This paper analytically studies the thermal radiation and chemical reaction effect on unsteady MHD convection through a porous medium bounded by an infinite vertical plate. The fluid considered here is a gray, absorbing-emitting but nonscattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The dimensionless governing equations are solved using Laplace transform technique. The resulting velocity, temperature and concentration profiles as well as the skin-friction, rate of heat, and mass transfer are shown graphically for different values of physical parameters involved.
In this paper, we employ the energy surface method to study a system of a two-level atom Bose–Einstein condensate coupled to a high-finesse optical cavity interacting with a single-mode electromagnetic field in the presence of the Stark-shift. The energy surface, the Phase transitions and the Berry phase of the two-level atom in Dicke model are obtained. Employing the Holstein–Primakoff representation of the angular momentum Lie algebra, the coupling line separation of the normal phase and the superradiant phase which occurs in a collection of fluorescent emitters (such as atoms), between a state containing few electromagnetic excitations are studied and a mean field description of the Dicke model is presented. We notice that in the thermodynamic limit, the energy surface takes a simple form for a direct description of the phase transition. Moreover, we show that the Stark-shift parameters and the atom–atom interactions can strongly affect the phase transition point. The results in the absence of the Stark-shift agree precisely with those obtained by Li, Liu and Zhou, who studied the same model using a different method.
In this work the Forchheimer, non-Boussinesq natural convection heat transfer of water around 4 o C. is analyzed, the following dimensionless parameters are found to describe the problem which are namely the modified Rayleigh number (Raw), the inclination angle (Ф), the aspect ratio of the enclosure (A), and the exponent for non-Boussinesq-approximation (n). It was found that the increasing of the modified Rayleigh number Raw increased the mass flow rates and the buoyancy forces and consequently increases the mean Nusselt number, it was found also that the increasing of the value of the exponent for nonBoussinesq-approximation (n); which physically means a non-linear temperature -density relationship, caused the mean Nusselt number and the dimensionless stream function to decrease to reach their minimum values at n=2, this is due to smaller temperature difference and consequently smaller buoyancy forces. The inclination angle (Ф), has a certain effect on heat transfer and fluid flow as the maximum heat transfer rate is obtained at inclination angels around Ф=30• -60• .
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