Search

Under axial and azimuthal magnetic inductions, the similarity solutions for a cylindrical shock wave in a weakly conducting ideal gas are determined using the Lie group invariance method. The axial and azimuthal magnetic inductions and density are presumed to vary in an ambient medium. This study determines the form of expression for axial and azimuthal magnetic inductions in the ambient medium. The ambient density is considered to be varying according to the power law of the shock radius. The weakly conducting medium causes inadequate magnetic freezing. We have numerically solved the system of ordinary differential equations that resulted from applying the Lie group invariance method to the system of partial differential equations. The impact of the variation in the ambient density exponent, the ratio of specific heats, magnetic Reynolds number, or the inverse square of axial and azimuthal Alfven Mach numbers on the shock strength and the flow variables behind the shock front is discussed. It is found that the shock strength decreases with an increase in the ratio of specific heats, magnetic Reynolds number, or the inverse square of axial and azimuthal Alfven Mach numbers. [ABSTRACT FROM AUTHOR]

This work demonstrates the study of the optimal system of solutions for shock wave propagation in a non-ideal self-gravitating gas in rotating medium with magnetic field (axial or azimuthal) for the adiabatic flow in cylindrical geometry by applying the group invariance technique. Using the group invariance technique, we have obtained the one-dimensional (1-D) optimal system of sub-algebra for the basic governing equations. The infinitesimal group optimal classes are obtained and the similarity solution in four possible cases (two cases for perfect gas and two cases for non-ideal gas) with exponential law shock path are discussed. The numerical solution by using the Runge Kutta 4th order method is obtained and the distribution of physical variables are shown via graph. The impact of the rotational parameter, non-idealness parameter, shock Cowling number, similarity exponent and gravitational parameter on the strength of the shock and flow variables are investigated. With an increase in the shock Cowling number, non-idealness and rotational parameters, the shock strength decreases, i.e., they have decaying impact on shock wave; whereas the shock strength increases with gravitational parameter and similarity exponent. Also, the strength of the shock is reduced by considering the magnetic field to be axial instead of azimuthal. [ABSTRACT FROM AUTHOR]

This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave. [ABSTRACT FROM AUTHOR]

Acinic Cell Carcinoma (AcCC) is a slow growing, malignant tumour of salivary glands, predominantly found in parotid gland and rarely in submandibular gland or minor salivary glands. Rarely, the tumour can arise in Heterotopic Salivary Gland Tissue (HSGT) and can present bilaterally. Synchronous contralateral tumour or tumour arising in HSGT is easily missed clinically. Fine Needle Aspiration Cytology (FNAC) is an important preoperative diagnostic investigation in cases of AcCC. Sometimes its diagnosis on cytology is very difficult and it is easily misdiagnosed as benign, affecting the long term prognosis. Here, we present two unusual cases of AcCC. One developed in HSGT and the other was synchronous bilateral. Though the histological features of AcCC appear to be characteristic but clinical suspicion and cytological features have been described as equally important for preoperative diagnosis. Present cases highlight the importance of a cytopathologist who plays an important role in its preliminary diagnosis. [ABSTRACT FROM AUTHOR]