Effect of Boundary Conditions on the Onset of Thermomagnetic Convection in a Ferrofluid Saturated Porous Medium

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
I. S. Shivakumara ◽  
C. E. Nanjundappa ◽  
M. Ravisha
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Porous Layer ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Lower Boundary ◽  
Fluid Viscosity ◽  
Thermomagnetic Convection ◽  
Upper Boundary

The onset of thermomagnetic convection in a ferrofluid saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated for a variety of velocity and temperature boundary conditions. The Brinkman–Lapwood extended Darcy equation, with fluid viscosity different from effective viscosity, is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-ferromagnetic, while the upper boundary is considered to be either rigid-ferromagnetic or stress-free. The thermal conditions include fixed heat flux at the lower boundary, and a general convective-radiative exchange at the upper boundary, which encompasses fixed temperature and heat flux as particular cases. The resulting eigenvalue problem is solved using the Galerkin technique and also by using regular perturbation technique when both boundaries are insulated to temperature perturbations. It is found that the increase in the Biot number and the viscosity ratio, and the decrease in the magnetic as well as in the Darcy number is to delay the onset of ferroconvection. Besides, the nonlinearity of fluid magnetization has no effect on the onset of convection in the case of fixed heat flux boundary conditions.

Effect of Velocity and Temperature Boundary Conditions on Convective Instability in a Ferrofluid Layer

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
C. E. Nanjundappa ◽  
I. S. Shivakumara
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Biot Number ◽  
Perturbation Technique ◽  
Lower Boundary ◽  
Thermal Conditions ◽  
Regular Perturbation ◽  
Fixed Temperature ◽  
Temperature Boundary ◽  
Upper Boundary

A variety of velocity and temperature boundary conditions on the onset of ferroconvection in an initially quiescent ferrofluid layer in the presence of a uniform magnetic field is investigated. The lower boundary of the ferrofluid layer is assumed to be rigid-ferromagnetic, while the upper boundary is considered to be either rigid-ferromagnetic or stress-free. The thermal conditions include a fixed heat flux at the lower boundary and a general convective, radiative exchange at the upper boundary, which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved using the Galerkin technique and also by the regular perturbation technique when both boundaries are insulated to temperature perturbations. It is observed that an increase in the magnetic number and the nonlinearity of fluid magnetization as well as a decrease in Biot number are to destabilize the system. Further, the nonlinearity of fluid magnetization is found to have no effect on the onset of ferroconvection in the absence of the Biot number.

The Onset of Brinkman-Benard Ferroconvection in a Saturated Porous Layer With Internal Heat Generation

2010 ◽  
Author(s):  
C. E. Nanjundappa ◽  
H. N. Prakash
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Lower Boundary ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Darcy Number ◽  
Internal Heat Generation ◽  
Fluid Viscosity ◽  
Thermomagnetic Convection ◽  
Saturated Porous Layer

The effect of internal heat generation on the criterion for the onset of thermomagnetic convection in a horizontal ferrofluid saturated porous layer in the presence of a uniform magnetic field is studied using the Brinkman-Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid – insulating and the upper surface is free and subject to the general thermal condition. The resulting eigenvalue problem is solved numerically using the Galerkin method with the Rayleigh number as the eigenvalue. The effect of increase in the value of dimensionless internal heat source strength Ns, magnetic number M1 and the non-linearity of fluid magnetization parameter M3 is to hasten, while increase in the value of inverse of Darcy number Da−1, viscosity ratio Λ, Biot number Bi and magnetic susceptibility χ is to delay the onset of thermomagnetic convection in a ferrofluid saturated porous layer. Further, increase in the value of Bi, Da−1 and Ns as well as decrease in Λ M1> and M3 is to diminish the dimension of convection cells.

The effects of thermal conditions on the cell sizes of two-dimensional convection

1994 ◽  
Vol 281 ◽  
pp. 33-50 ◽  
Author(s):  
Masaki Ishiwatari ◽  
Shin-Ichi Takehiro ◽  
Yoshi-Yuki Hayashi
Keyword(s):  
Heat Flux ◽  
Lower Boundary ◽  
Thermal Conditions ◽  
Heat Fluxes ◽  
Internal Cooling ◽  
Two Dimensional ◽  
Numerical Integrations ◽  
The Difference ◽  
Convective Cells ◽  
Upper Boundary

