Large Values Of Time Research Articles

Unsteady Hydromagnetic Natural Convection Flow Past a Vertical Plate with Time-Dependent Free Stream through a Porous Medium in the Presence of Hall Current, Rotation, and Heat Absorption

AbstractAn investigation of the unsteady hydromagnetic natural convection flow of a viscous, incompressible, electrically conducting, and heat-absorbing fluid past an infinite vertical plate through a fluid-saturated porous medium with a time-dependent free stream in a rotating system with Hall effects is carried out. An exact solution of the governing equations is obtained using the Laplace transform technique. Two cases of interest are discussed, viz, (1) the impulsive movement of the free stream and (2) the accelerated movement of the free stream. Expressions for the shear stresses at the plate as a result of the primary and secondary flows and the rate of heat transfer at the plate are derived. Asymptotic behavior of the solution is analyzed for both small and large values of time t to highlight the transient approach to the steady-state flow and to gain some physical insight into the flow pattern. A reverse flow exists in the secondary flow direction because of the presence of the thermal buoyancy fo...

Transient magnetohydrodynamic free convective flow in vertical micro-concentric annuli

This article analyses the transient magnetohydrodynamic free convective flow in vertical micro-concentric annuli in the presence of velocity slip and temperature jump at the outer surface of the inner cylinder and the inner surface of the outer cylinder. The Laplace transform technique has been used to find the solutions for the velocity and temperature fields by solving the governing partial differential equations in Laplace domain. However, the Riemann-sum approximation method is used to invert the Laplace domain to the time domain. The solution derived is validated by assenting comparison with exact solutions derived for the steady state which has been derived separately. An excellent agreement was found for transient and steady state at large value of time. The solution obtained for the velocity has been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of various flow parameters entering into the problem such as time, Prandtl number, curvature radius ratio, Hartmann number, rarefaction parameter, and fluid–wall interaction parameter are discussed with the aid of line graphs.

Combined effect of suction/injection on MHD free-convection flow in a vertical channel with thermal radiation

Abstract Transient hydromagnetic free-convection and thermal radiation flow of viscous, incompressible electrically conducting fluid in the presence of magnetic field in a vertical channel formed by two infinite porous plates is analyzed. The Rosseland diffusion approximation describes the radioactive heat flux in the energy equation. The non-linear time dependent energy and momentum equations under relevant initial and boundary conditions are solved numerically using implicit finite difference. To verify the accuracy of the numerical scheme, steady state version of the problem is solved by perturbation method. A series of numerical experiments show that time required to reach steady state velocity and temperature is directly proportional to the Prandtl number of the working fluid. In the course of numerical computation, an excellent agreement was found between transient and steady state solution at large value of time. The effect of various dimensionless parameters controlling the physical situation is extensively discussed with the aid of graphs.

A Semi-analytical Solution for Start-Up Flow in an Annulus Partially Filled with Porous Material

This study investigates the start-up flow in a horizontal annulus partially filled with clear fluid and partially with a fluid-saturated porous material (composite channel) as a result of the sudden application of constant pressure gradient in horizontal direction. Momentum transfer in the porous medium is simulated using the Brinkman-extended Darcy model. The fluid and porous regions are linked together by equating their velocities and incorporating the shear stress jump conditions at the interface. With the application of Laplace transform technique, the governing partial differential equations are transformed into ordinary differential equations which are solved in the Laplace domain to obtain exact solutions. Inversion of the exact solution in Laplace domain to time domain is done using the Riemann-sum approximation approach. Validation of the Riemann-sum approximation method is achieved by comparing numerical values obtained with those of exact solution obtained for steady state flow and transient solution obtained by implicit finite difference method. At large values of time, transient solution obtained using Riemann-sum approximation approach and implicit finite difference method coincide with closed form solution obtain exactly for steady state flow showing excellent agreement between these methods. Line graphs are used to discuss the effect of the different flow parameters involved in the flow formation.

