Effect of Gravity Modulation on the Onset of Rayleigh-Bénard Convection in a Weak Electrically Conducting Couple Stress Fluid with Saturated Porous Layer

Sameena Tarannum Sameena Tarannum,S Pranesh S Pranesh

doi:10.17577/ijertv5is010582

Sameena Tarannum Sameena Tarannum, S Pranesh S Pranesh

Open Access

https://doi.org/10.17577/ijertv5is010582

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Abstract

The effect of time-periodic body force (TBF, also called gravity modulation) of small amplitude in a weak electrically conducting couple stress fluid with saturated porous layer is investigated by using a linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number. The Venezian approach is adopted in arriving at the critical Rayleigh and wave number for small amplitudes of TBF. The effect of roles of Couple stress parameter, Hartmann number, Darcy number, Porous parameter and Prandtl number on the onset of convection is studied. It is found that TBF leads to delay in convection. Also the results suggest that instead of taking electrically non-conducting fluid it is better to consider electrically conducting fluid with weak electrical conductivity as this ensures a stable environment in the presence of a magnetic field. The system is most stable with respect to TBF.

Highlights

The Rayleigh- Bénard problem in its simplest form and one that was the earliest to be investigated is the so called infinite layer case
The main objective of this paper is to study the effects of fluctuating gravity in a weak electrically conducting couple stress fluid with a saturated porous layer on the onset of Rayleigh- Bénard convection
Where ⃗ is the velocity, is the constant density, is the pressure, is the density, ⃗ is the gravitational force, ∈ is the porosity, is the couple stress viscosity, is the effective viscosity, is the thermal conductivity, is the ratio of heat capacity, ⃗ is the current density, ⃗ is the magnetic induction vector, k is the permeability of the porous media, is the mean gravity, is the small amplitude of gravity modulation, is the frequency, t is the time, is the temperature, is the coefficient of thermal expansion, is the magnetic conductivity, is the magnetic permeability, ⃗ is the magnetic field

Summary

INTRODUCTION

The Rayleigh- Bénard problem in its simplest form and one that was the earliest to be investigated is the so called infinite layer case. Convection instability in a horizontal porous layer with uniform temperature gradient has been investigated extensively by several authors using Darcy model because of its relevance to variety of situations in science and engineering problems. In “two-phase flow” a liquid and a gas share the void space Typical studies in this field of flow through and over porous layers consider the porous medium to have constant porosity and permeability. The main objective of this paper is to study the effects of fluctuating gravity in a weak electrically conducting couple stress fluid with a saturated porous layer on the onset of Rayleigh- Bénard convection

MATHEMATICAL FORMULATION

LINEAR STABILITY ANALYSIS

RESULTS AND DISCUSSION

CONCLUSION