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

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. © 1995

Unicellular unsteady Rayleigh�Bénard convection in Newtonian liquids and Newtonian nanoliquids occupying enclosures: New findings

Rayleigh�Bénard convection in Newtonian liquids and Newtonian nanoliquids occupying rectangular, square and slender vertical enclosures is studied analytically in the paper using Buongiorno model with supplementary information on thermophysical properties of nanoliquids provided by phenomenological laws and mixture theory. The five-mode Lorenz model is derived under the assumptions of Boussinesq approximation, small-scale convective motions and some slip mechanisms like Brownian diffusion and thermophoresis. Inertia, Magnus effects, liquid drainage, diffusophoresis and gravity settling are neglected. Using multiscale method the analytically intractable Lorenz model of the problem is converted to a tractable Ginzburg�Landau equation the solution of which helps in quantifying the unsteady heat transport. The Ginzburg�Landau model derived directly from the governing equation is shown to be the same as that obtained via the Lorenz model. This point to the equivalence of the two models. Enhancement of heat transport due to the presence of nanoparticles is also clearly explained. Results on nanoliquids are discussed against the backdrop of Newtonian liquids without nanoparticles. Physical explanation is provided for all parameters� effects on onset and heat transport. The results pertaining to single-phase model are recovered as a limiting case of the present study. © 201

Effect of temperature/gravity modulation on the onset of magneto-convection in weak electrically conducting fluids with internal angular momentum

The effect of time-periodic temperature/gravity modulation at the onset of magneto-convection in weak electrically conducting fluids with internal angular momentum is investigated by making a linear stability analysis. The Venezian approach is adopted in arriving at the critical Rayleigh and wave numbers for small amplitude temperature/gravity modulation. The temperature modulation is shown to give rise to sub-critical motion and gravity modulation leads to delayed convection. An asymptotic analysis is also presented for small and large frequencies. © 1999 Elsevier Science B.V

Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet

We study the MHD flow and also heat transfer in a viscoelastic liquid over a stretching sheet in the presence of radiation. The stretching of the sheet is assumed to be proportional to the distance from the slit. Two different temperature conditions are studied, namely (i) the sheet with prescribed surface temperature (PST) and (ii) the sheet with prescribed wall heat flux (PHF). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The resulting non-linear momentum differential equation is solved exactly. The energy equation in the presence of viscous dissipation (or frictional heating), internal heat generation or absorption, and radiation is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation using a new variable and using the Rosseland approximation for the radiation. The governing differential equations are solved analytically and the effects of various parameters on velocity profiles, skin friction coefficient, temperature profile and wall heat transfer are presented graphically. The results have possible technological applications in liquid-based systems involving stretchable materials. © 2005 Elsevier Ltd. All rights reserved

Effects of nonuniform temperature gradient and magnetic field on the onset of convection in fluids with suspended particles under microgravity conditions

The effects of a nonuniform temp. gradient and magnetic field on the onset of convection driven by surface tension in a horizontal layer of Boussinesq fluid with suspended particles confined between an upper free​/adiabatic boundary and a lower rigid​/isothermal boundary are considered. A linear stability anal. is performed. The microrotation is assumed to vanish at the boundaries. The Galerkin technique is used to obtain the eigenvalues. The effect of various parameters on the onset of convection was analyzed. Six different nonuniform temp. profiles are considered and their comparative effect on onset is discussed. It is obsd. that the elec. conducting fluid layer with suspended particles heated from below is more stable compared to the classical elec. conducting fluid without suspended particles. The crit. wave no. is insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar no. The problem has possible applications in microgravity space situations

