SOLUTION OF THE RAYLEIGH PROBLEM FOR A POWER-LAW NON-NEWTONIAN CONDUCTING FLUID VIA GROUP METHOD

An investigation is made of the magnetic Rayleigh problem where a semi_infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non_Newtonian power law fluid of infinite extent. The solution of this highly non_linear problem is obtained by means of the transformation group theoretic approach. The one_parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.

Instability in Three-Dimensional Magnetohydrodynamic Flows of an Electrically Conducting Fluid

The three-dimensional instability of an electrically conducting fluid between two parallel plates affected by an imposed transversal magnetic field is numerically investigated by a Chebyshev collocation method. The QZ method is utilized to obtain neutral curves of the linear instability. The details of instability are analyzed by solving the generalized Orr-Sommerfeld equation. The critical Reynolds number Rec, the stream-wise and span-wise critical wave numbers αc and βc are obtained for a wide range of Hartmann number Ha. The effects of Lorentz force and span-wise perturbation on three-dimensional instability are investigated. The results show that magnetic field would suppress the instability and critical Reynolds number tends to be larger than that for two-dimensional instability.

Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel

This work reports the effects of magnetic field on an electrically conducting fluid with low electrical conductivity flowing in a smooth expanded channel. The governing nonlinear magnetohydrodynamic （MHD） equations in induction- free situations are derived in the framework of MHD approximations and solved numerically using the finite-difference technique. The critical values of Reynolds number （based on upstream mean velocity and channel height） for symmetry breaking bifurcation for a sudden expansion channel （1：4） is about 36, whereas the value in the case of the smooth expansion geometry used in this work is obtained as 298, approximately （non-magnetic case）. The flow of an electrically conducting fluid in the presence of an externally applied constant magnetic field perpendicular to the plane of the flow is reduced significantly depending on the magnetic parameter （M）. It is expansion （1：4） is about 475 for the magnetic parameter M found that the critical value of Reynolds number for smooth = 2. The separating regions developed behind the smooth symmetric expansion are decreased in length for increasing values of the magnetic parameter. The bifurcation diagram is shown for a symmetric smoothly expanding channel. It is noted that the critical values of Reynolds number increase with increasing magnetic field strength.

KINEMATICAL FORCE-FREE FIELDS OF A MAGNETIC ARCH

Basic equations are derived for kinematical force-free fields of a magnetic arch in a perfect conducting fluid, and the stationary and unsteady similarity solutions are discussed in this paper.

Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour efects

In this paper, we study the unsteady coupled heat and mass transfer of two-dimensional MHD fluid over a moving oscillatory stretching surface with Soret and Dufour effects. Viscous dissipation effects are adopted in the energy equation. A uniform magnetic field is applied vertically to the flow direction. The governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method （HAM）. The effects of some physical parameters such as magnetic parameter, Dufour number, Soret number, the Prandtl num- ber and the ratio of the oscillation frequency of the sheet to its stretching rate on the flow and heat transfer characteristics are illustrated and analyzed.

Application of Heterogeneous Composite Model with Consideration of Stress Sensitive in Low Permeability Gas Reservoir

Stress sensitivity is a key factor affecting the productivity of single wells in low permeability gas reservoirs. A well test model for heterogeneous composite gas reservoirs under the influence of stress-sensitive effects was established. Based on the theoretical model, the well test was designed by gradually increasing the pressure difference. The relationship between abnormal high pressure and reservoir stress sensitivity was analyzed. Theoretical research shows that stress sensitivity will cause permeability damage during the production process, and the pressure drop test curve shows that the physical properties of the reservoir have gradually deteriorated. The pressure recovery test curve shows that the physical properties of the reservoir are getting better. Field practice shows that stress sensitivity is related to the formation of abnormally high pressure in the formation without considering the micro-cracks in the formation. Stress-sensitive reservoirs are generally unbalanced and compacted due to overpressure, for fluid expansion/conduction overpressure in Ledong Area. For these reservoirs, there is almost no stress sensitivity. The research results have significance for guiding the design and data interpretation of stress-sensitive reservoir.

Electrical conductivity of hydrous silicate melts and aqueous fluids: Measurement and applications

The combination of magnetotelluric survey and laboratory measurements of electrical conductivity is a powerful approach for exploring the conditions of Earth's deep interior. Electrical conductivity of hydrous silicate melts and aqueous fluids is sensitive to composition, temperature, and pressure, making it useful for understanding partial melting and fluid activity at great depths. This study presents a review on the experimental studies of electrical conductivity of silicate melts and aqueous fluids, and introduces some important applications of experimental results. For silicate melts, electrical conductivity increases with increasing temperature but decreases with pressure. With a similar Na^+ concentration, along the calc-alkaline series electrical conductivity generally increases from basaltic to rhyolitic melt, accompanied by a decreasing activation enthalpy. Electrical conductivity of silicate melts is strongly enhanced with the incorporation of water due to promoted cation mobility. For aqueous fluids, research is focused on dilute electrolyte solutions. Electrical conductivity typically first increases and then decreases with increasing temperature, and increases with pressure before approaching a plateau value. The dissociation constant of electrolyte can be derived from conductivity data. To develop generally applicable quantitative models of electrical conductivity of melt/fluid addressing the dependences on temperature, pressure, and composition, it requires more electrical conductivity measurements of representative systems to be implemented in an extensive P-T range using up-to-date methods.

Heat Transfer Analysis of MHD Power Law Nano Fluid Flow through Annular Sector Duct

Flow and heat transfer analysis of an electrically conducting MHD power law nano fluid is carried out through annular sector duct,under the influence of constant pressure gradient.Two types of nano particles(i.e.Cu and TiO2)are used in power law nano fluid.Strongly implicit procedure,(SIP)is used to simulate the discretized coupled algebraic equations.It has been observed that volume fraction of nano particles,ϕand magnetic field parameter,Ha are favourable for the heat transfer rate,however,both resist the fluid flow.Impact of applied uniform transverse magnetic field exceeds in the case of shear thickening fluids(i.e.n>1)by increasing the value of Ha as compared to that in shear thinning fluids(i.e.n<1).Therefore,enhancement in heat transfer rate is comparably more in shear thickening fluid.Furthermore,comparable limiting case study with published result is also carried out in this research paper.