A numerical study has been performed to analyze the effect of radial magneticfield on free convective flow of an electrically conducting and viscous incompressiblefluid over the RAMPED moving vertical cylinder with RAMPED type TEMPERATURE and concentration considered at the surface of vertical cylinder. The governing partial differential equations which describe theflow formation have been solved numerically by using implicit finite difference method of Crank-Nicolson type. The simulation results of the considered model have been shown graphically. One of the interesting result of our analysis is that the local as well as average skin-friction, Nusselt number and Sherwood number have increasing tendency in time interval (0, 1), thereafter these quantities decrease. We have also compared the case of RAMPED type boundary conditions with that of constant boundary conditions with help of table. The advantage of taking RAMPED type boundary conditions is that initial heat transfer rate and mass transfer rate are minimum in this case.

Investigation of unsteady hydromagnetic natural convection flow with heat and mass transfer of a viscous, incompressible, electrically conducting, chemically reactive and optically thin radiating fluid past an exponentially accelerated moving vertical plate with ARBITRARY RAMPED TEMPERATURE embedded in a fluid saturated porous medium is carried out. Exact solutions of momentum, energy and concentration equations are obtained in closed form by Laplace transform technique. The expressions for the shear stress, rate of heat transfer and rate of mass transfer at the plate for both RAMPED TEMPERATURE and isothermal plates are derived. The numerical values of fluid velocity, fluid TEMPERATURE and species concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. It is found that, for isothermal plate, the fluid TEMPERATURE approaches steady state when t >1.5. Consequently, the rate of heat transfer at isothermal plate approaches steady state when t >1.5.

The effect of radiation on natural convection incompressible viscous fluid near a vertical flat plate with RAMPED wall TEMPERATURE has been studied. An analytical solution of the governing equation has been obtained by employing Laplace transform technique. It is examined that two different solutions for the fluid velocities, one valid for fluids of Prandtl number(Pr) different from 1+Ra, Ra being the radiation parameter and the other for which the Prandtl number equal to 1+Ra. The variations of velocities and fluid TEMPERATURE are presented graphically. Furthermore, the radiative heat transfer on natural convection flow near a RAMPED plate TEMPERATURE has been compared with the flow near a plate with the constant wall TEMPERATURE. It is found that an increase in radiation parameter leads to rise the fluid velocity as well as TEMPERATURE.

This study explores the time-dependent flow of MHD Oldroyd-B fluid under the effect of RAMPED wall velocity and TEMPERATURE. The flow is confined to an infinite vertical plate embedded in a permeable surface with the impact of heat generation and thermal radiation. Solutions of velocity, TEMPERATURE, and concentration are derived symmetrically by applying non-dimensional parameters along with Laplace transformation (LT) and numerical inversion algorithm. Graphical results for different physical constraints are produced for the velocity, TEMPERATURE, and concentration profiles. Velocity and TEMPERATURE profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. Velocity is decreasing for κ, , M, Prreff, and Sc while increasing for Gr and Gc. TEMPERATURE is an increasing function of the fractional parameter. Additionally, Atangana-Baleanu (ABC) model is good to explain the dynamics of fluid with better memory effect as compared to other fractional operators.

The unsteady flow and heat transfer of a viscous incompressible, electrically conducting dusty fluid past vertical plate under the influence of a transverse magnetic field is studied with a view to examine the combined effects of suction, heat absorption and RAMPED wall TEMPERATURE. The TEMPERATURE of the wall is assumed to have a temporarily RAMPED profile which goes on increasing up to a certain time limit and then becomes constant. To investigate the effect of RAMPEDness in wall TEMPERATURE, the solution for the flow past an isothermal wall is also obtained. The governing partial differential equations are solved using Laplace transformation technique in which the inversion is obtained numerically using Matlab. To validate the results of numerical inversion a comparison between the numerical and analytical values of fluid and particle TEMPERATUREs and Nusselt number is also presented. The effects of pertinent flow parameters affecting the flow and heat transfer are investigated with the help of graphs and tables. It is found that the increase in suction, heat absorption and particle concentration contribute in thinning the thermal and momentum boundary layers and the velocity and TEMPERATURE for both the fluid and particle phases are higher in the case of a flow past an isothermal plate than that of a flow past a plate with RAMPED TEMPERATURE.

