Search

This work deals with a Darcy–Bénard convection problem in the presence of combustion and with local thermal non-equilibrium between the fluid and the solid phases. The effects of combustion and local thermal non-equilibrium on the onset of convection is studied in the linear and nonlinear regimes. Unlike all reported local thermal non-equilibrium problems reported so far, the present problem has a unique situation of having thermal non-equilibrium not only in the perturbed state but also in the basic state. Further, we observe that local thermal non-equilibrium does not, under any circumstance, lead to local thermal equilibrium except in an approximate sense when the combustion is quite weak. The effect of combustion is to advance the onset of convection compared to that in its absence. The effect of local thermal non-equilibrium is to reinforce the effect of combustion. In the presence of both these effects, sub-critical instability exists. The results are obtained numerically and have implication in practical porous medium convection problems. [ABSTRACT FROM AUTHOR]

Nanofluids have various operations and prospects in heat transfer engineering to produce novel technological equipment for cooling purposes. In response to nanofluid's possible application, the transient convective alumina-water nanofluid flow in a square vessel in the presence of magnetic field and exothermic chemical reaction has been numerically investigated. We consider a square vessel, where the lower boundary of the vessel is heated, the two vertical side walls are relatively cold, and the upper wall is insulated. The finite element method based on Galerkin scheme is used to solve the governing partial differential equations along the imposing boundary conditions. We verified the present results with the standard experimental published results. The flow and thermal forms, and local Nusselt number are investigated for the numerous appropriate parameters. The time effects on the heat transfer is examined. The result shows that as the Rayleigh number increased from 105 to 106, the heat transfer increased by 72.78%. Compared with the base fluid water, the heat transfer of the alumina-water nanofluid with a nanoparticle volume fraction of 6% increased by 10.42%. The magnetic field and the Arrhenius chemical reaction parameters regulates the nanofluid flow and the heat transfer.

• Deriving a generalized Vadasz–Lorenz model for a system with combustion. • Showing the symmetry, dissipative and energy-conserving natures of the model. • Reporting Rayleigh number expression for onset of regular and chaotic motions. • Quantifying the contribution of combustion to the 'enhanced heat transport situation'. Linear and weakly nonlinear stability analyses of Darcy–Bénard convection of a Newtonian fluid undergoing combustion are investigated in the paper using a zeroth-order chemical reaction model. The Frank-Kamenetskii-Vadasz-Lorenz model that has in it the influence of combustion is derived and transformed into a Ginzburg–Landau equation using a method of multiscales. An analytical expression for the Frank-Kamenetskii-Darcy-Rayleigh number and the Hopf-Frank-Kamenetskii-Darcy-Rayleigh number is reported. In the limiting case, these expressions are validated with the results of previous investigations. Using an analytical solution of the Ginzburg–Landau equation, heat transport in the combusting fluid is studied. The clear blow-up of the Nusselt number in the post-ignition regime is shown. The overall effect of combustion is to advance the onset of regular convective and chaotic motions and to enhance the heat transport. The symmetry in the Frank-Kamenetskii-Vadasz-Lorenz model and its Hamiltonian nature are shown. The appearance of chaotic/periodic motion in the system for large values of the eigenvalue (with the butterfly diagram being trapped in an ellipsoidal region) are highlighted in the paper. One new feature in the problem is the favouring of prolonged periodic convection in a larger range of values of the scaled Darcy-Frank-Kamenetskii-Rayleigh number compared with no combustion. The exact nature of the influence of combustion on Darcy–Bénard convection is visualized with the help of a bivariate, least-squares surface fit of the data and some important conclusions are drawn. [ABSTRACT FROM AUTHOR]

Investigation of the fluids purification process, either by filtration or by undesirable substances destruction, is conducted. A convective flow in a reactive porous medium with an axisymmetrical geometry is considered. The momentum equation for the forced convection through a porous substrate is modelled by using the Darcy-Brinkman-Forchheimer model, while the temperature and the concentration fields are obtained subsequently from the energy and diffusion equations. The effects of the main governing parameters such as solid-to-fluid conductivity ratio, Reynolds number, Biot number, as well as the modified Frank-Kamenetskii number (FK)