Abstract:
In this paper, we make an initial value investigation of the unsteady flow of incompressible viscous fluid between two rigid non-conducting rotating parallel plates bounded by a porous medium under the influence of a uniform magnetic field of strength H0 inclined at an angle of inclination α with normal to the boundaries taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate while the lower plate is at rest. The flow in the porous medium is governed by the Brinkman’s equations. The exact solution of the velocity in the porous medium consists of steady state and transient state. The time required for the transient state to decay is evaluated in detail and the ultimate quasi-steady state solution has been derived analytically. Its behaviour is computationally discussed with reference to the various governing parameters. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed.

Abstract:
This communication investigates the effect of free convection on the heat transfer and the flow through a highly porous medium bounded by two vertical parallel porous plates. It is assume that free stream velocity oscillates in times about a constant mean. Assuming periodic temperature at the moving plate, the approximate solutions for velocity field, emperature field, skin-friction and the rate of heat transfer are obtained and discussed with the help of graphs and tables.

Abstract:
Unsteady hydromagnetic convective flow of a viscous incompressible electrically conducting heat generating/absorbing fluid within a parallel plate rotating channel in a uniform porous medium under slip boundary conditions is investigated. Exact solution of the governing equations for fully developed flow is obtained in closed form. Expressions for skin friction due to primary and secondary flows and Nusselt number at the plate = 1are also derived. Asymptotic behavior of the solution for the fluid velocity is analyzed for large values of frequency parameter ù to gain some physical insight into the flow pattern. The numerical values of the primary and secondary velocities and fluid temperature are displayed graphically versus channel width variable for various values of pertinent flow parameters whereas numerical values of skin frictions due to primary and secondary flows and Nusselt number at the plate =1 are presented in tabular form for different values of pertinent flow parameters.

Abstract:
A self-similar solution of unsteady mixed convection flow on a rotating cone embedded in a porous medium saturated with a rotating fluid in the presence of the first and second orders resistances has been obtained. It has been shown that a self-similar solution is possible when the free stream angular velocity and the angular velocity of the cone vary inversely as a linear function of time. The system of ordinary differential equations governing the flow has been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. Both prescribe wall temperature and prescribed heat flux conditions are considered. Numerical results are reported for the skin friction coefficients, Nusselt number and Sherwood number. The effect of various parameters on the velocity, temperature and concentration profiles are also presented here.

Abstract:
The present study the free convection in unsteady Couette flow of a viscous incompressible fluid confined between two vertical parallel plates in the presence of thermal radiation with heat source in the presence of uniform magnetic field is presented. The flow is induced by means of Couette motion and free convection currents occurring as a result of application of constant heat flux on the wall with a uniform vertical motion in its own plane while constant temperature on the stationary wall. The fluid considered here is a gray, absorbing-emitting but non-scattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the analysis. The dimensionless governing partial differential equations are solved by using regular perturbation technique. The results for the velocity, temperature and the skin-friction are shown graphically. The effects of different parameters are discussed.

Abstract:
The present discussion deals with the study of an unsteady flow and heat transfer of a dusty fluid through a rectangular channel under the influence of pulsatile pressure gradient along with the effect of a uniform magnetic field. The analytical solutions of the problem are obtained using variable separable and Fourier transform techniques. The graphs are drawn for the velocity fields of both fluid and dust phases under the effect of Reynolds number. Further, changes in the Nusselt number are shown graphically, and, on the basis of these, the conclusions and discussions are given. 1. Introduction The concept of an unsteady flow and heat transfer of a dusty fluid has a wide range of applications in refrigeration, air conditioning, space heating, power generation, chemical processing, pumps, accelerators, nuclear reactors, filtration and geothermal systems, and so forth. One common example of heat transfer is the radiator in a car, in which the hot radiator fluid is cooled by the flow of air over the radiator surface. On this basis many mathematicians were attracted by this field. Saffman [1] has formulated the governing equations for the flow of dusty fluid and has discussed the stability of the laminar flow of a dusty gas in which the dust particles are uniformly distributed. Datta et al. [2] have obtained the solution of unsteady heat transfer to pulsatile flow of a dusty viscous incompressible fluid in a channel. Heat transfer in unsteady laminar flow through a channel was analyzed by Ariel [3]. Ghosh et al. [4] have made the solution for hall effects on MHD flow in a rotating system with heat transfer characteristics. Ezzat et al. [5] analyzed a space approach to the hydromagnetic flow of a dusty fluid through a porous medium. Some researchers like Anjali Devi and Jothimani [6] have discussed the heat transfer in unsteady MHD oscillatory flow. Further, Malashetty et al. [7] have investigated the convective magnetohydrodynamic two phase flow and heat transfer of a fluid in an inclined channel. Palani and Ganesan [8] have discussed the heat transfer effects on dusty gas flow past a semi-infinite inclined plate. Attia [9] has investigated an unsteady MHD Couette flow and heat transfer of dusty fluid with variable physical properties. Unsteady hydromagnetic flow and heat transfer from a nonisothermal stretching sheet immersed in a porous medium was discussed by Chamkha [10]. Mishra et al. [11] have studied the two-dimensional transient conduction and radiation heat transfer with temperature-dependent thermal conductivity. MHD flow and heat transfer of a

Abstract:
Unsteady hydromagnetic Couette flow of a viscous, incompressible and electrically conducting fluid between two infinitely long parallel porous plates, taking Hall current into account, in the presence of a transverse magnetic field is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel. Magnetic lines of force are assumed to be fixed relative to the moving plate. Solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. Asymptotic behavior of the solution valid for small and large values of time t is analyzed to gain some physical insight into the flow pattern. Numerical values of the primary and secondary velocities are displayed graphically versus non-dimensional channel width variable η for various values of Hall current parameter m, magnetic parameter M2 , suction/injection parameter S and time t whereas the numerical values of shear stress at the moving plate due to primary and secondary flows are presented in tabular form for different values of m, M2 , S and t.

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:
We discussed the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate. The flow in the clean fluid region is governed by Navier-Stoke’s equations while in the porous bed the equations are based on Darcy-Lapwood model. The exact solutions of velocity in the clean fluid and the porous medium consist of steady state and transient state. The time required for the transient state to decay is evaluated in detail and ultimate quasi-steady state solution has been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters. The shear stresses on the boundaries and the mass flux are also obtained analytically and their behaviour is computationally discussed.

Abstract:
We consider the energy equation of an Arrheniusly reacting flow through a porous medium with variable permeability. A self similar solution was obtained for the unsteady case of the flow using shooting numerical method. We report the effects of the coefficient of the variable permeability and the Frank-Kamenetskii parameter on the temperature field of the system.