The effects of radiation and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving infinite vertical plate with RAMPED TEMPERATURE in a porous medium are investigated. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. To compare the results obtained in this case with that of isothermal plate, exact solution of the governing equations is also obtained for isothermal plate. The expressions for the primary and secondary skin frictions and Nusselt number are also derived. It is noticed that, for both RAMPED TEMPERATURE and isothermal plates, rotation retards fluid flow in the primary flow direction whereas it accelerates fluid flow in the secondary flow direction in the boundary layer region while radiation exerts accelerating influence on the fluid flow in both the primary and secondary flow directions. For RAMPED TEMPERATURE plate radiation reduces primary skin friction whereas it tends to increase secondary skin friction. For isothermal plate radiation has tendency to reduce secondary skin friction. Radiation tends to increase fluid TEMPERATURE for both RAMPED TEMPERATURE and isothermal plates. With the increase in time the rate of heat transfer at the plate is reduced for isothermal plate while it is increased for RAMPED TEMPERATURE plate.

When an intense laser beam propagates in plasma, due to relativistic electrons resulting from the laser electric field, the plasma refractive index alters. Subsequently, the plasma behaves initially similar to a positive lens that decreases the laser spot size. In this article, the propagation of the laser beam in collisional quantum plasmas is investigated with considering a RAMPED density profile. Using WKB and paraxial approximations through parabolic equation, a mathematical formulation for the beam width parameter is obtained from the wave equation. Acquired equations are numerically solved by employing the fourth-order Runge-Kutta method. In the collisionless plasma, by increasing the ramp slope, the beam width focuses with less oscillation amplitude, smaller laser spot size and more oscillations. In the collisional quantum plasma, due to energy absorption, the oscillation amplitude enhances by passing through the plasma and the laser beam defocuses at a few lengths. For the greater values of the slope and the collision frequency, the laser spot size oscillates with the higher amplitude and defocuses in a shallower plasma depth. Also, greater plasma density results in smaller laser spot size and bigger oscillation frequency. Then, this effect is compared in the strong and weak quantum and classical plasmas. Decreasing the plasma TEMPERATURE improves the magnetization due to the ponderomotive force related to the time variation, the beam-width oscillates with greater frequency and deeper penetration in the strong quantum plasma in comparison with the weak quantum or the classical cases.

One of the main difficulties of conceptual and particularly realization-based dependence of moral attributes on religion is the irregularity of God’s will and voluntary actions and hence arbitrariness of morality derived from it. According to this critique, divine will and reluctance or command and prohibition without criteria and standards can shape moral concepts such as good and bad or at least have an influence on qualification of human actions to the predicates. But some philosophers and theologians, apart from other critiques against these two versions of religious morality, have attempted to resolve this problem by accommodating some determining factors in God, invoking to logical contradiction of bad actions, favour to attributes as divine simplicity and the like. These answers essentially have been incapable of solving this problem unless we consider the real object of God’s will and the fixed subjects of ethical propositions.

ARBITRARY amplitude dust acoustic waves(DAWs) in a quantum dusty plasma including the effect of dust size distribution (DSD) is presented. By using the Sagdeev pseudopotential method for large amplitude waves, the energy integral is derived which includes Sagdeev potential. By applying the conditions in which a solitary solution can be existed, the upper and lower limits of Mach number is presented. Two cases are studied, a mono sized dust grains case and dust grains possessing power law size distribution case. The result shows that, the allowed Mach number’s range is increased for mono sized dust grains case. Sagdeev potential is also plotted and it is seen that in mono sized dust grains case, solitary waves are propagated. Whereas, for different sized dust grains having power law size distribution, the solitary waves transform into cnoidal ones.. The phase portrait is also plotted and comprised of Two different sets of orbits, a periodic orbit and a homoclinic one that correspond to periodic traveling wave solution and solitary wave solution, respectively

We show that for each positive integer n, there exist a group G and a subgroup H such that the ordinary depth d(H,G) is 2n. This solves the open problem posed by Lars Kadison whether even ordinary depth larger than 6 can occur.