In this paper, we have investigated the two-dimensional magnetohydrodynamic steady boundary layer flow of a viscous magnetomicropolar liquid via an extending area. The impact of heat sink/source and chemical reaction is considered. The governing equations are modeled in Cartesian coordinate system. Using the suitable similarity transformations, the partial differential equations system is changed into the nonlinear ordinary differential equations system. The resulting system of equations is solved via mathematical renowned software Mathematica. The impact of diverse parameters through microrotation, concentration, temperature and velocity is examined via graphs. The present study reveals that the velocity is rising function of Soret number, Richardson number and Grashof number. It is mentioned that the greater velocity is located in the case of Newtonian liquid in contrast with the micropolar liquid. In the absence of chemical reaction parameter, the velocity is more as compared with higher chemical reaction parameter. Radiation, Hartmann and chemical reaction parameters augment the temperature. Concentration is a reducing function of radiation, Hartmann and chemical reaction parameters.
The cipher block chaining (CBC) block cipher mode of operation was invented by IBM (International Business Machine) in 1976. It presents a very popular way of encrypting which is used in various applications. In this paper, we have mathematically proven that, under some conditions, the CBC mode of operation can admit a chaotic behaviour according to Devaney. Some cases will be properly studied in order to put in evidence this idea.
A 3-D original numerical study of entropy generation in the case of liquid metal laminar natural convection in a differentially heated cubic cavity and in the presence of an external magnetic field orthogonal to the isothermal walls is carried out. The effect of this field on the various types of irreversibilities is analyzed. It was observed that in the presence of a magnetic field the generated entropy is distributed on the entire cavity and that the magnetic field limits the 3-D character of the distribution of the generated entropy.
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