Heat and Hall Effect of an Oscillating Plate in a Porous Medium

An exact solution of the flow of heat and viscous fluid on a porous plate by using perturbation is obtained for the conjugate problem of an electrically conducting fluid in the presence of strong magnetic field by introducing the Hall currents. The fluid half-space is considered to be porous. Large time solution and effects of porous medium are discussed. It was shown that Hall Effect setup an opposing force which reduces the velocity. Temperature and velocity distributions have been obtained and the effect of various values of nondimensional physical parameters on streamline patterns and skin friction coefficient and Nusselt number are presented and discusse

Effect of Slip Velocity on Oscillatory MHD Flow of Stretched Surface with Radiative Heat Transfer and Variable Suction

The study of unsteady magnetohydrodynamic heat and mass transfer in MHD flow of an incompressible, electrically conducting, viscous fluid past an infinite vertical porous plate along with porous medium of time dependent permeability with radiative heat transfer and variable suction has been made. Analytical solution of an oscillatory boundary layer flow bounded by two horizontal flat plates, one of which is oscillating in its own plane and the other at rest, is developed by asymptotic expansion in order of epsilon for velocity, temperature and magnetic fields. The fluid and the plates are in a state of solid body rotation with constant angular velocity about the z-axis normal to the plates. The structure of the boundary layers is also discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered. A parametric study of all parameters involved was considered, and a representative set of results showing the effect of controlling parameters are illustrated

Entropy Generation in MHD Flow of a Uniformly Stretched Vertical Permeable Surface under Oscillatory Suction Velocity

This paper reports the analytical calculation of the entropy generation due to heat and mass transfer and fluid friction in steady state of a uniformly stretched vertical permeable surface with heat and mass diffusive walls, by solving analytically the mass, momentum, species concentration and energy balance equation, using asymptotic method. The velocity, temperature and concentration profiles were reported and discussed. The influences of the chemical reaction parameter, the thermal and mass Grashof numbers, heat generation/absorption and Hartmann number on total entropy generation were investigated, reported and discussed

MHD Flow of a Uniformly Stretched Vertical Permeable Membrane in the Presence of Zero Order Reaction and Quadratic Heat Generation

We present a magneto - hydrodynamic flow of a uniformly stretched vertical permeable surface undergoing Arrhenius heat reaction. The analytical solutions are obtained for concentration, temperature and velocity fields using an asymptotic approximation, similar to that of Ayeni et al 2004. It is shown that the temperature field and the velocity field depend heavily on the thermal grashof numbers, heat generation/absorption, magnetic induction, chemical reaction parameters and reaction order. It is also established that maximum velocity occurs in the body of the fluid close to the surface and not the surface

Heat Transfer in Boundary Layer Viscolastic Fluid Flow Over Anexponentially Stretching Sheet

The paper presents the study of momentum and heat transfer characteristics in a visco-elastic boundary layer fluid flow over an exponentially stretching continuous sheet with non-uniform heat source. The flow is generated solely by the application of two equal and opposite forces along the x-axis such that stretching of the boundary surface is of exponential order in x and influenced by uniform magnetic field applied vertically. The non-linear boundary layer equation for momentum is converted into ordinary differential equation by means of similarity transformation. Approximate analytical similarity solutions is obtained for the dimensionless stream function and velocity distribution function after transforming the boundary layer equation into Riccati type and solving it sequentially. Heat transfer equation is then solved using Runge-Kutta fourth order method. The accuracy of the analytical solutions is also verified by comparing the solutions obtained to those in literature when Hartmann number is zero. The effects of various physical parameters on velocity, skin friction, temperature and Nusselt number profiles are presented graphically

MHD Free Convection Flow Past an Oscillating Plate in the Presence of Heat Generation/Absorption and Chemical Reaction

The study of unsteady magnetohydrodynamic heat and mass transfer in MHD flow past an infinite vertical oscillating plate through porous medium, taking account of the presence of free convection and mass transfer. The energy and chemical species equations are solved in closed form by Laplace-transform technique and then perturbation expansion for the momentum equation. The results are obtained for velocity, temperature, concentration, Sherwood number, Nusselt number and skin-friction. The effects of various material parameters are discussed on flow variables and presented by graphs. A parametric study of all parameters involved was considered, and a representative set of results showing the effect of heat radiation, reaction parameter, Grashof numbers, Hartmann number and permeability factor were illustrated

Analytical Solution of Mass Transfer Effects on Unsteady Flow Past an Accelerated Vertical Porous Plate with Suction

This paper discussed the analytical solution of unsteady free convection and mass transfer flow past an accelerated infinite vertical porous flat plate with suction, heat generation and chemical species when the plate accelerates in its own plane. The governing equations are solved analytically using perturbation technique. The flow occurrence is described with the help of flow parameters such as porosity parameter (α), Grashof numbers (Grt, Grc), Hartmann’s number (M), heat generation/absorption (β) and reaction parameter (γ). The effects of various parameters are discussed on flow variables and presented by graphs. A parametric study of all parameters involved was considered, and a representative set of results showing the effects of the control parameters were illustrated

Influence of Power-law Exponent on an Unsteady Endothermic Reaction

In [6], the solution of a steady Arrhenious endothermic chemical reaction where the exponential term was reduced to a power-law approximation was studied. A numerical solution obtained using a shooting technique with second order Runge-Kutta scheme showed that the minimum temperature of the reactant increases as the power-law index increases. In this paper, the scope of the work was extended to a solution of an unsteady Arrhenious endothermic reaction using shooting technique [3]. The result showed that the temperature of the reactant depends greatly on the power-law exponent. The temperature of the reactant increases as the power-law exponent α increase, whereas the temperature decreases as the Frank- Kamenestkii parameter β increases

A Contingent Claim Approach to Bank Valuation

In this paper, the model formulated incorporated stochastic variables such as bank loans and deposits as well as some deterministic variables: cash available, depreciation, capital expenditure, tax and costs, comprising variable costs and fixed costs. This paper assumes that the dynamics of bank loans and deposits at time t follow a geometric Brownian motion, therefore, it satisfies certain stochastic differential equations (SDEs) formulated on some probability space. On the other hand, the growth rate μL(t) in loan at time t, growth rate μD(t) in deposit at time t, and the variable cost η(t) at time t are assumed to be driven by mean-reverting Ornstein-Uhlenbeck processes. The SDEs of the dynamics of bank loans, growth rate in loans, bank deposits, growth rate in deposits and variable cost arising from the model were solved by means of the ItÔ Lemma. Discrete time approximations of the exact solutions of the SDEs were derived and used in a Monte Carlos simulation softwar

Transient Heat and Mass Transfer of Hydromagnetic Effects on the Flow Past a Porous Medium with Movable Vertical Permeablesheet

An unsteady flow of heat and species transport through a porous medium in an infinite movable vertical permeable flat surface is considered. The hydromagnetic chemical reactive fluid flow is stimulated by the thermal and solutant convection, and propelled by the movement of the surface. The formulated nonlinear flow equations in time space are solved analytically by asymptotic expansions to obtain solutions for the flow momentum, energy and chemical concentration for various thermo-physical parameters. The existence of flow characteristic is defined with the assistance of the flow parameters. In the study, the impact of some pertinent flow terms is reported and discussed. The study revealed that the species boundary layer increases with a generative chemical reaction and decreases with a destructive chemical reaction. Also, arise in the generative species reaction term reduces the flow momentum for the cooling surface. The impact of other flow governing parameters is displayed graphically as well as the fluid wall friction, wall energy and species gradients. The results of this study are important in chemical thermal engineering for monitoring processes to avoid solution blow up