On a scale invariant model of statistical mechanics and invariant forms of conservation equations

A scale-invariant model of statistical mechanics is described and applied to introduce the invariant Boltzmann equation and the corresponding invariant Enskog equation of change. The invariant modified as well as classical forms of mass, thermal energy, linear momentum, and angular momentum conservation equations are derived. Also, an invariant definition of reaction rate for any scale within the hierarchy of statistical fields is introduced. Following Cauchy, the total stress tensor for fluids P_ijβ = p_iβδ_ijβ - (μ_iβ/3)∇.v_iβδ_ijβ is introduced that is consistent with the fact that by definition fluids can only support compressive normal forces. Solutions of modified forms of conservation equations are determination to describe hydro-thermo-diffusive structure of normal shock in pure gas. Also, exact solution of modified form of equation of motion for the problems of laminar and turbulent flow over a flat plate are described and shown to be in close agreement with experimental data in literature. Finally, the solution of the modified Helmholtz vorticity equation for the problem of flow within a droplet located at the stagnation point of opposed cylindricallysymmetric gaseous finite jets is presented.