**6. Conclusions**

In the present work, we have successfully used the Sakurai [4] approach to find the first-order approximate analytical solution of the planar and cylindrical symmetric flow under the presence of transverse magnetic field in a non-ideal medium. However, Sakurai [4] has obtained a solution in gas dynamics by using this method; there is no study afterwards that provides approximate analytical solution of the problem with magnetic field in non-ideal medium. We have tried to fill the gap by providing approximate analytical solutions of the problem with magnetic and non-ideal effects. These findings are quite useful for the groups working in the field of Magneto Hydrodynamics (MHD) or Computational Fluid Dynamics (CFD). To generate confidence in our results, we have recovered all results of Sakurai's [4] published work as a particular case of our problem (i.e., *C*0 = 0) in Tables 1 and 2. The effects of non-ideal medium and transverse magnetic field on flow variables are depicted in Figures 1–4.

Figure 1 consists of the profiles of velocity, density, pressure, and magnetic pressure for planar shocks (*m* = 0 ) with *γ* = 1.4, *C*0 = 0, and *α* = 0.00, 0.015, 0.025, 0.050. It is clearly seen from Figure 1 that the dimensionless profiles of flow variables decrease as value of parameter *α* increases except the pressure which increases with the small increase in the parameter *α*. This is expected physically as gas particles will collide more frequently with the increase of non-idealness *α* which results in the rise in pressure with the increment of *α*. In Figure 2, we observe that the pressure and density decrease as we increase the value of *C*0, while the magnetic pressure increases for planar motion (*m* = 0) after a certain point. It is again an expected result as the charged particles will be transported away very quickly with the increase of *C*0. It results in dropping in pressure after the blast. At the point of explosion, the process is not fully self-similar and therefore the initial dynamics is a bit off. It agrees with blast wave theory. It is well known that the phenomena are not self-similar at very near the center or axis of explosion. However, point explosions can be self-similar at considerable distance from the source (see Sakurai [3,4]). Figures 3 and 4 display the profiles of the flow variables for cylindrically symmetric flow (*m* = 1). From Figures 3a and 4a, we observed that as we increase the value of *α* and *C*0, velocity increases. Figure 3b shows that as the value of parameter *α* increases, pressure also increases after a certain point. This describes the physics of the post-shock process very well as increase in *α* makes the collision of the gas particles more frequent. Figure 4b shows that an increment in the value of *C*0 causes a decrease in pressure for the cylindrically symmetric flow. It is attributed to the fact that the ionized gas molecules are carried away by a strong magnetic field. It is one of the reasons that the instabilities at the shock front can be suppressed under the presence of a magnetic field. Figure 4c shows that the density of the medium decreases as *C*0 increases. Figure 4d shows that as the value of *C*0 increases, magnetic pressure also increases.

**Author Contributions:** All authors contributed equally in the paper.

**Funding:** This research was funded by University Grant Commission (UGC), India gran<sup>t</sup> number "2121440656" and Ref. No; 21/12/2014(ii)EU-V.

**Acknowledgments:** Astha Chauhan is thankful to the "University Grant Commission", New Delhi for the financial support to project.

**Conflicts of Interest:** The authors declare no conflict of interest.
