IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11, Issue 3 Ver. I (May - Jun. 2015), PP 97-104 www.iosrjournals.org DOI: 10.9790/5728-113197104 www.iosrjournals.org 97 | Page The Effect of MHD Flow in Shock Formation in One-Dimensional Gas Flow Abraham Osogo Nyakebogo 1, Prof. Johanna Kibet Sigey 2 , Dr. Jeconia Abonyo Okelo 3, Dr. James Mariita Okwoyo 4. 1. Msc. Applied Mathematics Student at Jomo Kenyatta University (JKUAT)-Kenya. 2. Prof. Johanna Kibet Sigey. Director JKUAT Kisii- CBD-Kenya. 3. Senior lecturer Jomo Kenyatta University of Agriculture and Technology (JKUAT)-Kenya. 4. Lecturer, University of Nairobi (UON)-Kenya. Abstract: This study investigated the effect of MHD flow in shock formation in one dimensional gas flow. A conducting gas has been considered with the flow occurring in the presence of varying magnetic field intensity H. The shock zone has been assumed to be a thin legume that is stationary. An analysis of the velocity profiles, density profiles and temperature distribution that have been obtained has been done. In addition, an investigation on how the Prandtl number, Hartmann number and Eckert number affect the velocity profiles and temperature distribution has been carried out. Differential equations that have been generated from this study are non-linear. The equations have been solved by finite difference method using the MATLAB software and results presented graphically. It has been noted that an increase in Hartmann number causes an increase in velocity profiles while an increase in Prandtl number leads to an increase in temperature distribution and an increase in Eckert number leads to an increase in temperature distribution. Keywords: Magnetohydrodynamics, compressible flow, shock wave, normal shock, oblique shock, weak shock, strong shock. I. Introduction Effect of Magnetohydrodynamics (MHD) flow in compressible fluid flow has become significant. Further, MHD flow effect on shock formation has very wide range of applications in astrophysical world and in engineering. Astrophysicists discovered that ionized gases and strong magnetic fields exist in the universe and hence the need to explain certain phenomena in the universe by use of MHD. Engineers employ MHD flow in shock formation in the design of heat exchangers, shock absorbers for locomotive machines and electromagnetic pumps, Kinyanjui et al (2003). Studies of magnetohydrodynamic shock waves in gases have been reported in the literature. Rankine (1870) and Hugoniot (1889) came up with shock jumps for flow parameters famously known as the Rankine- Hugoniot conditions. Wu (1990) considered the formation, structure and stability of intermediate shocks in dissipative MHD. A conclusion was that, there are free parameters in the structure of intermediate shocks, and that these parameters are related to the shock stability. Sterk et al (1990), carried out a study of two- dimensional numerical of a planar field – aligned ideal MHD bow shock flow in a regime where fast MHD switch – on shocks are possible. Numerical problems encountered when high - resolution numerical MHD schemes derived from common computational fluid dynamics approaches used to stimulate this kind of flows were discussed. It is observed that the MHD shock formation effects of our simulations may occur in processes, in the corona of the sun. Angail (2004), studied the MHD model of boundary layer equations for conducting viscous fluids, the effect of free convection with two relaxation times on the flow of viscous conducting fluid was studied. He adopted the solution of one – dimensional transient problem to a whole space distribution of heat sources. He observed that as the Alfven velocity increases, the velocity of the fluid increased. He also noted that the velocity increased as the Grashof number (Gr) increased while it decreases when Prandtl number (Pr) increases. Hyesang et al (2007), considered a study of the statistics and energetics of shocks formed in cosmological simulations of a concordance universe, with special emphasis on the effects of non – gravitational processes such as radiative cooling, photoionization / heating, and galactic super wind feedbacks. They also examined the vorticity generated mostly at curved shocks in cosmological simulations. They found out that the dynamics and energetic of shocks are governed primarily by the gravity of matter; hence other non-gravitational processes do not significantly affect the global energy dissipation and vorticity generation at cosmological shocks Their results reinforce scenarios in which the intra cluster medium and warm – hot intergalactic medium contain energetically significant population of non – thermal particles and turbulent flow motions. Mallick and Schramn (2013), observed that shockwaves constitute discontinuities in matters which are relevant in studying