Analytical investigation of the effects of MHD radiation and mass transfer parameters from galactic primary cosmic ray transport in steady state extra-terrestrial atmosphere

Abstract

The analytical study of the effect of Magneto-Hydro Dynamic (MHD) heat transfer parameters from galactic primary cosmic rays transport in a stratified steady state extra-terrestrial atmosphere is modelled by imposing a time dependent perturbation on the primary cosmic transport in the extra-terrestrialatmosphere containing randomly distributed giant diffused molecular particles. The temperatures involved are assumed to be large so that MHD Radiationand mass transfer parameter is significant. This renders the flow field highly nonlinear even on the assumptions of a differential approximation for the MHD in an adiabatic concentration and zero activated energy. When the perturbation is small, the transient flow is tackled by the Laplace transform technique, giving solution for stable steady state spectrum of the primary cosmic ray in the intergalactic temperature up and down stream concentration, also velocity is tackled and numerical solutions were obtained for temperature. The downstream, upstream Velocity profile and concentration in cases where MHD radiation heat and mass transfer through the stratifiedterrestrial atmosphere are taken into account. The incorporation of MHD radiation and mass transfer is of particular relevance to primary cosmic ray physics as the interaction between concentration and temperature component represent a state which often exists in the universe.The result shows and give solution for stable steady state component of the surface temperature ፀ⁰ at order zero and adiabatic concentration C⁰ and velocity q⁰ profile. Radiation shows dependence of ፀ⁰, C⁰ on Z at some point ፀ⁰ and C⁰³ approach unity. Furthermore, for γ = 10, β = 12 the variation of adiabatic concentration C⁰³ and ፀ⁰³ on Z for stable steady state flow. Also for the case where ፀ⁰ = 1. The transient component temperature exhibits a standing wave structure and the magnitude of the standing wave increases when the solute concentration C⁰ = 1, this means that for ፀ⁰ = 1 = C⁰ the intensity of MHD radiation heat is large that is when MHD radiation is large contrary to a relatively low emission when (MHD radiation is of order 0in which the standing wave structure is no longer exhibited by both the temperature and concentration field. The calculated energy spectrum of cosmic rays after propagation through the extra-terrestrial atmosphere is in good agreement with the spectrum measured at the earth surface. The graphs are compared and found to be in good agreement with the energy flow.This is relevant and very important in cosmic ray physics as the interaction between the temperature and concentration field component represents a state which often exist in the universe and cosmic ray consist in the transverse modulation of the same medium which cause the Astrophysics fluid to be incompressible.