The effects of thermal conditions on the patterns of two-dimensional Boussinesq convection are studied by numerical integration. The adopted thermal conditions are (i) the heat fluxes through both upper and lower boundaries are fixed, (ii) the same as (i) but with internal cooling, (iii) the temperature on the lower boundary and the heat flux through the upper boundary are fixed, (iv) the same as (iii) but with internal cooling, and (v) the temperatures on both upper and lower boundaries are fixed. The numerical integrations are performed with Ra = 104 and Pr = 1 over the region whose horizontal and vertical lengths are 8 and 1, respectively.The results confirm that convective cells with the larger horizontal sizes tend to form under the conditions where the temperature is not fixed on any boundaries. Regardless of the existence of internal cooling, one pair of cells spreading all over the region forms in the equilibrium states. On the other hand, three pairs of cells form and remain when the temperature on at least one boundary is fixed. The formation of single pairs of cells appearing under the fixed heat flux conditions shows different features with and without internal cooling. The difference emerges as the appearance of a phase change, whose existence can be suggested by the weak nonlinear equation derived by Chapman & Proctor (1980).

Linear and non-linear analyses of double-diffusive-Chandrasekhar convection coupled with cross-diffusion in micropolar fluid over saturated porous medium

2020 ◽  
Vol 17 (1) ◽  
pp. 211-236
Author(s):  
Maria Anncy ◽  
Thadathil Varghese Joseph ◽  
Subbarama Pranesh
Keyword(s):  
Porous Medium ◽  
Micropolar Fluid ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Critical Rayleigh Number ◽  
Series Representation ◽  
Content Type ◽  
Cross Diffusion ◽  
Non Linear ◽  
Double Diffusive

PurposeThe problem aims to find the effects of coupled cross-diffusion in micropolar fluid oversaturated porous medium, subjected to Double-Diffusive Chandrasekhar convection.Design/methodology/approachNormal mode and perturbation technique have been employed to determine the critical Rayleigh number. Non-linear analysis is carried out by deriving the Lorenz equations using truncated Fourier series representation. Heat and Mass transport are quantified by Nusselt and Sherwood numbers, respectively.FindingsAnalysis related to the effects of various parameters is plotted, and the results for the same are interpreted. It is observed from the results that the Dufour parameter and Soret parameter have an opposite influence on the system of cross-diffusion.Originality/valueThe effect of the magnetic field on the onset of double-diffusive convection in a porous medium coupled with cross-diffusion in a micropolar fluid is studied for the first time.

Experimental Study on the Identification of the Saturation of a Porous Media through Thermal Analysis

2014 ◽  
Vol 611-612 ◽  
pp. 1576-1583
Author(s):  
Maxime Villière ◽  
Sébastien Guéroult ◽  
Vincent Sobotka ◽  
Nicolas Boyard ◽  
Joel Breard ◽  
...  
Keyword(s):  
Thermal Analysis ◽  
Heat Flux ◽  
Porous Medium ◽  
Thermophysical Properties ◽  
Saturated Porous Medium ◽  
Homogenization Method ◽  
Saturation Curve ◽  
Mechanisms Of Formation ◽  
Mechanical Performances ◽  
The One

Resin Transfer Molding (RTM) is among the most commonly used fabrication processes for producing high quality and complex composite structural parts. RTM process consists of placing a dry fibrous preform into a mold cavity. A liquid resin is subsequently injected into that cavity. The consolidation of the part is then obtained by crosslinking in case of a thermosetting resin or by crystallization in case of thermoplastic one. Voids can be created in the porous medium during the flow of the resin. Presence of residual voids in the composite part at the end of the filling drastically affect mechanical performances. Even if several authors have contributed to a better understanding and modeling of the mechanisms of formation and transport of voids during injection, few experimental approaches allowed a direct measurement of the saturation curve. The aim of this study is then to identify the saturation of a fibrous preform by a liquid through thermal analysis. To address this issue, an experimental bench that allows the injection of a fluid into a textile preform has been used. This apparatus combines the measurement of temperatures and wall heat flux densities at several locations. A simplified modeling of the filling front has been performed with FEM using Comsol Multiphysics™. The saturation curve is modeled using several geometric parameters. Saturation is taken into account through the evolution of thermophysical properties. Effective thermophysical properties of the dry and completely-saturated porous medium in transverse and longitudinal directions have been measured by several methods, and their results have been then cross-checked and compared with good accuracy. The evolution between these two states has been modeled. A particular attention has been paid for the modeling of the transverse thermal conductivity. This parameter has been modeled using a periodic homogenization method as a function of the micro- and macro-saturation. The saturation curve parameters are determined by minimizing the cost function defined as the square difference between the measured and computed heat flux. The obtained saturation curve is finally compared with the one measured by a conductometric sensor.

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