluid of Order One. Applied Mathematics and Optimization, 84(S1), 631-650. https://doi.org/10.1007/s00245-021-09781-9

We present a model for convection in a Kelvin–Voigt fluid of order one when the layer is heated from below and simultaneously salted from below, a problem of competitive double diffusion since heating from below promotes instability, but salting from... Read More about Competitive Double Diffusive Convection in a Kelvin–Voigt Fluid of Order One.

Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order (2021)
Journal Article
Straughan, B. (2022). Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order. Rendiconti del Circolo Matematico di Palermo Series 2, 71(1), 187-206. https://doi.org/10.1007/s12215-020-00588-1

We present numerical techniques for calculating instability thresholds in a model for thermal convection in a complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid for various orders of an exponential fading memory term, and... Read More about Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order.

Continuous dependence for the Brinkman–Darcy–Kelvin–Voigt equations backward in time (2020)
Journal Article
Straughan, B. (2021). Continuous dependence for the Brinkman–Darcy–Kelvin–Voigt equations backward in time. Mathematical Methods in the Applied Sciences, 44(6), 4999-5004. https://doi.org/10.1002/mma.7082

We show that the solution to the Brinkman–Darcy–Kelvin–Voigt equations backward in time depends Hölder continuously upon the final data. A logarithmic convexity technique is employed, and uniqueness of the solution is simultaneously achieved.

Stability in Kelvin–Voigt poroelasticity (2020)
Journal Article
Straughan, B. (2021). Stability in Kelvin–Voigt poroelasticity. Bollettino dell'Unione Matematica Italiana, 14(2), 357-366. https://doi.org/10.1007/s40574-020-00268-z

Hölder continuous dependence of solutions upon the initial data is established for the linear theory of Kelvin–Voigt poroelasticity requiring only symmetry conditions upon the elastic coefficients. A novel functional is introduced to which a logarith... Read More about Stability in Kelvin–Voigt poroelasticity.

Thermosolutal Convection with a Navier–Stokes–Voigt Fluid (2020)
Journal Article
Straughan, B. (2021). Thermosolutal Convection with a Navier–Stokes–Voigt Fluid. Applied Mathematics and Optimization, 84(3), 2587-2599. https://doi.org/10.1007/s00245-020-09719-7

We present a model for convection in a Navier–Stokes–Voigt fluid when the layer is heated from below and simultaneously salted from below, the thermosolutal convection problem. Instability thresholds are calculated for thermal convection with a disso... Read More about Thermosolutal Convection with a Navier–Stokes–Voigt Fluid.

Jordan – Cattaneo waves: Analogues of compressible flow (2020)
Journal Article
Straughan, B. (2020). Jordan – Cattaneo waves: Analogues of compressible flow. Wave Motion, 98, Article 102637. https://doi.org/10.1016/j.wavemoti.2020.102637

We review work of Jordan on a hyperbolic variant of the Fisher - KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee – Infante equation. Extensi... Read More about Jordan – Cattaneo waves: Analogues of compressible flow.

Nonlinear Stability for Thermal Convection in a Brinkman Porous Material with Viscous Dissipation (2020)
Journal Article
Straughan, B. (2020). Nonlinear Stability for Thermal Convection in a Brinkman Porous Material with Viscous Dissipation. Transport in Porous Media, 134(2), 303-314. https://doi.org/10.1007/s11242-020-01446-5

We investigate nonlinear stability in a model for thermal convection in a saturated porous material using Brinkman theory, taking into account viscous dissipation effects. There are (at least) two models for viscous dissipation available, and we incl... Read More about Nonlinear Stability for Thermal Convection in a Brinkman Porous Material with Viscous Dissipation.

Bidispersive thermal convection with relatively large macropores (2020)
Journal Article
Gentile, M., & Straughan, B. (2020). Bidispersive thermal convection with relatively large macropores. Journal of Fluid Mechanics, 898, Article a14. https://doi.org/10.1017/jfm.2020.411

We derive linear instability and nonlinear stability thresholds for a problem of thermal convection in a bidispersive porous medium with a single temperature when Darcy theory is employed in the micropores whereas Brinkman theory is utilized in the m... Read More about Bidispersive thermal convection with relatively large macropores.

Continuous dependence on boundary and Soret coefficients in double diffusive bidispersive convection (2020)
Journal Article
Franchi, F., Nibbi, R., & Straughan, B. (2020). Continuous dependence on boundary and Soret coefficients in double diffusive bidispersive convection. Mathematical Methods in the Applied Sciences, 43(15), 8882-8893. https://doi.org/10.1002/mma.6581

We develop a theory for double diffusive convection in a double porosity material along the Brinkman scheme. The Soret effect is included whereby a temperature gradient may directly influence salt concentration. The boundary conditions on the tempera... Read More about Continuous dependence on boundary and Soret coefficients in double diffusive bidispersive convection.