**Astha Chauhan 1, Rajan Arora 1 and Mohd Junaid Siddiqui 2,\***


Received: 6 March 2019; Accepted: 27 March 2019; Published: 1 April 2019

**Abstract:** Blast waves are generated when an area grows abruptly with a supersonic speed, as in explosions. This problem is quite interesting, as a large amount of energy is released in the process. In contrast to the situation of imploding shocks in ideal gas, where a vast literature is available on the effect of magnetic fields, very little is known about blast waves propagating in a magnetic field. As this problem is highly nonlinear, there are very few techniques that may provide even an approximate analytical solution. We have considered a problem on planar and radially symmetric blast waves to find an approximate solution analytically using Sakurai's technique. A magnetic field has been taken in the transverse direction. Gas particles are supposed to be propagating orthogonally to the magnetic field in a non-deal medium. We have further assumed that specific conductance of the medium is infinite. Using Sakurai's approach, we have constructed the solution in a power series of (*C*/*U*)2, where *C* is the velocity of sound in an ideal gas and *U* is the velocity of shock front. A comparison of obtained results in the absence of a magnetic field within the published work of Sakurai has been made to generate the confidence in our results. Our results match well with the results reported by Sakurai for gas dynamics. The flow variables are computed behind the leading shock and are shown graphically. It is very interesting that the solution of the problem is obtained in closed form.

**Keywords:** blast waves; non-ideal gas; Rankine–Hugoniot conditions; magnetogasdynamics

**MSC:** 35L67; 58J45
