Unsteady MHD flow of viscous and second grade fluids in a porous medium

In this thesis, the unsteady magnetohydrodynamic (MHD) free convection flows of viscous and second grade fluids past an infinite inclined plate in a porous medium are studied. These viscous and second grade fluids are under the conditions of ramped wall temperature and isothermal plate. Analytic solutions are developed by using Laplace transform technique. The main finding of this thesis is to determine the expressions of exact solutions for velocity, temperature and concentration profiles. All these profiles are graphically plotted for various physical parameters such as radiation, heat absorption, porosity, rotation and second grade parameters. The results show that when temperature decreases, high radiation and heat absorption occurs which consequently decreases the velocity. For larger values of magnetic parameter, the fluid velocity decreases. The velocity is found to increase with increasing values of the porosity parameter. It is also observed that when the second grade parameter increases, the velocity shows an oscillating behavior where the velocity first decreases and then increases. An interesting result for the velocity is observed from the comparison of ramped wall temperature and isothermal. It is found that fluid velocity retarded in the case of ramped wall temperature compared to isothermal case. In limiting cases, the present solutions are reduced in order to compare with existing results. As expected, the results are found identical, verifying the validity of the obtainable solutions. The numerical results of skin-friction, Nusselt number and Sherwood number are also computed and displayed in tables, and also analyzed in details

Exact solutions for unsteady MHD free convection flow with time dependent shear stress

In this paper, the effects of MHD on unsteady free convection flow with time dependent shear stress are analyzed. The effects of thermal radiation and porosity on the flow are also studied. Closed-form solutions in general form are obtained by using the Laplace transform technique. The obtained results for velocity and temperature are found to satisfy all the imposed initial and boundary conditions and can be reduced to known solutions from the literature as limiting cases. The velocity profile is presented as a sum of convective and mechanical parts. The effects of shear stress and effective Prandtl number on velocity as well as temperature profiles are presented graphically and discussed in details

Stokes' second problem for rotating MHD flow of a maxwell fluid in a porous medium

An analysis is presented to establish the exact solution of Stokes' second problem for magnetohydrodynamic (MHD) rotating flows of Maxwell fluid in a porous medium. Based on modified Darcy's law the expressions for dimensionless velocity are obtained by using Laplace transform method. The derived steady and transient solutions satisfying the involved differential equations and imposed boundary and initial conditions. The influence of various parameters on the velocity has been analyzed in graphs and discussed

Transient Axisymmetric Flows of Casson Fluids with Generalized Cattaneo’s Law over a Vertical Cylinder

Unsteady axial symmetric flows of an incompressible and electrically conducting Casson fluid over a vertical cylinder with time-variable temperature under the influence of an external transversely magnetic field are studied. The thermal transport is described by a generalized mathematical model based on the time-fractional differential equation of Cattaneo’s law with the Caputo derivative. In this way, our model is able to highlight the effect of the temperature gradient history on heat transport and fluid motion. The generalized mathematical model of thermal transport can be particularized to obtain the classical Cattaneo’s law and the classical Fourier’s law. The comparison of the three models could offer the optimal model of heat transport. The problem solution has been determined in the general case when cylinder surface temperature is described by a function f(t); therefore, the obtained solutions can be used to study different convective flows over a cylinder. In the particular case of surface temperature varying exponentially in time, it is found that fractional models lead to a small temperature rise according to the Cattaneo model

MHD casson fluid with radiative heat and mass transfer past an impulsively moving inclined plate

This paper explores the flow of Casson fluid that passes a moving inclined plate with the influence of double diffusions and radiation, where the fluid is imposed electrically conductive and moves through a porous medium. Several suitable non-dimensional variables are suggested in the model using partial differential equations with initial and boundary conditions. The corresponding non-dimensional governing equations are solved with the help of Laplace transform method. Analytical solutions to momentum, energy, and concentration are obtained, and the expression is in exponential and complementary error functions of Gauss. Finding solutions is limited to similar solutions for previous studies on Casson and viscous fluids as a special case. Computations are performed, where the outcomes are examined for embedded flow parameters

A Study of MHD Free Convection Flow Past an Infinite Inclined Plate

In the present article, we have studied the magnetohydrodynamic (MHD) free convection flow past an infinite inclined plate. In order to explore the effects of velocity, temperature and concentration, Laplace transform technique has been used in this study. This method is adapted to accomplish the analytical solution of governing equation. The impact of various embedded parameter on concentration, velocity and temperature such as chemical reaction, magnetic parameter, radiation and inclination angle has been discussed graphically with numerical results

Heat generation effects on maxwell nanofluid passing over an oscillating vertical plate

This article investigates the flow of Maxwell nanofluid over an oscillating plate with copper nanoparticles and kerosene oil as a base fluid. Novel aspects of heat generation, free convection and thermophysical properties of nanofluids are given special attention in this research. Revised model for passive control of nanoparticle volume fraction at the plate is used in this study. The formulated differential system is solved analytically using Laplace transform technique. The solutions acquired for momentum, temperature and shear stress are greatly influenced with the variation of the volume fraction and Maxwell parameter. The computational software MathCAD-15 has been used for plotting the graphs

The convection of unsteady casson fluid over an infinite inclined isothermal plate

An analytical solution of chemical reaction on unsteady Casson fluid over an infinite inclined isothermal plate has been presented in this article. Laplace transform technique has been used in this study to obtain the results of velocity, temperature and concentration. The analytical solution for governing equations are solved by using this method. The effects of various embedded solution on velocity, temperature and concentration such as chemical reaction, magnetic parameter and radiation has been discussed graphically with numerical results

Analysis of heat transfer in Jeffrey fluid over an infinite vertical plate

This paper studies the heat transfer analysis in Jeffrey fluid over an infinite vertical plate. Using the constitutive equations of Jeffery fluid and thermal radiation in the energy equation, the governing equations are modeled. These equations are first simplified by using appropriate dimensionless variables and then solved analytically by using the Laplace transform technique. Closed form solutions of velocity and temperature are obtained. It is found that they satisfy the governing equations and imposed conditions

Numerical solution on mixed convection heat transfer of ferrofluid over a horizontal circular cylinder

Becomes highly magnetized in the presence of a magnetic field. Classified into two groups which are surfacted ferrofluid (SFF) and ionic ferrofluid (IFF). Composed of 5% volume of small particles ( 3 -15 nm) solid, magnetic, single domain particles coated namely magnetite (Fe3O4), maghemite ( y- Fe2O3), cobalt ferrite (CoFe2O4) and other compounds having iron with a molecular layer of dispersant which suspended in 85% volume of base fluid (water, oil, ethylene glycol, etc.) as well as 10% volume of surfactants (lauric acid, oleic acid, etc.). Exhibits superparamagnetism of magnetic behavior. The understanding of ferrofluid characteristic has greatly helped the researchers in analyzing the ferrofluid flow problems in different geometries when many researchers have experimentally proven the water based magnetite nanofluid can enhance the thermal conductivity