Abstract:
A steady two dimensional MHD convective flow of an incompressible viscous and electrically conducting fluid past a continuously moving porous vertical plate with Soret and Dufour effects is analyzed. A magnetic field of uniform strength is assumed to be applied transversely to the direction of the main flow. The solutions for thevelocity field, temperature and concentrations are performed for a wide range of the governing flow parameters viz the Soret number, Prandtl number, Schmidt number, Grashof number for heat transfer, Dufour number, Solutal Grashof number and Hartmann number. The effects of these flow parameters on the velocity, temperature, concentration, skin friction coefficient and Sherwood number are discussed graphically.

Abstract:
We analyse the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium in presence of heat source. An exact solution of the governing equations in dimensionless form is obtained by Laplace transform technique in ramped temperature case. To compare the results obtained in this case with that of isothermal plate, the exact solution of the governing equations is also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases. 1. Introduction The study of convective heat transfer from a solid body with different geometries embedded in a fluid saturated porous medium has varied and wide applications in many areas of science and engineering such as geothermal reservoirs, drying of porous solids, chemical catalytic reactors, thermal insulators, nuclear waste repositories, heat exchanger devices, enhanced oil and gas recovery, and underground energy transport. An investigation of an influence of magnetic field on viscous incompressible flow of electrically conducting fluid has its importance in many applications such as extrusion of plastics in the manufacture of rayon and nylon, paper industry, and textile industry and in different geophysical cases and so forth. Keeping the above applications, Krishna et al. [1] studied the effects of thermal radiation and chemical reaction on the steady two-dimensional stagnation point flow of a viscous incompressible electrically conducting fluid over a stretching surface with suction in the presence of heat generation. The combined effects of rotation and radiation on MHD flow past an impulsively started vertical plate with variable temperature were studied by Rajput and Kumar [2]. Sandeep and Sugunamma [3] discussed the effects of inclined magnetic field on unsteady free convection flow of a dusty viscous fluid between two infinite flat plates filled by a porous medium. Jha and Ajibade [4] have studied the unsteady free convective Couette flow of heat generating/absorbing fluid. Saxena and Dubey [5] discussed the unsteady MHD heat and mass transfer free convection flow of polar fluids past a vertical moving porous plate in a porous medium with heat generation and thermal diffusion. The radiation effects on MHD Couette flow with heat transfer between two parallel plates have been examined by Mebine [6]. Vijayalakshmi [7] have studied radiation effects on free convection flow past an impulsively

Abstract:
This paper deals with the problem of a steady two dimensional boundary layer flow of an incompressible, viscous and electrically conducting fluid, with heat and mass transfer, past a moving vertical porous plate in the presence of uniform magnetic field applied normal to the plate, taking into account the effects of variable viscosity and viscous dissipation. The equations of motion, heat and mass transfer are transformed into a system of coupled ordinary differential equations in the non-dimensional form which are solved numerically. The effects of various parameters such as Prandtl number, Eckert number and Schmidt number on the velocity, temperature and concentration fields are discussed with the help of graphs.

Abstract:
The flow of a viscous incompressible electrically conducting fluid on a continuous moving flat plate in presence of uniform transverse magnetic field, is studied. The flat plate which is continuously moving in its own plane with a constant speed is considered to be isothermally heated. Assuming the fluid viscosity as an inverse linear function of temperature, the nature of fluid velocity and temperature in presence of uniform magnetic field are shown for changing viscosity parameter at different layers of the medium. Numerical solutions are obtained by using Runge-Kutta and Shooting method. The coefficient of skin friction and the rate of heat transfer are calculated at different viscosity parameter and Prandt l number. .

Abstract:
The present paper is concerned with the analysis of inherent irreversibility in hydromagnetic boundary layer flow of variable viscosity fluid over a semi-infinite flat plate under the influence of thermal radiation and Newtonian heating. Using local similarity solution technique and shooting quadrature, the velocity and temperature profiles are obtained numerically and utilized to compute the entropy generation number. The effects of magnetic field parameter, Brinkmann number, the Prandtl number, variable viscosity parameter, radiation parameter and local Biot number on the fluid velocity profiles, temperature profiles, local skin friction and local Nusselt number are presented. The influences of the same parameters and the dimensionless group parameter on the entropy generation rate in the flow regime and Bejan number are calculated, depicted graphically and discussed quantitatively. It is observed that the peak of entropy generation rate is attained within the boundary layer region and plate surface act as a strong source of entropy generation and heat transfer irreversibility.

