Similarity solutions for cylindrical shock waves in a non-ideal gas under the action of monochromatic radiation. (English) Zbl 1519.76290
Summary: A theoretical model for the propagation of cylindrical shock waves in the adiabatic flow of a non-ideal gas with the effect of monochromatic radiation into the stellar interiors is studied. We obtain some special class of self-similar solutions to the considered problem using the Lie group of transformations. Here, we assume that the density is uniform in the undisturbed medium. The radiation flux is considered to be moving through the non-ideal gas. The flow variables behind the shock front are discussed through graphs. Also, the effects of variation in the non-ideal parameter, radiation parameter and adiabatic exponent on the flow variables are explained. The obtained results are quite similar to the results obtained by J. P. Vishwakarma and V. K. Pandey [“Self-similar flow under the action of monochromatic radiation behind a strong cylindrical shock wave in a non-ideal gas”, Int. J. Phys. Math. Sci. 2, No. 1, 27–37 (2012), https://www.cibtech.org/J-PHYSICS-MATHEMATICAL-SCIENCES/PUBLICATIONS/2012/Vol\%202\%20No.\%201/009\%20VISHWAKARMA...pdf]. The software package ‘MATLAB’ has performed all the computational work.
MSC:
| 76N15 | Gas dynamics (general theory) |
| 76M55 | Dimensional analysis and similarity applied to problems in fluid mechanics |
| 76L05 | Shock waves and blast waves in fluid mechanics |
Keywords:
shock waves; monochromatic radiation; non-ideal gas; Lie group of transformations; similarity solutionsSoftware:
MatlabReferences:
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