Unsteady MHD natural convection flow with exponentially accelerated free-stream past a vertical plate in the presence of hall current and rotation

Investigation of unsteady MHD natural convection flow of an electrically conducting, viscous, incompressible and heat absorbing fluid past an infinite vertical plate through a fluid saturated porous medium with exponentially accelerated free-stream in a rotating system with Hall effects is carried out. Exact solution for fluid temperature and fluid velocity are obtained using Laplace transform technique. Expressions for the shear stresses at the plate due to primary and secondary flows and rate of heat transfer at the plate are also derived. In order to get some physical insight into the flow pattern, asymptotic behavior of the solution for fluid temperature and fluid velocity are analyzed for small as well as large values of time. It is interesting to note that there exists reverse flow in the secondary flow direction due to presence of thermal buoyancy force.

Optical properties of spherical quantum dot with on-center hydrogen impurity in magnetic field

This paper studies linear and nonlinear optical properties of the GaAs spherical quantum dot (QD) with impenetrable walls, containing on-center hydrogen impurity, under the presence of the static magnetic field. Transition energy and electric dipole transition matrix element between the impurity electron ground and the first excited state with \(m = 0\) have been computed using the Lagrange mesh method within the effective mass approximation. The linear and the third-order nonlinear optical absorption coefficients (ACs) are obtained using the iterative procedure in the framework of the density matrix approach, and their behavior with respect to the incident photon energy is discussed. In addition, the dependence of these coefficients on the QD radius, magnetic field strength, intensity of the applied laser field and relaxation time is studied. It has been found that for large values of relaxation time, the nonlinear AC prevails over the linear one and the total AC becomes negative.

Dynamics of momentumless turbulent wake in a shear flow of a linearly stratified medium

The numerical model of momentumless turbulent wake in a horizontally homogeneous shear flow of linearly stratified medium has been constructed. Based on this model, the investigation of the wake dynamics has been performed. The obtained data demonstrate the transformation of the zone of turbulent perturbations and internal waves generated by the wake under the action of shear flow, which leads to the deceleration of turbulence decay at large time values after the body passage.

Numerical Solution to a One-Dimensional, Nonlinear Problem of Thermoelasticity with Volume Force and Heat Supply in a Slab

A numerical solution is presented for a one-dimensional, nonlinear boundary-value problem of thermoelasticity with variable volume force and heat supply in a slab. One surface of the body is subjected to a given periodic displacement and Robin thermal condition, while the other is kept fixed and at zero temperature. Other conditions may be equally treated as well. The volume force and bulk heating simulate the effect of a beam of hot particles infiltrating the medium. The present study is a continuation of previous work by the same authors for the half-space [1]. The presented Figures display the process of propagation and reflection of the coupled nonlinear thermoelastic waves in the slab. They also show the effects of volume force and heat supply on the distributions of the mechanical displacements and temperature inside the medium. The propagation of beats provides evidence for sufficiently large time values.

Unsteady Hydromagnetic Natural Convection Flow of a Heat Absorbing Fluid within a Rotating Vertical Channel in Porous Medium with Hall Effects

Unsteady hydromagnetic natural convection flow of a viscous, incompressible, electrically conducting and temperature dependent heat absorbing fluid confined within a parallel plate rotating vertical channel in porous medium is investigated. Fluid flow within the channel is induced due to impulsive movement of one of the plates of the channel. Exact solution for the governing equations for fluid velocity and fluid temperature are obtained by Laplace transform technique. The expressions for the shear stress at the moving plate due to primary and secondary flows and those of rate of heat transfer at the moving and stationary plates are also derived. In order to gain some physical insight into the flow pattern, asymptotic behavior of the solution for fluid velocity and fluid temperature are analyzed for small and large values of time. The numerical values of primary and secondary fluid velocities and fluid temperature are displayed graphically whereas those of shear stress at the moving plate and rate of heat transfer at both the moving and stationary plates are presented in tabular form for various values of pertinent flow parameters.

The general class of Bianchi cosmological models in f(R, T) gravity with dark energy in viscous cosmology

The general class of Bianchi cosmological models in f(R, T) gravity with dark energy in the form of standard and modified Chaplygin gas and bulk viscosity have been considered. We have discussed three types of average scale factor by using a special law for deceleration parameter which is linear in time with negative slope. The model describes an accelerating universe for large value of time t, wherein the effective negative pressure induced by Chaplygin gas and bulk viscous pressure are driving the acceleration.