Abstract:
The steady, laminar boundary layer flow with a convective boundary condition, to a continuously moving flat plate is studied taking into account the variation of viscosity with temperature in the presence of a magnetic field, heat generation and thermal radiation. The fluid viscosity is assumed to vary as a linear function of temperature. The resulting, governing equations are non-dimensionalized and transformed using a similarity transformation and then solved numerically by sixth order Runge-Kutta method alongside with shooting method. Comparison with previously published work is performed and there was a perfect agreement at large value of the Biot number. A parametric study of all the embedded flow parameters involved is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the skin-friction parameter and the Nusselt number is illustrated graphically to show typical trend of the solutions. It is worth pointing out that, when the variation of viscosity with temperature is strong in the presence of the effect of a magnetic field, radiation, heat generation, the results of the present work are completely different from those that studied the same problem in the absence of magnetic field, thermal radiation and the heat generation. It is interesting to note that higher the values of Prandtl number lesser the effects of Biot number and the magnetic field intensity.

Abstract:
The effect of different types of nanoparticles on the heat transfer from a continuously moving stretching surface in a concurrent, parallel free stream has been studied. The stretching surface is assumed to have power-law velocity and temperature. The governing equations are converted into a dimensionless system of equations using nonsimilarity variables. Resulting equations are solved numerically for various values of flow parameters. The effect of physical quantities on the temperature profiles is discussed in detail. 1. Introduction The thermal management of continuously moving surfaces in a quiescent or flowing fluid plays a major role in determining the quality of final products and production rates during many manufacturing processes such as extrusion of metal or polymer sheets, wire drawing, glass fiber production, continuous casting, and paper production. Since the pioneering work of Sakiadis [1], considerable attention has been given to the flow and heat transfer over a continuously moving surface by many researchers. Elbashbeshy and Bazid [2] investigated the heat transfer over an unsteady stretching surface. This study reveals that the rate of the heat transfer increases with the increase of the unsteadiness parameter and Prandtl number. Tsou et al. [3] obtained analytical and experimental results for the flow and heat transfer over a continuously moving surface. Gupta and Gupta [4] analyzed the heat and mass transfer in the flow over a porous stretching sheet. Chen [5] studied the flow and heat transfer from a heated flat surface continuously moving in a parallel free stream of non-Newtonian fluid and found that the heat transfer rate increases with an increase in the ratio of the free stream velocity to the wall velocity. Devi and Thiyagarajan [6] investigated the hydromagnetic flow and heat transfer over a nonlinearly stretching sheet with variable surface temperature. Hassanien et al. [7] studied the boundary layer solutions for the flow and heat transfer over a continuously flat surface moving in a parallel free stream. Al-Sanea and Ali [8] investigated the effect of extrusion slit on the flow and heat transfer from a continuously moving material with suction or injection. Cortell [9] performed a numerical analysis for the flow and heat transfer in a viscous fluid over a nonlinearly stretching sheet. It is well known that conventional heat transfer fluids used in the above-mentioned studies have low thermal properties. Rapid developments in modern manufacturing techniques allow for the production of nanosized metallic or nonmetallic

Abstract:
This research focuses on the issue of modeling continuously moving regions and a new approach called constraint rectangle is presented. According to the new approach, a continuously moving region is represented as a set of constraint rectangles and both x-dimension and y-dimension of each constraint rectangle are functions of time. We develop algorithms to represent a continuously moving region into constraint rectangles and prove the correctness of the algorithms. Furthermore, a prototype is implemented to demonstrate the rightness and effectiveness of the new approach. The experiment results show the constraint rectangle model is not only able to represent continuously moving regions effectively and practically, but also able to support historical and future queries on continuously moving regions.

Abstract:
In the framework of a cylindrical symmetry model for convective motions in the asthenosphere, a new profile for the viscosity coefficient depending on depth is suggested here. The numerical elaboration of the above mentioned model leads to interesting results which fit well with experimental observations. In particular these continuously varying viscosity solutions probably describe the convective motions within the Earth better than simple constant viscosity solutions. Consequently the temperature values seem to be a realistic representation of the possible thermal behaviour in the upper mantle.