Linear and nonlinear electroconvection under AC electric field

Linear and non-linear stability analyses of electroconvection under an AC electric field are investigated using the normal mode method and truncated representation of Fourier series respectively. The principle of exchange of stabilities is shown to be valid and subcritical instability is ruled out. Several qualitative results on stability are discussed on the governing linear autonomous system, and also by using the concept of a self-adjoint operator. Spectral analysis of electroconvection is also made to provide information on the relative dominance of various modes on convection. The quantification of heat transfer is done on the Nusselt number-Rayleigh number plane for steady finite amplitude convection and through time series plots of the Nusselt number for unsteady finite amplitude convection. The effect of the electric number on stream line pattern and Nusselt number is delineated. Time series plots of the amplitudes of thermal conduction and convection are also presented. It is found that the effect of increasing the electric number is to enhance the amplitudes and thereby the heat transport. The sensitive dependence of the solution of the Lorenz system of electroconvection to the choice of initial conditions points to the possibility of chaos. © 2011 Elsevier B.V

Effect of time-periodic Boundary temperatures/body Force on Rayleigh-Benard Convection in a Ferromagnetic Fluid

We discuss the thermal instability in a layer of a ferromagnetic fluid when the boundaries of the layer are subjected to synchronous/asynchronous imposed time-periodic boundary temperatures (ITBT)/ time-periodic body force (TBF). Only infinitesimal disturbances are considered. The Venezian approach is adopted in arriving at the critical Rayleigh and wave numbers for small amplitudes of ITBT. A pertur- bation solution in powers of the amplitude of the applied temperature field is obtained. When the ITBT at the two walls are synchronized then, for moderate frequency values, the role of magnetization in inducing sub-critical instabilities is delineated. A similar role is shown to be played by the Prandtl number. The magnetization parameters and Prandtl number have the opposite effect at large frequencies. The system is most stable when the ITBT is asynchronous. The effect of TBF on the onset of convection is found to be qualitatively similar to the effect of an asynchronous ITBT. Low Prandtl number fluids are shown to be more easily vulnerable to destabilization by TBF compared to very large Prandtl number fluids. The problem has relevance in many ferromagnetic fluid applications wherein regulation of thermal convection is called for

A theoretical study of enhanced heat transfer in nanoliquids with volumetric heat source

Rayleigh�Bénard convection in nanoliquids is studied in the presence of volumetric heat source. The present analytical work concerns twenty nanoliquids. Carrier liquids considered are water, ethylene glycol, engine oil and glycerine and with them five different nanoparticles considered are copper, copper oxide, silver, alumina and titania. Expression for the thermophysical properties of the nanoliquids is chosen from phenomenological laws or mixture theory. Heat source is characterized by an internal nanoliquid Rayleigh number (Formula presented.). Heat source adds to the energy of the system and hence an advanced onset is observed in this case compared to the problem with no heat source. In the case of heat sink, however, heat is drawn from the system leading to delay in onset. The individual effect of all the nanoparticles is to advance convection. Enhanced heat transport situation is observed in each of the nanoliquids with engine-oil-silver transporting maximum heat and water-titania the least. Additional Fourier modes are found not to have any profound effect on the results predicted by minimal modes. The connection between the Lorenz model and the Ginzburg�Landau model is clearly shown in the paper. © 2017 Korean Society for Computational and Applied Mathematic

A Weak Nonlinear Stability Analysis of Double Diffusive Convection with Cross-diffusion in a Fluid-saturated Porous Medium

he effect of “Cross Diffusion” on the linear and nonlinear stability of double diffusive convection in a fluid-saturated porous medium has been studied analytically. In the case of linear theory, the normal mode technique has been used and the condition for the maintenance of “finger” and “diffusive” instabilities have been obtained. It has been found that fingers can form by taking cross diffusion terms of appropriate sign and magnitude even though both components make stabilizing contributions to the net vertical density gradient. It has also been shown that “finger” and “diffusive” instabilities can never occur simultaneously. The nonlinear theory is based on the truncated representation of Fourier series and it has been found that the finite amplitude convection may occur when both initial property gradients are stabilizing. Further, the region of finite amplitude instability always encloses the region of infinitesimal oscillatory instability. The effects of permeability and cross-diffusion terms on the heat and mass transports have also been clearly brought out

Analytical Solution to the MHD Flow of Micropolar Fluid Over a Linear Stretching Sheet

The flow due to a linear stretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions