P. G. Siddheshwar

Effect of a non-uniform basic temperature gradient on Rayleigh–Benard convection in a micropolar fluid

Abstract The qualitative effect of a non-uniform basic temperature gradient on the linear stability analysis of the Rayleigh–Benard convection in an Eringens micropolar fluid is studied numerically using a single-term Galerkin technique. The eigenvalue is obtained for free–free, rigid–free, and rigid–rigid velocity boundary combinations with isothermal and adiabatic temperature conditions on the spin-vanishing boundaries. The eigenvalues are also obtained for lower rigid isothermal and upper free adiabatic boundaries with vanishing spin. The influence of various micropolar fluid parameters on the onset of stationary convection has been analysed. Six different basic temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the Rayleigh number obtained is lower than that of the corresponding Newtonian fluid problem. Some important mechanisms of advancing or delaying convection are discussed.

Convective instability of ferromagnetic fluids bounded by fluid-permeable, magnetic boundaries

Abstract Convective instability of a ferromagnetic fluid in a Rayleigh—Benard situation between fluid-permeable, magnetic boundaries and subject to an external constraint of a uniform, transverse magnetic field is studied. The fluid-permeable, magnetic boundaries require general boundary conditions on the velocity and the scalar magnetic potential. For these, the Garlerkin method predicts the critical eigenvalue to be between that of free—free and rigid—rigid boundaries. The paper also reaffirms the qualitative findings of earlier investigations which are, in fact, limiting cases of the present study.

Magnetoconvection in fluids with suspended particles under 1g and μg

The role of magnetic field in the inhibition of natural convection driven by combined buoyancy and surface tension forces in a horizontal layer of an electrically conducting Boussinesq fluid with suspended particles confined between an upper free/adiabatic and a lower rigid/isothermal boundary is considered in 1g and μg situations. The inhibition of convection is caused by a stationary and uniform magnetic field parallel to the gravity field. The magnetically-inert suspended particles are not directly influenced by the magnetic field but are influenced indirectly by the magnetically responding carrier fluid in which they are suspended. A linear stability analysis of the system is performed. The Rayleigh–Ritz technique is used to obtain the eigenvalues. The influence of various parameters on the onset of convection has been analysed. Six different reference steady-state temperature profiles are considered and their comparative influence on onset is discussed. Treating Marangoni number as the critical parameter it is shown that any particular infinitesimal disturbance can be stabilized with a sufficiently strong magnetic field. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classical electrically conducting fluid layer without suspended particles. The critical wave number is found to be insensitive to the changes in the suspension parameters but sensitive to the changes in the Chandrasekhar number. The problem has possible space applications.

An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity modulation

The article deals with nonlinear thermal instability problem of double-diffusive convection in a porous medium subjected to temperature/gravity modulation. Three types of imposed time-periodic boundary temperature (ITBT) are considered. The effect of imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent periodic part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time-periodic part. Using power series expansion in terms of the amplitude of modulation, which is assumed to be small, the problem has been studied using the Ginzburg–Landau amplitude equation. The individual effects of temperature and gravity modulation on heat and mass transports have been investigated in terms of Nusselt number and Sherwood number, respectively. Further the effects of various parameters on heat and mass transports have been analyzed and depicted graphically.

Unsteady convective diffusion with heterogeneous chemical reaction in a plane-Poiseuille flow of a micropolar fluid

The paper examines the influence of heterogeneous chemical reaction on the exchange coefficient, convective coefficient and diffusive coefficient arising in the study of dispersion in a micropolar fluid flow. The first of the three coefficients emanates exclusively from the incorporation of the catalytic wall reaction. The wall reaction also influences the other two coefficients. The effect of wall-catalysed reaction on dispersion is investigated against the background of the no-reaction problem. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when reaction is absent. The Taylor [1] and Aris [2] regimes of dispersion for the present problem are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical study that might be undertaken considering non-asymptotic all-time analysis. The problem may find application in industries letting away waste into the environment, in crude oil conveyance, in chromatography and in extracorporeal biomechanical problems.

Effects of Time-Periodic Thermal Boundary Conditions and Internal Heating on Heat Transport in a Porous Medium

The effects of time-periodic boundary temperatures and internal heating on Nusselt number in the Bénard–Darcy convective problem has been considered. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small. By performing a weakly non-linear stability analysis, the Nusselt number is obtained in terms of the amplitude of convection, which is governed by the non-autonomous Ginzburg–Landau equation, derived for the stationary mode of convection. The effects of internal Rayleigh number, amplitude and frequency of modulation, thermo-mechanical anisotropies, and Vadasz number on heat transport have been analyzed and depicted graphically. Increasing values of internal Rayleigh number results in the enhancement of heat transport in the system. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system.

An analytical study of linear and non-linear convection in Boussinesq–Stokes suspensions

The Rayleigh–Benard situation in Boussinesq–Stokes suspensions is investigated using both linear and non-linear stability analyses. The linear and non-linear analyses are based on a normal mode solution and minimal representation of double Fourier series, respectively. The effect of suspended particles on convection is delineated against the background of the results of the clean fluid. The realm of non-linear convection warrants the quantification of heat transfer and this has been achieved on the Rayleigh–Nusselt plane. Possibility of aperiodic convection is discussed.

Linear and non-linear analyses of convection in a micropolar fluid occupying a porous medium

Abstract Linear and weakly non-linear analyses of convection in a micropolar fluid occupying a high-porosity medium are performed. The Brinkman–Eringen momentum equation is considered. The linear and non-linear analyses are, respectively, based on the normal mode technique and truncated representation of Fourier series. The linear theory for a two-phase system reiterates that the preferred mode of convection is stationary as in the case of a single-phase system. An autonomous system of differential equations representing cellular convection arising in the study is considered to analyse the critical points. The Nusselt number is obtained as a function of micropolar and porous medium parameters.

Rayleigh-Benard convection in a viscoelastic fluid-filled high-porosity medium with nonuniform basic temperature gradient

The qualitative effect of nonuniform temperature gradient on the linear stability analysis of the Rayleigh-Benard convection problem in a Boussinesquian, viscoelastic fluid-filled, high-porosity medium is studied numerically using the single-term Galerkin technique. The eigenvalue is obtained for free-free, free-rigid, and rigid-rigid boundary combinations with isothermal temperature conditions. Thermodynamics and also the present stability analysis dictates the strain retardation time to be less than the stress relaxation time for convection to set in as oscillatory motions in a high-porosity medium. Furthermore, the analysis predicts the critical eigenvalue for the viscoelastic problem to be less than that of the corresponding Newtonian fluid problem.

On double-diffusive convection and cross diffusion effects on a horizontal wavy surface in a porous medium

An analysis of double diffusive convection induced by a uniformly heated and salted horizontal wavy surface in a porous medium is presented. The wavy surface is first transformed into a smooth surface via a suitable coordinate transformation and the transformed nonsimilar coupled nonlinear parabolic equations are solved using the Keller box method. The local and average Nusselt and Sherwood numbers are given as functions of the streamwise coordinate and the effects of various physical parameters are discussed in detail. The effects of the Lewis number, buoyancy ratio, and wavy geometry on the dynamics of the flow are studied. It was found, among other observations, that the combined effect of Dufour and Soret parameters is to reduce both heat and mass transfer.MSC:34B15, 65N30, 76M20.