A biological treatment of industrial wastewaters: Contois kinetics

This paper analyses the steady-state operation of a generalized bioreactor model that encompasses a continuous-flow bioreactor and an idealized continuous-flow membrane bioreactor as limiting cases. A biodegradation of organic materials is modelled using Contois growth kinetics. The bioreactor performance is analysed by finding the steady-state solutions of the model and determining their stability as a function of the dimensionless residence time. We show that an effective recycle parameter improves the performance of the bioreactor at moderate values of the dimensionless residence time. However, at sufficiently large values of the dimensionless residence time, the performance of the bioreactor is independent of the recycle ratio. doi:10.1017/S144618111500005X

Unsteady MHD free convective Couette flow between vertical porous plates with thermal radiation

This study investigates the unsteady MHD free convective Couette flow of viscous incompressible electrically conducting fluid between two infinite vertical porous plates in the presence of transverse magnetic field and thermal radiation. Solutions for time dependent energy and momentum equations are obtained by the implicit finite difference method. To check the accuracy of the numerical solutions, steady state solutions for energy and momentum equations are obtained by using the perturbation method. The effect of various parameters controlling the physical situation is discussed with the aid of line graphs. Significant results from this study are that both velocity and temperature increase with the increase in thermal radiation parameter and time. A series of numerical experiments show that steady state velocity and temperature occur when the dimensionless time approaches the values of Prandtl number of the fluid. During the course of numerical computation, an excellent agreement was found between unsteady and steady state solutions at large value of time.

The unsteady flow of a third-grade fluid caused by the periodic motion of an infinite wall with transpiration

In this work, the unidirectional flow of an incompressible electrically conducting third-grade fluid past a vertical transpiration wall through a porous medium with time-dependent periodic motion is presented. The nonlinear partial differential equations are transformed to ordinary differential equation by means of symmetry reductions. The reduced equation is then solved analytically for steady-state and time-dependent transient parts. The time series of the transient flow velocity for different pertinent parameters are examined through plots. During the course of computation, it was observed that the time-dependent transient and steady-state solutions agree very well at large value of time when the ratio is related to fluid parameters γ∗γ>1.

On Hydromagnetic Flow of an Oldroyd-B Fluid Between Two Oscillating Plates

An initial value investigation is made of the motion of an incompressible, viscoelastic, electrically conducting Oldroyd-B fluid bounded by two infinite rigid non-conducting plates. The flow is generated impulsively from rest in the fluid due to rectilinear oscillations of given frequencies superimposed on the plates in their own planes in presence of an external magnetic field acting transversely to the plates. The operational method is used to derive exact solutions for the fluid velocity and the shear stress on the walls. The quantitative evaluation of the results is considered when two plates oscillate in phase but with different frequencies. The results are shown graphically for different time periods of oscillations of the plates which represent the cases: (i) the lower plate oscillates with a time period less than the upper, (ii) both the plates oscillate with the same time period and (iii) the lower plate oscillates with a time period grater than the upper. It is seen that the effect of fluid elasticity on the flow depends on the advancing and retarding motion of the plates. On the other hand, the magnetic field damps the fluid motion for all values of the time period of oscillations of the plates. The drag on the plates, for small and large time, are shown graphically when the time period of oscillation of the lower plate is small. For small values of time, the drag on the lower plate is negative with the amplitude decreasing continuously till the oscillations occur from moderately large values of time. Similar phenomenon also occurs for the drag which is positive at the upper plate for small values of time. In all cases, the amount of drag on the plates increases with the increase of the elasticity of the fluid and the magnetic field. Some particular results for the fluid velocity are derived as special cases of the present solution.

First-passage times in integrate-and-fire neurons with stochastic thresholds.

We consider a leaky integrate-and-fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed widespread variation of neural firing thresholds. We show numerically that the mean first-passage time can depend nonmonotonically on the noise amplitude. For sufficiently large values of the correlation time of the stochastic threshold the mean first-passage time is maximal for nonvanishing noise. We provide an explanation for this effect by analytically transforming the original model into a first-passage-time problem for Brownian motion. This transformation also allows for a perturbative calculation of the first-passage-time histograms. In turn this provides quantitative insights into the mechanisms that lead to the nonmonotonic behavior of the mean first-passage time. The perturbation expansion is in excellent agreement with direct numerical simulations. The approach developed here can be applied to any deterministic subthreshold dynamics and any Gauss-Markov processes for the firing threshold. This opens up the possibility to incorporate biophysically detailed components into the subthreshold dynamics, rendering our approach a powerful framework that sits between traditional integrate-and-fire models and complex mechanistic descriptions of neural dynamics.

A BIOLOGICAL TREATMENT OF INDUSTRIAL WASTEWATERS: CONTOIS KINETICS

This paper analyses the steady-state operation of a generalized bioreactor model that encompasses a continuous-flow bioreactor and an idealized continuous-flow membrane bioreactor as limiting cases. A biodegradation of organic materials is modelled using Contois growth kinetics. The bioreactor performance is analysed by finding the steady-state solutions of the model and determining their stability as a function of the dimensionless residence time. We show that an effective recycle parameter improves the performance of the bioreactor at moderate values of the dimensionless residence time. However, at sufficiently large values of the dimensionless residence time, the performance of the bioreactor is independent of the recycle ratio.

Nonlinear problems with unknown initial temperature and without final temperature, solved by the GL(N, [formula omitted]) shooting method

We consider a nonlinear heat conduction equation for recovering unknown initial temperature under Dirichlet or Neumann boundary conditions. This problem is a generalized backward heat conduction problem (GBHCP), which not necessarily subjects to data at a final time. The GBHCP is known to be highly ill-posed, for which we develop a novel GL(N,R) shooting method (GLSM) in the spatial direction. It can retrieve very well the initial data with a high order accuracy. Several numerical examples of the GBHCP demonstrate that the GLSM is applicable, even for those of strongly ill-posed ones with large values of final time. Under the noisy final data the GLSM is robust against the disturbance. The new method is applicable for a case with a final data very small in the order of 10−87, and the relative noise level is in the order of 100, of which the numerical solution still has an accuracy in the order of 10−2. These results are quite remarkable in the computations of GBHCP.

Dynamics of a momentumless turbulent wake in a shear flow

Numerical modeling and investigation of the dynamics of a momentumless turbulent wake in a horizontally homogeneous shear flow are performed. The obtained data demonstrate transformation of the turbulized region in awake under the action of a shear flow, and also substantial generation of turbulence energy by averaged motion, which leads to slower turbulence degeneracy at large time values after passage of the body. Some considerations on flow similarity by shear Froude number are presented along with calculation results illustrating this similarity.

Unsteady Couette Flow in a Composite Channel Partially Filled with Porous Material: A Semi-analytical Approach

This study is devoted to investigate the unsteady fully developed time-dependent Couette flow in a composite channel partially filled with porous material. The Brinkman-extended Darcy model is used to simulate momentum transfer in the porous medium. The fluid and porous regions are interlinked by equating the velocity and by considering shear stress jump conditions in the interface. The solutions of the governing equations are obtained using a Laplace transform technique. However, the Riemann-sum approximation method is used to invert from Laplace domain to time domain. The solution obtained is validated by presenting comparisons with closed form solution obtained for steady flow which has been derived separately and also by implicit finite difference method. During the course of numerical comparison, an excellent agreement was found between steady-state solution obtained exactly and unsteady solution obtained by implicit finite difference method or Riemann-sum approximation method at large values of time. The effect of various flow parameters entering into the problem is discussed with the aid of line graphs. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated time-dependent Couette flow in composite channel.

Erratum to “Modified diffusion with memory for cyclone track fluctuations” [Phys. Lett. A 378 (2014) 2016–2019

Abstract In our recent Letter, the specific example chosen contains a misprint which leads to an incorrect mean square displacement (MSD). This is corrected by a proper memory function that gives the main result of our Letter, i.e., matching the behavior of MSD versus time graphs for cyclones even for large values of time.